K TO 12 GRADE 5 LEARNER’S MATERIAL IN MATHEMATICS (Q1-Q4)

Lesson 1: Visualizing Numbers up to 10 000 000 with emphasis on
numbers 100 001 – 10 000 000
A group of doctors donated a total of 234 534 kilograms of rice to the
earthquake victims. Can you imagine how big the number 234 534 is? One way
you can imagine is to think of discs to represent the number shown below.
Two 100 000 Three 10 000 Four 1 000 Five 100 Three 10 Four 1
200 000 30 000 4 000 500 30 4
234 534
What number is represented by these number discs? Write your answer in your
notebook.
100 000
100 000
10 000
10 000
10 000 1 000
1 000
1 000
1 000
100
100
100
100
100
10
10
10
1
1
1
1
100 000
100 000
10 000
10 000
100 000
1 000
1 000
1 000
1 000
100
100
100
1 000
10 000
10
10
100
1
1
10
10
Get Moving!
Explore and Discover!

Use number discs to show the following numbers.
1. 10 345 789
2. 389 456
3. 4 234 789
4. 123 098
5. 4 456 678
Read the following items. Then, write your answer to each item in your notebook.
1. There were 345 895 children and adults who watched the football game. Draw number
discs to show the given number.
2. How will you show the number 2 345 789 using number discs?
3. There were 1 234 897 tree seedlings distributed to the barangays by the Department of
Environment and Natural Resources. Draw number discs to show the given number.
4. Mrs. Angeles bought some appliances worth Php 156 907. Represent this amount using
number disc.
5. Which number is 100 000 smaller than 234 456?
a. 134 456
b. 334 456
c. 34 456
d. 434 456
Keep Moving!
Apply Your Skills!

Lesson 2 : Reading and Writing Numbers up to 10 000 000 in Symbols
and in Words
EXPLORE AND DISCOVER!
The Department of Agriculture distributed 1 456 897 eggplant seedlings in some farmers
in Region IVA.
How do you read and write the number 1 456 897 in words and in symbol?
The number 1 456 897 is read as “ one million four hundred fifty-six thousand eight
hundred ninety-seven”. In symbol it is 1 456 897.
GET MOVING!
A. Write the following numbers in words.
1. 10 345 897
2. 7 456 902
3. 234 713
4. 678 345
5. 1 097 234
B. Rewrite the numbers correctly by putting a space in the correct places in column A. In
column B, write the numbers in words.
Number Column A Column B
1234678
6578234
10234123
123987
23908

KEEP MOVING!
Write the numbers in symbols.
1. Three million seven hundred eighty-six thousand four hundred 10
2. Five hundred ten thousand twenty- six
3. Ten million two hundred seven thousand one hundred seven
4. Six million eighty-three
5. Four million seven hundred twenty thousand three hundred eight
APPLY YOUR SKILLS!
A. 1. What is largest 7- digit number having different digits?
Write it in symbols and in words ___________________________________
2. What is the number next to 234 456?
Write it in symbol and in words ___________________________________
3. What is the smallest 6-digit number having different digits?
4. What is the number before 1 567 678?
5.What is the number between 890 789 and 890 791?
Write it in symbol and in words ____________________________________

1
Lesson 3 : Rounding Numbers to the Nearest Hundred Thousands and Millions
The circumference of the earth is 40 053 840 meters.
About how many million meters is the circumference of the earth?
You can find the answer by rounding 40 053 840 to the nearest millions.
Study these examples.
Number
Rounded to
Millions Hundred thousands
3 456 789 3 000 000 3 500 000
14 578 907 15 000 000 14 600 000
2 389 897 2 000 000 2 400 000
1 345 890 1 000 000 1 300 000
7 567 079 8 000 000 7 600 000
GET MOVING!
A. Round each number to the place value of the underlined digit.
1. 12 234 556 ______________________
2. 3 456 871 ______________________
3. 5 098 678 ______________________
4. 9 789 123 ______________________
5. 6 234 189 ______________________
B. Complete the table.
Number
Round to the nearest
Millions Hundred thousands
4 496 709
13 508 807
5 889 897
6 045 890
7 527 099

2
KEEP MOVING!
A. Encircle the numbers that can be rounded to the given number.
1. 8 900 000
8 923 567 8 984 456 8 908 671 8 938 123 8 971 109
2. 7 000 000
6 821 507 7 284 471 7 578 653 6 968 123 7 771 178
3. 4 500 000
4 493 517 4 381 426 4 508 671 4 561 126 4 478 120
4. 3 200 000
3 194 100 3 283 401 3 221 611 3 138 170 3 201 156
5. 6 000 000
5 622 160 6 904 431 5 998 601 6 868 173 6 001 101
B. Round to the highest place value.
1. 345 789 ______________________________
2. 1 563 890 ______________________________
3. 3 213 456 ______________________________
4. 9 912 123 ______________________________
5. 312 465 ______________________________

3
APPLY YOUR SKILLS!
A. Complete the table.
Greatest Number Rounded Number Least Number
3 000 000
2 400 000
10 200 000
6 300 000
1 000 000
B. Read the problem and complete the table below.
Mrs. Angeles bought the following cars for her 5 children.
Honda Civic – Php 1 289 980
Limousine - Php 5 561 003
Ferrari - Php 8 123 315
Jaguar - Php 4 123 980
BMW - Php 3 901 312
Copy the price of each item. Then, round each to the nearest hundred thousand and
millions.
Item Price Hundred Thousands Millions
Honda Civic Php 1 289 980
Limousine Php 5 561 003
Ferrari Php 8 123 315
Jaguar Php 4 123 980
BMW Php 3 901 312

Lesson 4: Using Divisibility rules for 2, 5 and 10 to find common
factors
Jaira has 70 collected stamps. Can she shared that equally to 2 friends? 5 Friends? 10
friends?
To solve the problem, you need to know if 2 5 and 10 are factors of 70 or if 70 is divisible
by 2 5 and 10.
To see if the number is divisible by 2, 5 or 10 ,test by checking the ones digit
DIVISIBILITY TEST 70
By 2: Is the ones digit 0,2,4,6 or 8? YES
By 5: Is the ones digit 0 or 5? YES
By 10: Is the ones digit 0? YES
Get Moving!
A. Put a check under each column to identify whether each number is divisible by 3, 6 or 9.
2 5 10
54180
912
2700
5605
568
3765
233
80

B. Determine whether the first number listed is divisible by the second number. Write Yes
or No on the blank.
Yes or No
1. 45 ; 2 ____________
2. 5080 ; 5 ____________
3. 90 ; 5 ____________
4. 1180 ; 10 ____________
5. 6998 2 ____________
Keep Moving!
Underline the answer that makes each sentence correct.
1. Twenty is (divisible/not divisible) by ten.
2. Three hundred is (divisible/not divisible) by five.
3. Nine hundred ninety is (divisible/not divisible) by two.
4. One hundred six is (divisible/not divisible) by five.
5. Ten thousand four hundred two is (divisible/not divisible) by two.
Apply Your Skills!
Use divisibility rules to help you solve the following problems.
1. Frances has a collection of 672 stamps. She wants to place the stamps in 2 envelopes
.Can she place the same number of stamps in each envelope?
2. The number of books in Karla’s collection is divisible by 2,5 and 10. She has more than
11 books and fewer than 25 books. How many books does Karla have?

Lesson 5: Using Divisibility rules for 3, 6 or 9 to find common factors
Nena’s garden has 414 bougainvillea plants. She wants to arrange them in either rows
of 3, 6 or 9. Which are the possible arrangements of the plants?
To solve the problem, you need to know if 3 6 or 9 are factors of 414 or if 414 is divisible
by 3, 6 or 9.
Recall the rules:
 Divisible by 3: sum of digits of the number is divisible by 3
414= 4+1+4=9, 9 is divisible by 3,therefore 414 is divisible by 3
 Divisible by 6: number is divisible by both 2 and 3
414 is divisible by 2 and 3, therefore 414 is divisible by 6
 Divisible by 9: sum of the digits of the number is divisible by 9
414= 4+1+4=9, 9 is divisible by 9, therefore 414 is divisible by 9
Get Moving!
A. Put a check under each column to identify whether each number is divisible by 3, 6 or 9.
3 6 9
528
1242
3456
624
852
2547
324
120
B. Write the letter of the correct answer on your notebook.
1. Which of the following is divisible by 3?
a.11 b.36 c.23
a. 108 b.100 c.124
a. 71 b.134 c.234
4. 3 is a factor of
a.272 b.153 c.92
5. 6 is a factor of
a.84 b.75 c.53

Keep Moving!
A . Tell whether each number is divisible by 6 or not.
1.906
2.1322
3.4714
4.5166
5.84510
B. Tell whether each number is divisible by 9 or not.
1.89019
2.4617
3.48753
4.1404
5.75834
Apply Your Skills!
Answer the following questions and write the answers on your notebook.
1. Are all numbers divisible by 9 also divisible by 3?
2. How many numbers between 50 to 100 are divisible by 3?
3. Marjorie wants to arrange her 186 books in three rows. Would it be possible?

Lesson 5: Using Divisibility rules for 4, 8, 12 and 11 to find common factors
The school auditorium has 372 chairs. Mrs.Cruz, the principal wants to align them in
either rows of 4,8,12 or 11. Which are the possible alignments of the chairs?
To solve the problem, you need to know if 4, 8,12 or 11 are factors of 372 or if 372 is
divisible by 4, 8, 12 or 11.
Recall the rules:
 Divisible by 4: if the last two digits form a number that is divisible by 4.Also, numbers
ending in two zeros are divisible by 4
372→ 72 ÷ 4 = 18, therefore 372 is divisible by 4,chairs can be aligned by 4
 Divisible by 8: if the number formed by the last 3 digits is divisible by 8.Also, a number
ending in three zeros are also divisible by 8
372 ÷4 = 93,therefore 372 is divisible by 8,chairs can be aligned by 8
 Divisible by 12: if the sum of the digits of the number is divisible by 2 and 3
372= 3+7+2=12, 12 is divisible by 2 and 3, therefore 372 is divisible by 12
 Divisible by 11:if the sum of the digits in the odd places and the sum of the digits in the
even places are equal or their difference is a multiple of 11.
372→(3+2)-7= -2,therefore 372 is not divisible by 11,chairs CANNOT be aligned by 11
Get Moving!
A. Encircle 4,8,11 and 12 if these are factors by these numbers.
1. 1572 - 4 8 11 12
2. 88 - 4 8 11 12
3. 160 - 4 8 11 12
4. 642 - 4 8 11 12
5. 2400 - 4 8 11 12
B. Write on the blank before each number whether it is divisible by 4,8,11 or 12.
_____1. 500
_____2. 3000

_____3. 121
_____4. 492
_____5. 648
Keep Moving!
Supply the missing number to make the number divisible by the number opposite it.
1.273_ - 4
2.216_ - 8
3.91_ - 12
4.26_ - 11
5.38_ - 12
Apply Your Skills!
Answer the following questions and write the answers on your notebook.
1. Can 88 stamps be shared equally by 4 friends? 8 friends? 11 friends? 12 friends?
2. Annie wants to distribute his 276 marbles to 12 children. Will each child receive the
same number of marbles?

Lesson 7: Solving Routine and Non – Routine Problems Involving Factors, Multiples and
i
Divisibility Rules for 2,3,4,5,6,7,8,9,10,11 and 12
Read the problems below.
Can you solve the problem?
Here are the steps in analyzing and solving word problems.
Study the solution below.
Problem 1:
Michael has to split 60 students in
his class into different groups with
equal number of students each .Not
all students can be in one group and
each group has to have more than
one student. In how many ways can
he form these groups?
Mila baked cookies for her 3 sons
and 2 daughters. If she baked 45
cookies only. How many cookies did
her 3 sons have and 2 daughters
have?
 Understand
Know what is asked: In how many ways can he form these groups?
Know the given facts: 60 students, different groups with equal number of students
each
 Plan
Determine the way/s to be used: factoring, finding the multiples and divisibility rules
 Solve
Show your solution:
A. Find the factors of 60.
60= 4X15= 2X2X3X5
B. Get the numbers(once) on the given factors. Then find the multiples of each
number till you reach 60.
 Multiples of 2 = 2, 4, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40,
42, 44, 46, 48, 50, 52, 54, 56, 58, 60
 Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60
 Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
Members 2 3 4 5 6 10 12 15 20 30
Groups 30 20 15 12 10 6 5 4 3 2
Ways 10 ways
C. Identify the number that can divide 24 equally.
Answer: There are 10 ways to form a group.

Problem 2:
Which of the problems do you think is easier to solve? Why?
Can you try solving this problem?
Do this with your partner.
1. A farmer in Calauan gathered 96 pineapples. If he would want to distribute those 96
pineapples in baskets, how many ways can he distribute when each basket has the
same number of pineapples?
Get Moving!
Solve the following problems:
1. Josephine planted 600 onions equally in 20 rows. How many onions were planted in
each row?
Understand:____________________________________________________________
Plan:__________________________________________________________________
Solve:_________________________________________________________________
Check and Look back:____________________________________________________
2. The product of numbers is 138.If one factor is 2, hat is the other factor?
Understand:____________________________________________________________
Plan:__________________________________________________________________
Solve:_________________________________________________________________
 Understand
Know what is asked: How many cookies did her 2 sons have? How many cookies
did they have individually?
Know the given facts: 3 sons and 12 daughters ,30 cookies
 Plan
Determine the way/s to be used: Finding Multiples
 Solve
Find the multiples of 2 and 1 till you get the sum of 30.
3 sons 3 6 9 12 15 18
2 daughters 2 4 6 8 10 12
sum 5 10 15 20 25 30
Answer: There are 18 cookies for her 3 sons and 12 cookies for her 3 daughters.
Show your solution:
 Check and Look back
Review and recheck your answer:

3. How many 5,00 are there in 50,000?
Understand:____________________________________________________________
Plan:__________________________________________________________________
Solve:_________________________________________________________________
Keep Moving!
Solve the following word problems
1. Joel and Harry love playing marbles. Joel has 60 marbles while Harry has 80 marbles .
They plan to keep their marbles in a clay jar. How many clays are there?
2. What is the smallest number of avocados that can be placed in baskets with 50 and 75
pieces ?
3. Joseph has some chocolates. If he shares them equally among 4 friends or 5 friends,
there are always 2 exrta chocolates left. What is the possible number of chocolates
Joseph Could have?
Apply Your Skills!
Try solving more problems.
Read and analyze more problems. Then write your solutions and answers in your
notebook.
1. Lorna earns Php 10,000 a month. How much does she earn in 2 years?
2. A farmer planted 180 monggo seeds equally in 3 big bowls. How many monggo were
planted each row?

Lesson 8: Creates Problem (with Reasonable Answers) Factors, Multiples and Divisibility
Rules
Arrange the sentences to form a word problem
Get Moving!
Use the data inside the box to complete the problems below. Solve the problem in your
notebook.
1. The average of five consecutive odd numbers is 155.
What are the five odd numbers?
2. I am thinking of a number . Twice the number plus . What is my number?
3. How many are there on a n 8-by-8 checkerboard?
4. The average of consecutive numbers is 112. What is the largest number?
and the total payment of T-shirts
Ronald paid P155.00 each T-shirts for his indigent students for the to use as a
uniform and the total payment of T-shirts he bought is P1,240.00. How many T-
shirts did he buy?
How many T-shirts did he buy?
P
he bought is P1,240.00.
Ronald paid P155.00 each T-shirts
Answer:
for his indigent students for the to use as a uniform
115 equals 52 squares 5 even

Keep Moving!
Study the story problems given below. Complete each problem by creating a question for what
is asked. Then, solve the problem.
1. Karen collected 28 recipes of salad. She devided them equally into different categories.
Fruit salad is her favourite category.
Question:_____________________________________________________________?
Solution and Answer:
2. Mike 42 seashells. He places an equal number of seashells in different boxes.
Question:_____________________________________________________________?
3. Sarah wants to invite her cousins to see a volleyball game with her. She has
Php500.Each ticket costs Php85
Question:_____________________________________________________________?
Apply Your Skills!
Create a problem using the given data. Then solve the problem.
1. Given : 31 sachet of shampoos / month
1 year
Asked: total number of sachet of shampoos in 1year
Problem:_____________________________________________________
Solution and answer:
2. Given : 12 apples / day
3 months
Asked: total number of apples in 3 months
Problem:_____________________________________________________
3. Given : 36 red mangoes for Anny
40 green mangoes for Sonia
4 mangoes a day
Asked: total number of mangoes mangoes last individually.
Problem:_____________________________________________________

Lesson 9: Stating, Explaining, and Interpreting Parenthesis, Multiplication, Division,
Addition, Subtraction (PMDAS) or Grouping, Multiplication, Division, Addition,
Subtraction (GMDAS) rule.
Study the rules in the order of operations.
Examples:
1. 12 ÷ 6 × 2 + 4 – 5
2. 6 ÷ 3 × 2 + 5 – 1
3. 3 ×[4 - 2 × (10 -8) + 12 ÷ 6 × 1]
How will you solve the order of operations?
To solve the order of operations, follow the rules listed above.
Solutions:
1. 12 ÷ 6 × 2 + 4 – 5
2 × 2 + 4 – 5
1. Perform the operations within each pair of grouping symbols
(parenthesis, brackets, and braces) beginning with the innermost pair.
2. Simplify the expression with exponents.
3. Perform multiplication and division as they occur from left to right.
4. Perform addition and subtraction as they occur from left to right.
4 + 4 -5
8 - 5
3
Rule 3
Rule 3
Rule 4

2. 6 ÷ 3 × 2 + 5 – 1
3. 3 ×[4 - 2 × (10 -8) + 12 ÷ 6 × 1]
2× 2 + 5 – 1
4+ 5 – 1
9– 1
8
Rule 3
Rule 3
Rule 4
3 × 2
3 × [4 - 2 × 2 + 12 ÷ 6 × 1]
3 × [4 – 4 + 12 ÷ 6 × 1]
3 × [4 – 4 + 2 × 1]
3 × [4 – 4 + 2]
3 × [o + 2]
3 × 2
6
Rule 1
Rule 3
Rule 3
Rule 4
Rule 1
Rule 3

Get Moving
Solve the expression below by following the rules.
1. 32 ÷ 2 × 2
2. 6 ÷ 2 +1 × 4
3. (15 – 6) + (4 – 1) × 23
4. 3 × [3 + 2 × (10 -3)]
5. 12 + 3 × 3 {3 × [4 +(9 – 8) – 2] – 3}
Keep Moving
Perform the indicated operations.
1. (12 + 3) – 7 = N
2. 4 (6 + 8) = N
3. 25 ÷ 5 + 9 = N
4. (18 – 4) + (5 + 3) = N
5. (6 ÷ 3) + (10 × 3) = N
Apply Your Skills!
A. Place parenthesis in the equation so that each equation will be a true statement.
1. 16 – 7 + 8 = 1
2. 3 × 5 – 4 = 3
3. 18 ÷ 6 × 3 = 1
4. 16 – 7 + 8 = 17
5. 12 ÷ 2 + 4 = 2
B. Use the numbers 3, 4, 6, and 8 once in each exercise to make a true statement.
( ______ × _______ ) ÷ ( _____ + ______ ) = 2
______ × _______ ÷ ( ______ × _______ ) = 1
______ × ( ______ × ______ ) ÷ _______ = 18
______ ÷ ( _______ - _______ ) + _______ = 14

Lesson 10 : Simplifies a series of operations on whole numbers
involving more than two operations using the PMDAS or GMDAS rule.
A lot of problems in mathematics involve more than one operation. Some may contain a
series of operations and different grouping symbols such as parenthesis ( ),
brackets[ ], and braces { }
 Simplify 4 + 32
.
You need to simplify the term with the exponent before trying to add in the 4:
4 + 32
= 4 + 9 = 13
 Simplify 4 + (2 + 1)2
.
You have to simplify inside the parentheses before I can take the exponent through.
Only then can I do the addition of the 4.
4 + (2 + 1)2
= 4 + (3)2
= 4 + 9 = 13
 Simplify 4 + [–1(–2 – 1)]2
.
You shouldn't try to do these nested parentheses from left to right; that method is simply
too error-prone. Instead, you will try to work from the inside out. First you will simplify
inside the curvy parentheses, then simplify inside the square brackets, and only then
take care of the squaring. After that is done, then you can finally add in the 4:
4 + [–1(–2 – 1)]2
= 4 + [–1(–3)]2
= 4 + [3]2
= 4 + 9
= 13

Get Moving!
A. Simplify the following expressions in your notebook following the PEMDAS or
GEMDAS rule.
1. 3 + 52
– 2
2. (2 – 5 ) + 42
– 10 ÷ 5
3. ( 4 – 1 )2
+ 15 ÷ 3 – 1
4. 10 – ( 3 + 4 ÷ 2 )2
+ 15
5. (3 + 2 ) + 8 ÷ 2 x 4
B. Complete the table. Write the order of operations to simplify the given
expression.
Expression Operation first to perform Answer
6) 6 + 5 x 3 – 7
7 ) 6 + 15 - 7
8) 14 – 7 + 18 ÷ 3
To simplify series of operations on whole numbers involving more than two
operations using PEMDAS or GEMDAs rule.
 First, perform operations inside the innermost grouping symbols,
if any.
 Next, evaluate powers.
 Then, perform multiplication/division from left to right.
 Finally, perform addition/subtraction from left to right.

9) 7 + (15 - 6 x 2)
10) 2 ( 2 + 5 ) 2
Keep Moving!
A. Simplify the following expressions in your notebook following the PEMDAS or
GEMDAS rule.
1. (25 + 5) x 3 – 13
2. 19 + 12 x 3 – 5
3. 54 + 23 ÷ 2
4. 21 + 34 x 3 ÷ 2
5. (5 + 3) x (3 + 8)
6. 2 + 16 x 7 – 3
7. 11 + 5 x 5 – 10
8. 31 – 24 ÷ 1 -7
9. 21 + 16 – 8 ÷ 9
10.(19 – 3 ) x 3
Apply Your Skills!
A. Write the expression and solve the given problems.
1. Peter has 450 pesos. He spends 210 pesos on food. Later he divides all the
money into four parts out of which three parts were distributed and one part he

keeps for himself. Then he found 50 pesos on the road. Write the final
expression and find the money he has left?
2. You pay 10.00 pesos to buy a package of paper napkins costing 640 pesos. How
much change will you get back? Give the expression also.
3. Liza has 1,000 pesos to be distributed among two groups equally. Later, the first
part is divided among five children and second part is divided among two
brothers. Give the expression that represents how the money distribution
between two groups was dispersed?
Challenge yourself with this problem!
Read the problem and then write the answers to the questions in your notebook.
1) Flora bought 3 notebooks for 10 pesos each, a box of pencils for 21.00
pesos, and a box of pens for 35.00 pesos.
2) Darwin had 35 500 pesos and withdrew 5200 pesos from his bank account.
He bought a pair of trousers for 340 pesos, 2 shirts for 360 pesos each, and 2
pairs of shoes for 540 each. Give the final expression, and determine how
much money Darwin had at the end of the shopping day.

1
Lesson 11: Finding the common factors and the GCF of two - four
numbers using continuous division
You find the common factors and Greatest Common Factor or (GCF) of 24, 30 and 42.
Using Continuous Division
2 24 30 42
3 12 15 21
3 5 7
A. Find the common factors and GCF of the following numbers.
1) 24 32 4) 4 6 20
2) 12, 30 42 5) 8 56 84 112
3) 28 32 40
Mrs. Ragas bought 24 mangoes, 30 apples and 42
bananas. If she is going to group these equally, what is
the greatest number of mangoes, apples and bananas in
each group?
GCF: 2 x 3 = 6
The greatest number of mangoes, apples and
bananas is 6.
Get Moving!

2
B. Find the GCF of the following problems using continuous division.
1) Miss Dela Cueva has to prepare number of exercises for her lesson for the
day. She has three classes. One class has 48 pupils, another class has 50,
and another has 46. What must be the largest number of exercises she
should prepare so that each class will have the same number of pupils
working on different problems?
2) There are 10 green, 14 blue, 20 red and 24 yellow bulbs to be used for a
birthday party. They are to be placed in plastic bags so that each bag
contains the same number of green, blue, red and yellow bulbs. What is the
largest number of plastic bags that will be needed?
A. Determine the GCF.
1) 3 72 99 126 GCF = ________
3 24 33 42
8 11 14
2) 5 90 135 180 195 GCF = ________
8 17 36 39
3) 2 42 56 70 98 GCF = ________
7 21 28 35 49
3 4 5 7
A. Find the common factors and GCF the following word problems.
4) The mathematics teacher in a certain elementary school is planning to have
an educational tour for four grade levels with 800 pupils in Grade II, 560
Keep Moving!

3
pupils in Grade III, 480 pupils in Grade IV and 400 pupils in Grade V. What is
the largest number of pupils in a group in each grade level so that each group
has the same number of pupils?
5) A group of 45 dancers will march behind a group of 30 clowns in a parade.
You want to arrange the two groups in rows with the same number of people
in each row, but without mixing the group. What is the greatest number of
people you can have in each row?
6) A group of 45 dancers will march behind a group of 30 clowns in a parade.
You want to arrange the two groups in rows with the same number of people
in each row, but without mixing the group. What is the greatest number of
people you can have in each row?
Read and solve the common factors and GCF the following word problems.
1) The mathematics teacher in a certain elementary school is planning to have
an educational tour for four grade levels with 800 pupils in Grade II, 560
pupils in Grade III, 480 pupils in Grade IV and 400 pupils in Grade V. What is
the largest number of pupils in a group in each grade level so that each group
has the same number of pupils?
2) The parents are making sandwiches for the class picnic. They have 72 ham
slices, 48 cheese slices, and 96 tomato slices. What is the greatest number of
sandwiches they can make if each sandwich has the same filling?
Apply Your Skills!

4
1) Gina has two pieces of cloth. One piece is 72 inches wide and the other piece
is 90 inches wide. She wants to cut both pieces into strips of equal width that
are as wide as possible. How wide should she cut the strips?
2) The GCF of 40 and a number 8. What is the number if it lies between 70 and
80?
3) Two numbers have a GCF of 6. If their difference is also equal to their GCF,
what are the numbers?
4) Find three consecutive even numbers such that their GCF is the lowest of the
three even numbers.

Lesson 12: Finds the common multiples and LCM of two - four
numbers using continuous division
To solve the problem, you need to find the least common multiple or LCM of 6
and 9 using continuous division.
Here’s how you do it.
3 6 9
2 3
LCM = 2 x 3 x 3 = 18
 Notice that 18 is the least common multiple or LCM of 6 and 9. Therefore, the
smallest number of roses and daisies that she will need for her bouquets is 18.
 You do not include when dealing with common multiples.
Get Moving!
A. Write the letter of the correct answer in your notebook.
1) The common multiples of 6 and 4 are
a. 2, 3, 4 b. 4, 6, 8 c. 8, 12, 16 d. 12, 24, 36
2) The common multiples of 4, 5 and 8 are
a. 8, 10, 16 b. 16, 20, 24 c. 40, 80, 120 d. 50, 90, 100
Lovelyn and Zerma are going to
prepare bouquets with 6 roses to a bouquets
and with 8 daisies to a bouquet. What will be
the smallest number of roses and daisies that
she will need for their bouquets?

3) The LCM of 15 and 9 is
a. 3 b. 15 c. 45 d. 135
4) The LCM of 2, 3, 4 and 5 is
a. 20 b. 30 c. 50 d. 60
5) A common multiple of 3, 5, 9 and 10 is
a. 30 b. 50 c. 90 d. 100
B. Determine the LCM.
1) 3 9 12 LCM = ________
3 4
2) 5 5 10 30 45 LCM = ________
1 2 6 9
3) 2 12 16 20 28 LCM = ________
2 6 8 10 14
3 4 5 7
Keep Moving!
A. Find the Least Common Multiple (LCM) of the given sets of numbers use
continuous division.
1) 3 15 21 LCM = ________
2) 4, 8, 16, 20 LCM = ________
3) 5, 10, 25, 30 LCM = ________
4) 6, 12, 15, 60 LCM = ________
5) 2, 6, 10, 14, LCM = ________

B. Find the Least Common Multiple (LCM) the following word problems using
continuous division.
1. What is the least number of candies that can be divided equally among 8, 9,
and 12 children?
2. You bring the drinks for your basketball team every sixth game. Every third
game is a home game. When will you first bring the drinks to a home game?
If there are 20 games in an annual sportsfest, how many times will you bring
the drinks to a home game?
Apply Your Skills!
Read and solve the common factors and GCF the following word problems.
1. Chill water her petchay every 2 days, and her cabbage every 3 days. Not
counting the first day, when is the first time both plants are waters on the same
day? When is the next time?
2. Efren goes home every other day. His wife Fely goes home every 4 days. His
daughter Edlin goes home every 6 days. If they see each other today, when will
they see each other again at home?
A. Mr. Placido, a security guard, has 3 successive night duties a week? His wife
who is a nurse has 2 successive night duties. When will they see again if they
are together now?

B. Two films were played at the same time. But the length of time of each film is
different from each other. Film A took 120 minutes while Film B took minutes.
After how many minutes will the two films be played at the same time again?
C. Find the LCM of each pair of number.
a. 33
and 23
b. 23
and 42
c. 8, 16, 24 and 48
d. 12, 30, 42, and 66

Lesson 13: Solves real life problems involving GCF and LCM of 2-3 given numbers.
Elmer wants to cut as many pieces of wood of equal lengths from three pieces with
lengths 35dm, 49dm, and 56 dm. What is the longest that he could cut each piece? How will you
solve for the answer to the problem?
You can use the 4 - step plan in solving for the answer.
Understand:
What does the problem? The longest that he could cut each piece.
What facts are given? 35 dm, 49 dm, 56 dm of wood.
Plan
How will you solve the problem? By finding the Greatest Common Factor (GCF) and Least
Common Multiple (LCM)
Solve:
How is the solution done? By listing the factors
35: 1, 5, 7, 35
49: 1, 7, 49
56: 1, 2, 4, 7, 8, 14, 28, 56
GCF: 7
By Prime Factorization
35: 5 x 7
49: 7 x 7
56: 7 x 2 x 2 x 2
GCF: 7
Check and Look Back:
What is the answer to the
problem?
7 dm is the longest cut can be done in the wood.
Can you think of other ways to solve the problem?
Get Moving!
Read each problem and answer the questions that follow. Write your answers in your notebook.
1. Mr Ramos has to prepare a number of exercises for his lesson for the day. He has three
classes. One class has 48 students, another class has 50, and another has 46. What
must be the largest number of exercises he should prepare so that each class will have
the same number of students working on different problems?
a. What is asked in the problem? __________________________________________
b. What facts are given? _________________________________________________
c. How will you solve the problem? _________________________________________
d. What is the answer to the problem? ______________________________________

2. Yesterday Tony bought 4 “Monay Bae” for Php. 5.00. He sold 3 “Monay Bae” for Php.
5.00. How many “Monay Bae” did he have to sell in order to make a profit of Php. 5.00.?
a. How will you solve the problem? ______________________________________
b. What is the answer to the problem? ___________________________________
Keep Moving!
Read and solve each problem. Write the solution in your notebook.
1. There are 14 blue and 20 red bulbs to be used for a birthday party. They are to be
placed in the plastic bags so that each bag contains the same number of blue and red
bulbs. What is the largest number of plastic bags that will be needed?
2. Liza has bought eight hair clips for Php. 10.00 and has sold them at 6 clips for
Php.10.00. How many hair clips have to be sold to make a profit of Php. 10.00?
Apply Your Skills!
Challenge yourself by solving these problems. Write your answers in your notebook.
1. Serena wants to create snack bags for a trip she is going on. She has 6 granola bars
and 10 pieces of dried fruit. If the snack bags should be identical without any food left
over, what is the greatest number of snack bags Serena can make?
2. Evelyn is packing equal numbers of apple slices and grapes for snacks. Evelyn bags the
apple slices in groups of 18 and the grapes in groups of 9. What is the smallest number
of grapes that she can pack?

Lesson 14: Create problems (with reasonable answers) involving GCF and LCM of 2-3
given numbers.
How will you create a problem involving Greatest Common Factor (GCF) or Least Common
Factor (LCM) given the following information?
You can create a problem by following this guide:
 Familiarize yourself with the concepts of GCF and LCM and their application to real life
situations.
 Think of the type of problem you want to create.
 Read some problems and study their solutions.
Problem 1:
Arielle is making flower arrangements. She has 7 roses and 14 daisies. She wants to
make all the arrangements identical and have no flowers left over.
Problem 2:
Tayli wishes to advertise her business, so she gives packs of 13 red flyers to
each restaurant owner and sets of 20 blue flyers to each clothing store owner. Tayli
realizes that she gave out the same number of red and blue flyers.
Study the following problems as examples for the above information.
Problem 1 involves finding the Greatest Common Factor (GCF)
Arielle is making flower arrangements. She has 7 roses and 14 daisies. She
wants to make all the arrangements identical and have no flowers left over.
What is the greatest possible number of flower arrangements she can make?
Problem 2 involves finding the Least Common Multiple (LCM)
Tayli wishes to advertise her business, so she gives packs of 13 red flyers to each
restaurant owner and sets of 20 blue flyers to each clothing store owner. Tayli realizes that she
gave out the same number of red and blue flyers.
What is the minimum number of flyers of each color she distributed?
Can you make another problem similar to these examples?

Get Moving!
A. Write a question to complete each item. Then, solve each problem.
1. Nathan is stocking bathrooms at the hotel where he works. He has 18 rolls of toilet paper and
9 bars of soap. If he wants all bathrooms to be stocked identically, with the same combination of
supplies in each one and nothing left over, what is the greatest combination of bathrooms
Nathan can stock?
2. Sarah’s Shipping and Ryan’s Mail Services both ship packages. Sarah’s trucks will only carry
loads of 18 packages. In contrast, Ryan’s trucks will only carry loads of 11 packages. If both
businesses ended up shipping the same number of packages this morning, what is the
minimum number of packages each must have shipped?
B. Create some problems involving GCF and LCM.
Keep Moving!
Write a problem for the numbers and phrases in the box.
1.
2.
3.
4.
Apply Your Skills!
Create problems involving GCF and LCM based on the following situations:
1. Alaiza arranged the fruits in a box.
2. Luisa shared her toys with her playmates.
3. Anthony is selling newspaper every morning.
4. Volunteers gives clothes in the orphanage.
5. Joey is preparing cake for her friends.
30 and 48 cookies Biggest numberPut inside the
identical container
32, 24, 16 balloons Arranged in a table Greatest number
5, 10 and 15
pictures
Smallest numberCollected
photographs
5, 6, 30 books Least numberNumber of books in
a shelve

Lesson 15: Adds fraction and mixed fraction without and with regrouping
A. Musician practiced very well for the concert. He practiced hours yesterday and hours
today. How many hours did he practice in two days?
The mathematical sentence is: + = n
Step 1 Step 2 Step 3
Find the LCD of the add the fractional Add the whole numbers
Given fractions and rename parts reduce in lowest term
These to similar fraction if needed
= = = 5 + 5 +
= = = = =
______ ______
= 5
Will become
While
Will become the answer will be

And will become in lowest term.
Get Moving!
Find the sum. Express your answer in lowest terms if possible.
1. 2. 18 3. 4. 5.
+ + + + +
_________ _________ _________ _________ _________
Keep Moving!
Add. Rename the sum in lowest terms if possible.
1. 2. 3. 4. 5.
+ 216 + + + +
_________ _________ _________ _________ _________
Apply Your Skills!
Read each Problem then, answer the question that follow.
1. Joshua picked 2½ buckets of strawberries. Joe picked 3½ buckets of strawberries. How
many buckets of strawberries did the two boys pick?
a. What is asked?
b. What are given?
c. What is the operation to be used?
d. What is the number sentence?
e. How is the solution done? Show your solution?
f. What is the complete answer?

2. Mrs. Gonzales used 2¼ cups of flour to make a plain cake, 3 ½ cups to make brownies and
2 ¾ cups to make doughnuts. How many cups of flour did she use?
a. What is asked?
b. What are given?
3. Three hogs weigh respectively kilograms, kilograms and kilograms. What
is the total weight?
a. What is asked?
b. What are given?

Lesson 16: Subtracting Fractions and Mixed fractions without and with Regrouping
Karen bought kilogram of lanzones and kilograms of banana.
How many more kilograms of lanzones than banana did she buy?
How will you answer the question in the problem?
To answer the question, subtract .
The number sentence is
= Change and to similar fractions by first finding
= the LCD OF 2 and 4.
Subtract the numerators.
Write the sum over the least common denominator
So, Karen bought kilogram more lanzones than banana.
Get Moving
Subtract the following fractions
1.
2.
3.
4.
5.
6.
7.
8.
LCD
LCD

Keep Moving
Subtract. Reduce the difference to lowest terms whenever possible.
1. 2. 3. 4. 5.
Apply Your Skills!
A. Read and solve each problem.
1. Jerrie can repair her car in hours. A mechanic can do the same job in 8/12 hour.
How much longer does it take Jerrie to do the job?
2. Pia spent hours in her grandparents’ house. This was of an hour more than
the time she spent at the mall. How much time did she spend at the mall?
3. Ana bought kg of grapes for her younger sister. They ate kg of it. How many
kilograms of grapes were left?
B. Read and solve each problem
1. Lailani has meters of yarn on a ball. After meters were unwound, how many
meters of yarn remained on the ball?
2. There are 5 pitchers of fruit juiced arranged in a row. The first pitcher contains
cups of juice. If each pitcher has cups less juice than the one before it, find the
amount of juice in each of the other pitchers.
3. Alvin weeded the garden in hours and watered the plants in hours. How
much longer did he spend weeding the garden than watering the plants?

First Quarter- Week 6
Lesson 17:Solving Routine and non routine problems involving addition and/ or subtraction of
fraction using appropriate problem solving strategies and tools.
EXPLORE AND DISCOVER
Darwin painted his room using 5/6 liter of blue paint and 2/3 liter of white paint.
What color of paint was used more than the other? How much more of it was used than
the other?
You can solve the problem using the following steps.
Understand:
 Know what is asked : The paint color that was used more and by
by how much more
 Know the given facts: 4/6 liter of blue paint; 4/5 liter of white paint
Plan:
 Draw a picture :
5/6
2/3 = 4/6 1/6
 Identify the operation to be use: Subtraction
 Write the number sentence : 5/6 – 2/3 = n
5/6 – 2/3= 5/6 – 4/6 = 1/6
Solve:
 Solution:
Check and Look back:
 Answer: a. more blue paint was used
b. by 1/6 liter
Get Moving

Read each problem carefully and then solve.
1. Mark wash his car in 4/5 of an hour, cleaned the garage in 2/6 of an hour, and painted
the garden fence in 2 hours. How long did it take him to do all the tasks?
2. Anthony walked ¼ of a kilometer to Jane’s house and 7/8 of a km to the park. How
far did he walk?
3. Jenny spends ¼ of her daily allowance for snacks, ½ for lunch, 1/8 for transportation,
and saves the rest. What part of her daily allowance does she save?
Keep Moving
Read and solve each problem.
1. Liza spent ¾ hour preparing the soil and 2/3 hour planting. How much time did she
spend in the garden?
2. In a fruit basket, 4/5 of the fruits are bananas and 3/8 are mangoes, which are more-
the bananas or the mangoes?
3. Ronnie had 7/8 gallon of paint. He used 4/5 of it. What fraction of a gallon of paint was
used? How much paint remained?
Apply Your Skills
1. Four fifths of a group of rallyists were students, If 3/8 of the students were female,
what part of the rallyists were male students?
2. Angie covered ¾ of a bulletin board with white paper. Then, she made a Math poster
on 2/3 of the white paper. What part of the board was covered by the poster?
3. A water tank was 20/21 full. If 3/5 of it was used to water the plants, what fraction of
the tank was used in watering the plants?

Lesson 18: Creating problems (with reasonable answers) involving addition and/or subtraction
Fraction using appropriate problem strategies
Explore and Discover
How do you create a word problem involving addition, subtraction, or addition and
subtraction of fractions?
You can create a word problem by observing the following guide:
 Familiarize yourselves with the concept of addition and subtraction of fractions
and their application to real- life situations
 Think of the problem you want to write.
You also consider the following when creating a problem:
a. Characters
b. Situation/ setting
c. Data
d. Key question
Study the table below:
Name Ribbons used/ left Quantity Unit
Liza White ribbon 2/8 meter
yellow 2/4 meter
Ribbons left 3/6 meter
Study the problem as an example for the given data.
Liza bought 2/8 m of white ribbon and 2/4 m of yellow ribbon to make flowers.
After making 5 flowers, she found out she had 3/6 m of ribbons left. How many
meters of ribbon did she use for the flowers?
Get Moving!
Use the data below to create a one-step word problem involving subtraction of
fractions.
Name Color of Paint used in the
classroom
Quantity Unit
James Blue 4/5 liter
Harold Green 3/6 liter

Keep Moving!
Use the data below to create a two- step word problem involving addition and
subtraction of fractions.
Name Quantity Unit Color of cloth
needed in science
project
Carmen 3/5 Meter White
Rowena 2/8 Meter Red
Aileen 5/6 Meter yellow
Apply Your Skills!
Using the table below, create a problem for each of the following.
1. One- step word problem involving addition of fractions (Group 1)
2. One-step word problem involving subtraction of fractions (Group 2)
3. Two-step word problem involving addition and subtraction of fractions (Group 3)
Name Quantity Quantity ( in kilograms)
Sharon Grapes 1/2
Vilma Papaya 3/4
Nora Lansones 4/8

1 x 1 = 1
5 2 10
LESSON 19 Visualizes Multiplication Of Fractions Using Models
Darwin had a piece of plastic cover ½ meter long. He used 1/5 of it to cover his book. What fractional
part of the plastic cover did he use?
To find the answer, get 1of 1.
5 2
The diagram below will help you find the answer.
If the rectangle represents 1 metre, the shaded part represents the plastic cover of Darwin.
To find 1 of 1 , we have to divide the shaded
parts into 5 equal parts and take 1 of the equal
parts 5 2
The part of the whole representing the product of 1/5 x 1/2 is the region that has been shaded twice.
Notice that the rectangle has been divided into 10 equal parts and 1 part is shaded twice so 1/5 x 1/2
must be 1/10, Darwin used 1/10 metre of plastic cover.
STUDY THESE EXAMPLE
Let us use a region to find 1/3 of 2/5 or 1/3 x 2/5.
The region at the left has been divided vertically into 5 parts of
the same size. Therefore each parts is 1/5 of the whole region.
Ask. How many fifths are shaded? What part of the region is
shaded?

Thus: 1 2122
3 of 5 equals 3 x 5 = 15
Get Moving
1. Write a multiplication equation for each visualization and find the answer
a
X = =
_________
b.
X =
= _________
c.
x = =
____
Next picture 2 horizontal lines have been drawn to divide
each 1/5 into 3 equal parts.
Into how many equal parts is the region now divided?
How many small regions are shaded?
Next , 1/3 of the shaded part has been shaded in
another direction. How many of the small regions are
now shaded twice ? What part of the whole region is
shaded twice?

Keep Moving !
Match the picture in Column A with the multiplication sentence in Column B. Write your answer
in your notebook.
A B
Apply Your Skills:
Write the multiplication equation for each and find the answer.
a. 11
2 of 4
b. 13
3 of 4
c. 11
5 of 2

x =
=
A. Illustrate and Find the Product
1 323 5. 31
3 45 4 5 4
x =
x
=
x
= x =
=
3.
4.
1.
2.

LESSON 20: MULTIPLIES A FRACTION AND A WHOLE NUMBER AND
ANOTHER FRACTION
First Quarter : Week 7
A. Michelle bought kg of carrots for her pet rabbit. Her
pet ate of this how many carrots did her pet
eat?
To know the amount of carrots the rabbit ate, let us compute of . How do we right of
in a number sentence ? x = N
Let’s solve this in two ways
First let us use an illustration to get the product.
3
4
133 1
3 4 12 4
The double shaded parts show the parts of the carrot eaten by the rabbit. .When reduced to
lowest terms is
So, Michelle’s pet ate ¼ of the carrots.
1
3
1
3
1
3
3
4
3
4
x = =
3
12
1
4
1
3
3
4

3
12
Let’s solve x again, this time through computations.
Multiply the numerators x =
Multiply the denominators x =
Reduce the product to lowest terms ÷ =
Study these other examples:
of == or x 8
If we have a whole number like 8 we can also write it as a fraction with a denominator of 1.
1
4 because 0r 2
GET MOVING
Direction : Cut each strip. You may paste them in a chipboard or cartolina to make them harder.
STEP 1
1
3 3
4
3
STEP 2
1
3
3
4
3
12
STEP 3
3
3
1
4
1
4 8
1
4
1
4
1 8
so4 x 8 = 4 = 2
X 8 = 2,
1
4
x 8
1
= 8
4

KEEP MOVING !
Read the problem:
A. Ramona has yard of a beautiful lace. She gave of it to her friend for their project.
If 2/3 of the apples above are green, then how many are green apples ? Color them to
show your answer ?
If 6/7 of the socks are black,
then how many pieces are
not black ? Color them to
show
ofof the pizza shown will be
given to my classmate. Draw line/s on it to
show the part to be given.
1
2
3
4
4
6
2
3

What part of the lace did Ramona give to her friend ?
B. Bon bought 8 kilos of mango in the market. He shared of it with his relatives for their
outing. How many kilos of mango did he share?
C. One fifth of the 40 pupils of Miss Ramos are Math Club members. How many pupils are
Math Club members ?
APPLY YOUR SKILLS !
Find the product. Always express answers in lowest terms.
1. What is 2,andof ? __________________
2. What is the product of 3/4 ,4 and ½ ? __________
3. What is the value of N ? 5 x ¾ x = N
4. Multiply, and 4.The answer is ________.
5. What is the product of 5 , ½ and? _________
2
3
5
6
3
4
2
4
3
4
2
6
3
6

Lesson 21: Multiplying Mentally Proper Fractions with the Denominators Up to 10.
Nelia has ½ piece of a cartolina. She shares 1/3 of it to Joe who needs it very badly for his
Science project. What part of the cartolina did Nelia Share?
How will you solve for the product of the fractions mentally?
Here’s how to do it.
Do these steps in your mind.
11 1x1 =1
2 x 3 = 2x3 =6 Step 1: Multiply the numerators.
1x1 = 1
Step 2: Multiply the denominators.
2x3 = 6
Step 3: Express the answer in lowest terms if needed.
Get Moving!
Solve the following mentally.
13318541 2 1
5 × 4 = 7 × 3 = 10 × 6= 9× 2 = 8×3 =
A. Find the product mentally.
7461256379
9 x 5 = 10x6 = 3x9 = 8x 5 = 8x 10 =
B. Find the value of N.
1237548134
2 x 3 =N 5 x 8 =N 6 x 9 =N 9 x 3 =N 7 x 5 =N
Apply Your Skills!
A. Read the problems, then solve them mentally.
1. Roy harvested 5/6 crates of mangoes. He sold 4/5 of them. What part of the crate of
mangoes was sold?
2. Dino bought ½ L of white paint. He used ½ of this to paint the doghouse that he
made. How many litres of paint did he use?
B. Understand the equations carefully, then answer it.

1. In the equation 2/3 x ½ =N, what is the value of N?
2. If you multiply ¼ and 2/3, what will be the product?
3. Multiply 2/5, 3/4 and 4/5. It will give a product of_____.
4. What is the product of 2/7,3/8, and ½ ? _______
5. Multiply 2/3, 5/6 and ¾. The answer is _______

1kilo
o
1kilo
o
1kilo
o
1kilo
o
1kilo
o
1kilo
o
1kilo
o
Lesson 22: Solving Routine or Non-routine Problems Involving
Multiplication Without or With
 Addition or Subtraction of Fractions and Whole Numbers
Using Appropriate Problem Solving Strategies or Tools.
Problem 1: Lucy’s mother worked in her boutique for 2 ½ hours each day for 2 weeks.
How many hours did she work in all?
You can solve the problem using the steps below:
 Understand
Know what is asked: No. of hours she worked in all.
Know the given facts: 2 ½ hours and 14 days = 2 weeks
 Plan
Determine the operation to be used: Multiplication
Write the number sentence: 2 ½ × 14 = N
 Solve: Show your solution:
2 ½ × 14 = N
2 ½ × 14/1 = N
5/2 × 14/1 = N
1 7
5/1 × 7/1 = 35/1 or 35 hours
Lucy’s mother worked 35 hours in 2 weeks or 14 days.
 Check and look back: Did I do the operation correctly?
Is my answer reasonable? Did I write my answer in a complete sentence?
Problem 2: Jose harvested 15 kilograms of guavas from the orchard. He gave 2/5 of them to
his neighbors. How many kilograms of guavas did he share to his neighbors?
 Understand
Know what is asked: No. of kilograms he shared to his neighbors.
Know the given facts: 15 kilograms of guava and 2/5 part shared to his
neighbors
 Plan: Make a diagram or drawing.
 Draw 15 kilograms of guavas

1kilo
o
1kilo 1kilo
1kilo
o
1kilo
o
1kilo
o
1kilo
o
1kilo
o
1kilo
o
1kilo
o
1kilo
o
Divide 15 kilograms of guavas into group of 5.
There will be 3 kilograms per group.
Circle 2 parts of it to show 2/5.
Each group shows 1/5 or 3 kilograms of guavas. There are 2 groups of 1/5 and
this shows 2/5.
So, 2 × 3 = 6 kilograms of guavas he shared to his neighbors.
 Look back: To check 15 × 2/5 = 6 kilograms.
15 × 2/5 = 3 15 × 2 =6 or 6 kilograms of guavas
1 5 1 1
Answer: He shared 6 kilograms of guavas to his neighbors.
Can you try solving the following problems?
1. One – fourth meter of the cloth was left from Evelyn’s uniform. Her friend asked
3/5 of it to her Science project. What part of the cloth did her friend get?
2. Mrs. Albano gathered 50 eggs from her poultry. She gave 4/8 of these to her co-
teachers. How many eggs were given to her co-teachers?
Get Moving!
Solve the following problems.
1. A recipe for doughnuts needs 1 ¼ cups of flour. Mother will prepare 1 1/3 times the
recipe. How much flour will she need?
2. On Jenny’s birthday, her mother prepared 48 cupcakes. If ¾ of the cupcakes were
served, how many cupcakes were served?
1kilo
3 kilo
1kilo1kilo1kilo
o
1kilo 1kilo
3 kilo 3 kilo
3 kilo 3 kilo
3 kilo
1kilo 1kilo 1kilo 1kilo 1kilo 1kilo 1kilo 1kilo1kilo

3. Nelson had 3 ½ liters of paint. He used 2/3 of it to paint their fence. What part of the
paint did he used?
4. Remy had ¾ meter long of lace. She gave 1/3 of it to her classmate to decorate her
Science project. What part of the lace was given to her classmate?
5. Everyday Alvin spends 3 ½ hours reading books. How many hours does he spend in a
week reading books?
Keep Moving!
Solve the following problems. Write your solutions and answers in your notebook.
1. Anselmo spent 6/8 of his time in morning studying Math and Science. He spent ¼ of this
time studying Science. What fraction of the total time did he spend studying Science?
2. What is the area of a rectangle whose length is 8/10 m and width is 2/3 m?
3. Aling Aning planted vegetables on 4/7 of her vacant lot. Two thirds of it was planted with
pechay. What fraction of the vacant lot had pechay?
4. Lorna had 2 ½ liters of beef broth. She used 3/5 of it to make soup. How much beef
broth did she use to make soup?
5. A recipe calls for 1 1/3 litres of milk. How many litres of milk do you need to make 2
recipes?
Apply Your Skills!
Try solving more problems!
1. Joanne signed up for 24 dancing lessons. She took ¾ of them by April. How many
dancing lessons did she take by April?
2. Father’s monthly salary amounts to ₱ 20,500. Every time he receives his salary, he
deposits 1/5 of it. How much is father’s monthly savings? How much is his annual
savings?
3. How far can father go in 8 ½ hours if he travels at an average speed of 15 kilometers an
hour?
4. Six pitchers each filled with ¾ liter of juice were served to Luisa’s visitors. Find the total
amount of juice served.
5. The school Home Economics Club had a buko pie sale. The member sold 2/3 of their
pies in the morning and 1/6 of their pies in the afternoon. If 150 pies were left, how many
pies had been sold?

Alice used ¼ teaspoon of salt on her cake recipe. How much salt is needed if
she will make 8 recipes of it?
Lesson 23: Creating Problems (with reasonable answer) Involving
Multiplication of Fractions
How do you create a word problem involving multiplication of fractions?
Observe the guide below in creating a word problem:
 Familiarize yourselves with the different Mathematical concepts
especially multiplication of fractions.
 Analyse the data and think of the type of problems you
want to create.
 Read and study some sample problems and be familiar with
the organization of data on the problem.
 Learn about the basic terms or word clues often used in mathematical problems.
The following data is important to be considered in creating a problem:
 Name/Character
 Situation/Setting
 Data
 Unit
 Key question
Study the given data below:
teaspoon of salt for cake recipe
8 recipes to make
Study the problem as an example for the data given.

Get Moving!
Create a one-step word problem involving multiplication of fractions using the
data given.
1. – part of Mrs. Marco’s class who joined the field trip
30 - total number of pupils
2. kg- mixed nuts bought by Ana
of it given to Alma
3. 12 km- distance of Elmo’s house to school
of total distance is being travelled by jeepney
4. Php 24,000- amount raised by PTA of Del Mundo Elementary School
spend for completing the school’s fence
5. 5 kg of rice bought by mother
cooked for dinner
Keep Moving
Create a one-step word problem involving multiplication of fractions using the data given.
1. kg meat bought by Mr. Guanson
kg cooked
2. Php 420 earnings of Gab every day in working at a printing house
for transportation allowance
3. 5 m ribbon bought by Kim for gift wrapping
used in wrapping square boxes
used in wrapping rectangular boxes

Apply Your Skills!
Create a word problem involving multiplication of fractions for each of the following. Use the
data below.
1. One-step word problem involving multiplication of fractions.
2. Two or more step word problem involving multiplication of fractions.
Name Monthly Salary Monthly Savings
Randy Php 12,000
Ryan Php 15, 000

4 x
𝟏
𝟒
=
𝟒
𝟏
x
𝟏
𝟒
=
𝟒
𝟒
= 1
𝟏
𝟐
𝟑
x
𝟑
𝟓
=
𝟓
𝟑
x
𝟑
𝟓
=
𝟏𝟓
𝟏𝟓
= 1
𝟑
𝟕
x 𝟐
𝟏
𝟑
=
𝟑
𝟕
x
𝟕
𝟑
=
𝟐𝟏
𝟐𝟏
= 1
Lesson 24: Show that multiplying a fraction by its
reciprocal is equal to 1
Janice shared the pizza she made among her 5 friends.
Each one received of the pizza. Nothing was left for her.
How much pizza did she make?
Find: 5 x
Solution:
5 x = x = = 1
Answer: Janice made 1 whole pizza divided among her five friends.
Study some more examples:
 Two numbers whose product is 1 are reciprocals of each other.
 To find the reciprocal of a fraction make the numerator of the
fraction the denominator of the reciprocal and the denominator of
the fraction the numerator of the reciprocal.
 Mixed fractions must first be converted to improper fractions
before the method can be applied.
 Write the reciprocal of a whole number as fraction.

Get Moving!
Give the reciprocal of each number.
1. 51 6. 11. 2
2. 3 7. 12. 35
3. 8. 13. 5
4. 9. 14. 12
5. 24 10.5 15.
Keep Moving!
Write the missing factor.
1. x = 1 6. x = 1
2. x = 1 7. x = 1
3. x = 1 8. 5 x = 1
4. 15 x = 1 9. x = 1
5. x = 1 10. x = 1
Apply Your Skills!
1. The reciprocal of a number is , and their product is 1. What is the number?
2. Two numbers are reciprocals of each other. One number is 36 times as large as the other. What
are the numbers?
X = 1
3. What is the reciprocal of a number whose numerator is 8 times as great as 3 and the
denominator is half the numerator?

Lesson 25: Visualizing Division of fraction
Janella helps her mother cut meter long ribbon from meter ribbon. How many strips can she
cut? Study the illustration and solution below.
Number sentence :
÷ = __________
From the figure we can see that there are twenty-eight in . Therefore, the answer is 28.
Get Moving!
Use illustrations to answer each question.
1. How many are there in 9?
2. How many s are there in ?
3. How many are there in 24?
4. How many are there in ?
5.
6. How many are there in ?
Keep Moving!
Illustrate to find the quotient.
1. ÷ = 2. ÷ = 3. ÷ = 4. ÷ = 5. ÷ =

Apply your Skills!
Use a model to solve the problem.
1. Camille needs m of cloth for a banner. If she has m of cloth, how many banner can
she make?
2. Mrs. Dator needs4 liters of fresh milk. The store has liter packs of fresh milk. How
many packs does she need to buy?
3. Mario has 8 logs to be cut in fourths to make fence posts. How many fence post can he
make?
4. Mother bought 5 apples. She divided them into halves. How many pieces of apple
were there?

Lesson 26: Dividing Simple Fractions and Whole Number and a Fraction
Nathan wants to share his buko pie with his friends. He has of the buko pie, and he wants to
give each friend of the buko pie. How many friends can Nathan feed?
Solution:
Without any illustration we can solve the problem following the steps in dividing simple fraction.
Solution:
÷ = n
÷ = n Write the reciprocal of the divisor
x = n Change the division sign into multiplication sign
x = Multiply the numerators then the denominators
÷ = 4 Express in lowest term if necessary
Therefore ÷ = 4
Nathan can feed 4 of his friends.
Problem 2.
Jane received 3 guavas from her friend. She cut it into pieces. How many halves did she
have?
Use real guava to solve the problem
Problem 3
Lina has of a chocolate bar. It will be divided equally among 4 persons, what part of the
chocolate bar will each one get?
We can solve the problem following these steps:
Step 1. Write thee number sentence. ÷ 4 = ___
Step 2. Rename the whole number in fraction form ÷ = ___
Step 3. Get the reciprocal of the divisor then proceed to
Multiplication of fractions. ÷ =

Step 4. Write the product of the numerators over the product
of the denominators; and reduce the fractions if needed
Get Moving!
Read and analyze each question then solve.
1. What is the quotient of and ?
2. If you divide by times, what is the answer?
3. What is the quotient of divided by ?
4. ÷ =
5. ÷ = n
Find the quotient. Show your solution.
1) 6  = n
2) 16  = n
3) 14  = n
4) 8 = n
5) 30 = n
Keep Moving!
Find each quotient.
1. ÷ = n 2. ÷ = n 3. ÷ = n 4. ÷ = n 5. ÷ = n
Find the quotient.
1. 10 = n 2. 15 = n 3. 45 = n 4. 36 = n 5. 28 =
Apply your Skills!
1. Find the number of eights ( ) in
2. AlingNarda repacked kg of pepper into kg bags . How many bags of pepper can she
make?
6
5
4
3
7
2
8
1
4
3

3. There are 4 kilograms of rice. Each girl scout can consume kg of rice per meal. For
how many girl scouts is the rice enough for a meal?
5
1

Lesson 27 : Solving Routine or Non-Routine Problems Involving Division Without or With
Any of the Other Operations of Fractions and Whole Numbers Using
Appropriate Problem Solving Strategies and Tools.
Read the problems below.
Can you solve the problem?
Here are the steps in analyzing and solving the problems.
Problem 1
A 4-meter piece of wood is to be
divided into pieces, each 2/3 m long.
How many pieces can be cut from it?
Nicole has 42 meters of ribbon. She
uses meters for every box she
makes. How many boxes can she
make from the ribbon?
 Understand
Know what is asked: Number of pieces that can be cut
Know the given facts: 4 meter piece of wood
m each long
 Plan
Determine the operation to be used: Division
Write the number sentence: 4 = n
 Solve
Show your solution:
4 = n x = or 6
Review and check your answer
Answer: There were 6 pieces of wood
 Check and look back
Did I do the operations correctly?
Is my answer reasonable?

Problem 2
Can you try solving the following problems?
1. If a skirt requires 1 ¼ meters of cloth, how many skirts can be made from 21
meters of cloth?
2. Linda made a trip of 112 kilometers in 2 ½ hours. What was her average
speed?
Get Moving!
1. A log 5 ¾ meters long will be cut into 6 equal pieces. How long will each piece
be?
 Understand: _____________________________________________
 Plan:___________________________________________________
 Solve: __________________________________________________
 Look back: ______________________________________________
2. Andrea has 35 meters of cloth. How many aprons can she make if each
apron requires meters?
 Understand: _____________________________________________
 Plan:___________________________________________________
 Solve: __________________________________________________
 Look back: ______________________________________________
 Understand
Know what is asked: The number of boxes that can be make from the ribbon
Know the given facts: 42 meters of ribbon
meters for each box
 Plan
Write the number sentence: 42 = n
Solve
Show your solution:
42 = n = = = 18
Using cancellation
= x = or 18
Review and recheck your answer:
Answer: Nicole can make 18 boxes from the ribbon.
Review and check your answer
Answer: There were 6 pieces of wood

3. Calix needs to divide cups of flour among 3 recipes. How many cups
of flour does each recipe need?
 Understand: _____________________________________________
 Plan:___________________________________________________
 Solve: __________________________________________________
 Look back: ______________________________________________
4. The class of Lora is repacking goods for the outreach. How many kg
packs of sugar can they make out of a bag that contains 15 kg of sugar?
 Understand: _____________________________________________
 Plan:___________________________________________________
 Solve: __________________________________________________
 Look back: ______________________________________________
5. Nikki has 8 meters of fabric to make shirts. If each shirt requires m of
fabric, how many shorts can she make?
 Understand: _____________________________________________
 Plan: ___________________________________________________
 Solve: __________________________________________________
 Look back: ______________________________________________
Keep Moving!
Solve the following problems. Write your solutions and answers in your notebook.
1. Jeff has meters of rope. He wants to make 3 pieces of clothes hanger
out of it. How long will each clothes hanger be?
2. A farmer bought kilograms of fertilizer for his rice, camote, and potato
crops. If the fertilizer will be used equally on the three crops, how much
will be used for each crop?
3. Mr. Reyes has a coconut plantation that measures hectares. If the
entire plantation is to be subdivided among 36 tenants, how much would
be each tenant’s share ?
4. Donald was able to harvest 2 ¼ kg of tomatoes from each of 4 plots.
Then he divided them equally into 6 piles. How many kilograms of
tomatoes did each pile have?
5. Lucy equally poured 4/5 liter of lemonade into 6 cups. How much
lemonade did each cup have?
Apply Your Skills!
Try solving more problems!
Read and analyze the following problems. Solve them in any method you like
1. Mrs. Gibe has to pack 50 kg of rice. How many plastic bags are needed if
each bag can contain kg of rice?
2. Merllie makes hand towels for sale. How many hand towels can she make
from 6 meters of cloth if meter is used for 1 hand towel?
3. How many meter of cloth can be cut from 40 meters of ribbon?

4. On their trip to Laguna, Mr. Santos’ family bought 4 baskets of lanzones.
Each basket contained kg of lanzones. The family shared the 4 baskets of
lanzones among 8 persons. How many kilograms of lanzones did each one
receive?
5. How many m pieces of ribbon can be cut from a 50 m of ribbon?

Lesson 28 : Creating Problems (with reasonable answers) Involving Division or With Any
of Other Operations of Fractions and Whole Numbers
How do you create a word problem involving division or with any of other operations of
fractions and whole number?
 Familiarized yourselves with the concepts division with other operation of
fractions and whole number and their application to real-life situations.
 Think of the problem you want to write.
You also consider the following when creating a problem:
a. Characters
b. Situation/Setting
c. Data
d. Key Question
Look at the given data below.
 60 kilograms of rice
 kg of rice in each plastic bag
 Number of plastic bags needed for repacking
Can you now complete the word problem below and solve for the correct answer, too?
Do this in your notebook.
Mrs. Ana has to pack _____________. How many plastic bags are needed if each bag
can contain______________?
Get Moving!
Create a word problem from the given data below.
Solve the problem in your notebook.
1. 12 kilograms of flour
¾ kilograms in each plastic bag
Number of plastic bags used
Problem:______________________________________________________________
Solution and Answer:____________________________________________________
2. 30 meters long of wood
1 ½ meters long for each piece
The pieces of woods that can be cut
Problem:______________________________________________________________

3. meters long of electric wire
6 equal pieces
The length of each wire
Problem:______________________________________________________________
4. of a pie
4 persons
The part of the pie each one gets
Problem:______________________________________________________________
5. 5 meters of cloth
2/3 meters for each scarf
The number of scarves that can be make
Problem:______________________________________________________________
Keep Moving!
Complete each problem by creating a question for what is asked. Then, solve the problem.
1. Ella has 15 kilograms of rice for sale. She placed these in plastic bags. Each bag
contains kilograms.
Question:________________________________________________________
Solution and Answer: ______________________________________________
2. A log meters long will be cut into 7 equal pieces.
Question:________________________________________________________
3. Nene has cake. She divided it among her 6 friends.
Question:________________________________________________________
4. Michelle needs to divide cups of flour among 3 recipes.
Question:________________________________________________________
5. A tailor has a bolt of cloth 20 meters long. Each uniform needs meters of cloth.
Question:________________________________________________________

Apply You Skills!
Create a problem using the given data. Then, solve the problem.
1. Given: 50 kilograms of cholcolate
kilograms packed in each box
Asked: Number of boxes used
Problem: _____________________________________________________
Solution and Answer: ___________________________________________
2. Given: 12 meters of fabric
meters for each shirt
Asked: Number of shirts that can make
Problem: _____________________________________________________
3. Given: 15 meters of cloth
meters for each cloth
Asked: Number of blouses that can make
Problem: _____________________________________________________
4. Given: 24 kilograms of rice
kilograms in each bag
Asked: Number of bags used
Problem: _____________________________________________________
5. Given: 8 meters piece of wood
meters long for each piece of wood
Asked: Pieces of woods that can be cut
Problem: _____________________________________________________

Lesson 29: Giving the Place Value and the Value of a Digit of a Given Decimal Number
through Ten Thousandths
Study the chart below.
PlaceValue
Tens
Ones
Decimal
point
Tenths
Hundredths
Thousandths
Ten
thousandths
Digits 0  5 9 8 7
Value 0  .5 .09 .008 .0007
In 0.5987 the digit 0 is a place holder of ones place. The digit 5 is in tenths place. Its
value is .5. The digit 9 is in the hundredths place. Its value is 0.09. The digit 8 is in the
thousandths place. Its value is 0.008 and digit 7 is in the ten thousandths place, its value is
.0007. Hence, 0.5987 means five thousand nine hundred eighty-seven ten thousandths.
Here are other examples:
1.3984
Digit Place Value Value
1 Ones 1
3 tenths 0.3
9 hundredths 0.09
8 Thousandths 0.008
4 Ten thousandths 0.0004

Get Moving!
Write each in symbols, then give the value and place value of the underlined digit.
Symbol Value Place Value
1. Five and three hundred ten thousandths
2. Twenty-five and two hundred ten
thousands
3. Fifteen hundredths
4. One hundred one and one tenths
5. Five hundred and three ten thousandths
6. Ten and ten hundredths
7. Ninety-nine ten thousandths
8. One and fifteen ten thousandths
9. Fifty-nine and four hundred ninety-eight
ten thousandths
10. Eight ten thousandths

Keep Moving!
A. Give the place value of the underlined digit.
1. 6.28 6. 4.3763
2. 0.0028 7. 0.7659
3. 0.827 8. 2.7854
4. 21.843 9. 3.9681
5. 9.375 10. 19.0365
B. Write the place value of the digit 8 in each number.
1. 29.378 6. 86. 047
2. 908.176 7. 45.801
3. 471.081 8. 567.3278
4. 57.8012 9. 67.8703
5. 870.2194 10. 0.2358
C. In 50 678.39241, identify the digit in the ….
a. Hundreds place _________
b. Thousandths place _______
c. Tenths place ________
d. Ten thousands place ______
e. Hundredths place _________

Apply Your Skills!
Read and answer the questions that follows:
1. Men’s gymnastics is divided into compulsory and optional events. In 1984, the United
States team members won the gold medal. Their score in the optional events was
296.0391. in the compulsory events they scored 259.3127.
a. Read 296.0391 259.3127
b. Identify the place value of each decimal numbers.
2. Copy all decimals that have 2 in ten thousandths place. Give the place value and
value of the digit before the digit in the ten thousandths place.
a. 6.28 d. 8.2902
b. 0.0028 e. 9.0092
c. 4.4689
3. Copy the decimals that have 5 in the ten thousandths place. Give the value and place
value of the digit after the decimal point.
a. 5.5543 d. 5555
b. 19.5555 e. 3.4835
c. 6.4625

Lesson 30: Reading and Writing Decimal Numbers through Ten Thousandths
What are the numbers in the situation? 45.8 and 43.75
What kind of number is that? Decimals
How do you read and write decimal numbers?
The decimal 45.8 is read as forty-five and eight tenths
The decimal 43.75 is read as forty-three and seventy-five hundredths
Decimals are just another way of writing fractions whose denominators are powers of ten
and the proper way to read them is the same as reading the corresponding fractions which they
are represent.
Here are other examples:
Decimal Fraction Read as:
0.6
10
6
Six tenths
0.12
100
12
Twelve hundredths
0.2568
10000
2568 Two thousand five hundred
sixty-eight ten thousandths
In the examples “zero” and the decimal point are not read nor write in words anymore.
Carl and his brother take good care of their bodies. They eat the
right kinds of foods to maintain their proper weights at their age. Carl
weighs 45.8 kilograms while his brother weighs 43.75 kilograms.

Get Moving!
A. Read each decimal number correctly.
1. 0.059 4. 0.0007
2. 20.7034 5. 7. 8254
3. 46. 340
B. Write a decimal number for each.
1. two hundred forty-six ten thousandths ______________
2. six and forty-eight thousandths ______________
3. twenty-six and eight tenths ______________
4. two hundred and forty-seven thousandths ______________
5. Seven hundred twelve and eleven ten thousandths ______________
6. thirty-one ten thousandths ______________
7. nine and nine tenths ______________
8. six hundredths ______________
9. three hundred seventy and four tenths ______________
10. ten and two thousand fifty-one ten thousandths ______________
Keep Moving!
A. Write in words.
1. 3.06 _________________________________________________________
2. 0.8009 _________________________________________________________
3. 0.014 _________________________________________________________
4. 15.300 _________________________________________________________
5. 18.009 _________________________________________________________
B. Write down as decimals.
1.
10
8
6.
10000
164

2.
1000
4
7.
10000
237
3.
100
45
8.
1000
258
4.
1000
17
9.
10000
10
5.
10000
69
10.
100
12
Apply Your Skills!
Read and answer the following:
1. The distance between the town church and the market is one and eighty-nine
thousandths kilometres. Write the distance as a decimal number.
2. How many decimal places does “one and three hundred sixteen ten-
thousandths”
have?
3. How many decimal places does thirty-three thousandths have?
4. I am a decimal number. My thousandths digit is three more than my tenths
digit.
My ones digit is 3 and so my tenths digits. All the other digits are 0 and I
have
four decimal places. What number I am?
5. How many hundredths are equal to 1.3?

Lesson 31. Rounding Decimal Numbers to the Nearest Hundredths and Thousandths
James climb a 483 meter hill. If there are 1000 meters in 1 kilometer,
what part of the hill and did Luis climb? Round to the nearest hundredths.
To know the part of the hill Luis climb.
1. Change meter to kilometre. (1000 m=1 km)
1000
483
= .483
Rounding off number using number line
.480 .481 .482 .483 .484 .485 .486 .487 .488 .489 .490
From the diagram, it is easy to see that .483 is nearer to .480 than .490. So .483 is rounded to
.480.
Now, let us try to round .483 to the nearest hundredths.
Study the illustration below.
.483
Rounding place
The digit to the right is smaller
than 5, so it rounds down.
.483 rounded to the nearest
thousandths is .480
 To round decimals
1. Identify the digit to be rounded-off.
2. Inspect the digit to the right of the required place.
a. If the digit is greater than 5, add 1 to the digit at the required place.
b. If the digit is less than 5, retain the digit at the required place. Then drop all
the digits to the right of the required place.
c. Copy all the digits to the left of the required place if there are any.

Get Moving!
A Round to the nearest hundredths.
1. 48.019 _____________________ 6. 0.925 ___________________
2. 16.975 ______________________ 7. 4.018 ___________________
3. 15.614 ______________________ 8. 12.3057 ___________________
4. 12.089 ______________________ 9. 8.1749 ____________________
5. 4.613 ______________________ 10. 1.001 ____________________
B. Round to the nearest thousandths.
1. 8.0079 ______________________ 6. 8.3056 ____________________
2. 1.4067 ______________________ 7. 1.6149 ____________________
3. 2.5974 ______________________ 8. 12.0192 ____________________
4. 0.1549 ______________________ 9. 3.8315 ____________________
5. 2.5973 ______________________ 10. 2.5615 _____________________
Keep Moving!
A. Complete the table.
Decimal Round to nearest hundredths Round to the nearest
thousandths
1. 2. 3842
2. 0.56893
3. 2.96425
4. 5.2358
5. 0.86302

B. Write the letter of the number that rounds off to the given number.
1. 3.65 a. 3.624 b. 3.580 c. 3.672 d. 3.647
2. 15.27 a. 15.225 b. 15.278 c. 15.278 d. 15. 273
3. 10.85 a. 10.859 b. 10.857 c. 10.851 d. 10.856
4. 32.548 a. 32.5476 b. 32.5488 c. 23.534 d.32.6437
5. 211.78 a. 211.789 b.211.784 c. 211.786 d. 211.7865
C. Get the quotient up to the nearest thousandths plce. Then round the decimal to the nearest
thousandths. Number 1 is done for you.
1. 36 ÷7 = 5.1425.14 4. 73÷ 8 = ______ ________
2. 47 ÷ 8 = ____ ____ 5. 78 ÷ 9 = ______ ________
3. 71 ÷ 8 = ____ _____ 6. 34 ÷ 9 = ______ ________
Apply Your Skills!
Answer the following:
1. a. What are the smallest and largest decimals in hundredths that rounds to 0.5?
b. What is the largest decimal in hundreths round to 0.5?
2. One centimeter is equivalent to about 0.3937 inch. Round off the given equivqlent to the
nearest hunderdths.
3. Mrs. Edlagan has a total deposit of 50 766.25. The annual interest at 3% simple interest
is 1 522.9875. Round off interest to the nearest hundredths and thousandths.
4. The decimal rounds to 3.2. The digit in the thousandths place is 4 times that in the
hundredths place. The sum of the digits is 15. What decimal is it?

Lesson 32: Comparing and Arranging Decimal Numbers
How do you compare decimal numbers?
There are three ways to compare decimal numbers. The first one is by using a number
line for small scale or difference between numbers and place value chart for numbers that
cannot be represented in a number line. The third way is by adding zero to make the digits of
decimal numbers the evenly.
Study the example below.
Start at the left side.
The number line starts with 12.326. It is the smallest value in the set which is located at
the leftmost part of the number line.
The number line ends with 12.346. It is the greatest value in the set which is located at
the rightmost part of the number line.
In the number line we can clearly locate that 12.329 is at the left side while 12.341 is
located at the right side.
So, 12.341 is greater than 12.329. We can write it in symbol as 12.341 > 12.329.
Let’s try another example using different strategy. We can add 0 to make the number of
digits equally. Which is greater 0.2 or 0.198? Let’s compare it using the table below.
Original Number
0 2
0 1 9 8
New Number Formed
by Adding 0
0 2 0 0
0 1 9 8
Which is less 12.341
or 12.329?
12.326 12.327 12.328 12.329 12.330 12.331 12.332 12.333 12.334 12.335 12.336 12.337 12.338 12.339 12.340 12.341 12.342 12.343 12.344 12.345 12.346

Which is greater,
12.789 or 12.765?
Now, let’s take another look. The given decimals have the same number of digits. Which
is greater 0.200 or 0.198? In this example, 0.200 is greater than 0.198. In symbol, we can write
this as 0.200 > 0.198.
Study another set of example using the place value chart.
A. Compare the following. Write >, <, or = in to make the sentence true.
1. 1.396 0.95 9. 2.35 2.53
2. 0.29 0.3 10. 0.1 0.99
3. 6.5 6.500 11. 4.07 4.017
4. 7.4 7.049 12. 10.07 10.067
5. 27.5 27.492 13. 1.0 1.01
6. 2.098 2.904 14. 2 2.00
7. 0.30 0.300 15. 3.607 3.670
8. 8.10 8.1
B. Order the following decimals from least to greatest.
1. 3.21, 3.021, 3.12, 3.121
2. 1.3, 1.309, 1.03, 1.39
3. 0.09, 0.012, 0.0089, 0.0189
4. 4.01, 4.0011, 4.011, 4.101
PlaceValue
Tens
Ones
Decimal
Point
Tenths
Hundredths
Thousandths
Value 10 1 
Digits 1 2  7 8 9
Digits 1 2  7 6 5
Get Moving!

5. 5.5, 5.059, 5.0090, 5.05
6. 1.7, 0.9, 1.07, 1.9, 0.7
7. 2.0342, 2.3042, 2.3104, 2.4
8. 5, 5.012, 5.1, 0.502
9. 0.6, 0.6065, 0.6059, 0.6061
10. 12.9, 12.09, 12.9100, 12.9150
A. Write <, >, or = on the blank to make the sentence true.
1. 0.1114 ____ 0.2202 9. 0.0120 _____ 0.012
2. 0.1090 ____ 0.1009 10. 16.8930 _____ 16.893
3. 0.999 ____ 0.1000 11. 0.7985 _____ 0.7895
4. 4.8934 ____ 4.8943 12. 12.1 _____ 12.0100
5. 0.6390 ____ 0.639 13. 40.04 _____ 40.041
6. 0.55 _____ 0.055 14. 8.627 _____ 8.649
7. 0.7894 _____ 0.7658 15. 0.213 _____ 0.0213
8. 0.3937 _____ 0.3198
B. Order numbers from greatest to least.
1. 3.756 37.56 375.6 0.3756
2. 0.2468 0.2486 0.2648 0.2846
3. 11.010 11.011 11.0110 1.1101
4. 2313.2 23.132 2.3132 231.32
5. 555.555 55.5555 5.5555 5555.55
6. 0.481 0.38 0.256 0.7349
7. 2.461 2.3392 2.6789 2.7666
8. 0.93 6.87 5.241 6.786
9. 62.1254 26.2351 262.351 26.5321
10. 905.928 95.7654 5.8642 5.6248
Keep Moving!

A. Read and solve the following.
1. Jeremiah and Catherine are both honor pupils in their school. For the first quarter,
Jeremiah’s average is 93.1 while Catherine’s average is 93.095. Who topped the
first quarter?
2. Team Narra and Team Mahogany undergo a water challenge. Their task is to transfer the
water in a cup from the first player to the tenth player without spilling within the allotted
time. After the task, the team captain measure the water collected using a measuring cup.
Team Narra collected 1. 402 liters while Team Mahogany collected 1. 045 liter of water,
which team got more water?
3. Robert was asked to arrange the following numbers from least to greatest. Which number
comes last?
4. In a bazaar, different items are sale for big discounts. Irene is looking for a school bag. She
visited three stalls to buy one for his younger brother. The stall offered the school bag of the
same quality but differs in price. The first stall offered if for P 749. 25, the second stall sold it
for P 792.45 and third stall gave it P 724. 95. If she wanted to save, from which stall will she
buy school bag?
5. Aling Mila bought 0.82 m of red fabric, 0.79 m of yellow fabric, 0.805 m of blue fabric and
0.782 m of white fabric. Which ribbon is the longest? the shortest? Arrange the lengths of
the fabric form longest to shortest?
Apply Your Skills
2.099 2.9 2.99 2.109 2.5

Lesson 33: Visualizing Addition and Subtraction of Decimals
Gab and Sassa goes to school together by walking. The school is 2 km from their house. For first five
minutes Sassa and Gab has walked and reached 0.28 kilometer, after the next 8 minutes they recorded 0. 59
km. How far are they from school?
How can we solve the problem?
First identify the given. We have the following.
2 km – distance of school from Gab and Sassa’s house
0.28 km – the distance they have walked and reached for the first 5 minutes
0. 59 km – the distance covered by them for the next 8 minutes
What is asked in the problem?
The problem is looking for the distance from the school that they need to cover after driving for 13
minutes. So, let’s add the distance they have walked for 5 minutes and the distance covered by them for the
next 8 minutes.
Use the model below. Each square represents 0.001.
A. Add or subtract the following. Use drawing or illustration if possible.
0.028 0.087
0.059
+ =
Get Moving!

1. 0.27 + 0.61 6. 0.8 – 0.3
2. 0.13 + 0.22 + 0.45 7. 0.57 – 0.4
3. 0.261 + 0.003 8. 0.095 – 0.002
4. 0.005 + 0.024+ 0.314 9. 0.631 – 0.385
5. 0.421 + 0.06 + 0.104 10. 0.457 – 0.104
B. Find the sum or difference.
1. 0.549 – 0.014 6. 0.31 + 0.42+ 0.16
2. 0.653 – 0.128 7. 0.473 – 0. 251
3. 0.56 + 0.23 + 0.2 8. 0.927 – 0.302
4. 0. 783 – 0.53 9. 0.07 + 0.009 + 0.4
5. 0.205 + 0.612 10. 0.365 + 0.13 + 0.283
C. Find the sum or difference.
1. 0.684 2. 0.83 3. 0.73 4. 0.9002
+ 0.295 + 0.567 + 0.3073 + 0.8634
5. 0.84 6. 0.84 7. 0.540 8. 0.3
+ 0.8056 - 0.6358 - 0.2365 - 0.076
9. 0.6 10. 0.9702
- 0.1858 - 0.1694
A. Add or subtract the following.
1. 2.198 – 1.439 6. 2.67 + 8.94 + 6.43
2. 38.026 – 49.183 7. 12.652 – 9.758
3. 5.072 – 3.861 8. 45.006 – 39. 248
4. 45.349 – 29. 465 9. 6.89 + 23. 574 + 16.045
5. 18.860 + 34. 257 10. 7.14 + 8.432 + 9.77
B. Find the sum or difference of the following.
1. 37.813 – 27.654 6. 9.87 + 10.163 + 19.054
2. 12.095 + 9.389 7. 98.764 – 87.365
3. 43.702 + 18. 419 8. 63.007 – 48.642
4. 16.206 – 13.076 9. 9.71 + 52.075
5. 89.652 + 17. 378 10. 84.349 – 49.182
C. Add or subtract.
1. 0.38 + 0.47 = n 6. 0.23 – 0.16 = n
Keep Moving!

2. 0.412 + 0.638 = n 7. 0.97 – 0.178 = n
3. 0.529 + 0.646 = n 8. 0.232 – 0.046 = n
4. 0.412 + 0.473 = n 9. 0.76 – 0.057 = n
5. 0.284 + 0.325 = n 10. 0. 200 – 0.099 =
A. Read, analyze and solve the following.
1. During a vacation, Ben’s records showed gasoline purchases of 19.75 gallons, 15.4
gallons, 13.85 gallons and 21.06 gallons. How many gallons of gasoline did he buy?
2. The perimeter of a triangle is equal to the sum of the length of its sides. Find the
perimeter of a triangle whose sides are 8.75 cm, 9.6 cm and 10.375 cm.
3. Rachel has P 3 316.40 in her savings account. If she made withdrawals of P 285.00,
P 472.46 and P 1 042.25, how much money is left in her account?
4. One week a jogger ran the following distances : 15.3 km , 18.75 km , 19 km , 21.5 km,
25.375 km and 30.25 km. If his weekly average is 150 km, did he run less or more?
5. Romeo has P 20 000 in available credit on his Visa charge card. If she purchases a
portable CD player for P 8 139.55, a boom box for P 399.95 and two way speakers
for P 3 425.05, how much available credit does she have left ?
Apply Your Skills!

Lesson 34: Adding and Subtracting Decimal Numbers through Thousandths
Without and With Regrouping
Mr.Acapulco acquired a lot in a remote area in
Batangas to be planted by different kinds of fruit bearing trees. He
already acquired 105.652 square meters in Barangay Masikap and
91.246 square meters of lands in Brgy. Matamis. If Mr.
Acapulco needs 398.166 square meters, what part of land area
does he need to acquire?
Step 1:
How do we solve the problem? To solve the problem, we must
need to add the first two given data, 105.692 square meters of land in
Barangay Masikap and 91.246 square meters of land in
Barangay Matamis. The number sentence is 105.652 sq. m + 98.276
sq. m = N.
Without Regrouping
Step 2: After
getting the sum.
We must now
answer the
question raised in
the problem.
To know the part of land Mr. Acapulco still needs to acquire. We may now subtract the sum that we get to the
land area intended to plant with different fruit bearing trees. Here’s the number sentence to use: 398.166 sq. m
– 196.898 sq. m = N.
With Regrouping
Hundreds Tens Ones Decimal
Points
Tenths Hundredths Thousandths
9 1  2 4 6
1 0 5  6 5 2
1 9 6  8 9 8
Hundreds Tens Ones Decimal
Points
Tenths Hundredths Thousandths
2 18 7 10 15 16
3 9 8  1 6 6
1 9 6  8 9 8
1 9 5  2 6 8
+ Sum
Difference-
Get Mo

A. Find the sum of the following.
1. 3.76 2. 23. 347 3. 37.786
+ 4.356 + 8.92 + 2. 632
4. 4. 762 5. 5. 703 6. 87.652
+ 1.69 + 17.74 + 51.764
7. 0.9154 8. 92.65 7 9. 15.421
+ 0.2515 + 24.57 3 + 37.88
10. 0.3276
+ 0.1178
B. Find the difference.
A. Solve for the sum or difference.
1. 75.267 2. 59.246 3. 43.823 4. 86. 576
- 63.122 - 28.132 - 21.51 + 53.123
5. 98.364 6. 21. 924 7. 85.376 8. 58.148
- 72. 225 - 17. 379 - 49. 528 + 67.251
1. 93. 152
- 29. 184
2. 61.41
- 37.532
3. 57.31
- 46. 653
4. 154. 76
- 85.493
5. 380.205
- 278.398
Keep Moving!

9. 70.542 10. 59. 647
- 53.891 - 27.958
A. Read, analyze and solve.
1. Alex traveled 41.3 kilometers on Monday and 53.75 kilometers on Tuesday. How many
kilometers did he travel in two days?
2. In a midnight sale, a radio cassette player was sold at P 1 449.95. If it’s regular price was
P 1 950.50, how much less was the sale price?
3. Anna bought a bunch of flowers for P 125.50. If she gave a P 100 bill and P 50 bill, how
much was her change?
4. The rainfall on four consecutive days during a typhoon was 10.31 cm, 12.72 cm, 18.39 cm
and 9.84 cm. Find the total rainfall during the typhoon.
5. Mother bought 2.35 kg of pork, 3.75 kg of chicken, 1.1 kg of beef, and 1 kg of liver. How
many kilograms of meat did Mother buy in all?
Apply Your Skills!

Lesson 35: Estimating the Sum or Difference of Decimal Numbers with Reasonable Results
A.
Nancy wants to buy a blouse for Php.118.50, a t-shirt for Php.99.75 and a pair of shoes for Php.215.50.
If she has Php.500-bill, does she have enough money to pay for them?
To answer the question, we need to estimate. We can use the rounding method.
Php.118.50Php.120
Php.99.75 Php.100
Php.215.50Php.220
Php.440
Yes, Nancy has enough money to buy the three items.
B.
A salesman drove 17.65 km to one town and 15.86 km to a second town. How much farther is the first
town than the second town?
17.6518 km
15.8616 km
2 km
The first town is less than 2 km farther than the second town.
Get Moving!
A. Using the rounding off technique, find the estimated sum of the given decimals.
1. 23.45 + 8.63 + 2.75
2. 8.05 + 7.93 + 1.62
3. 112.56 + 23.63 + 12.45
4. 0.91 + 0.86 + 8.75
5. 2.843 + 15.624 + 13.56

B. Using the rounding off technique, find the rough estimated difference of the given decimals.
1. 634.58 – 436.79
2. 37.86 – 19.92
3. 14.39 – 8.59
4. 7.45 – 2.93
5. 15.63 – 8.79
Keep Moving!
A. Round to the greatest place value and estimate each sum.
1. 2347.081 + 5834.501
2. 9452.8 + 4671.2
3. 23.5 + 15.03 + 9.54
4. 7.45 + 8.83 + 6.55
5. 12.4 + 14.8 + 21.53
B. Round to the greatest place value and estimate each difference.
1. 678.23 – 451.2
2. 818.9 – 489.06
3. 951.4 – 568.19
4. 7512.2 – 3725.9
5. 9301.67 – 4878.8
Apply Your Skills!
Estimate the answer to each problem.
1. Gloria bought a t-shirt for Php.95.75 and a book for Php.175.60. how much more did the book cost
than the t-shirt?
2. A salesman traveled 78.45 km in the morning and 25.24 km in the afternoon. Did he cover at least
100 km?
3. A household consumes 222.5 liters of water a day. One faucet leaks 12.25 liters of water a day.
Estimate how many liters of water a day a household consumes when the faucet is fixed?
4. The Math Club raised Php 1 225.00 during their fund raising campaign. The club will be buying 3
items worth Php495.00, Php347.50 and Php862.90. How much more money does the club need to
buy the items?
5. A rectangular garden measures 22.7 meters by 16.6 meters. Estimate how many meters of fencing
material are needed to enclose it.

Lesson 36- Solving Routine or Non-routine Problems Involving Addition and Subtraction of
Decimal Numbers Including Money Using Appropriate Problem Solving Strategies
and Tools
Problem 1 Problem 2
Which of the two problems is easier to solve? Why?
Get Moving
1. The perimeter of a quadrilateral is 412.95 cm. If the three known sides measures
85.56cm, 112.77 cm, and 85.26 cm, how long is the fourth side?
2. I bought 4 items worth P39.90, P68.60, P 58.75 and P120.25. How much change will I
get from P 500-bill?
3. A rectangle is 13.8cm. long and and 9.7 cm wide. Find its perimeter.
4. Obed and Dario hiked 15.1 km. In one day and 13.75 km in the next day. How many
kilometres did they hiked in all?
Mang Isko has 18.48 pesos . If she has
to devide it into her 6 children, How
much will each one receive?
Marlene opened her math book and
found that the sum of the pages
facing her was 243. What pages did
she open to?
Understand
Know what is asked? The amount of money
each child receive?
Know the given facts: 18.48 pesos, 6 children
Plan
Write the number sentence: 18.48÷6=n
Solve
Show your solution: 18.48÷6=3.08
Check and look back
Review and re check your answer: you can
use calculator to divide 18.46 by 6 or multiply
3.08 by 6
Understand
Know what is asked: The pages of the book
Know the given facts: The sum of two pages was 243
Plan
Determine the operation to be used: Addition
Write the number sentence: n+(n+1)= 243
Solve
Show your solution: Trial and error method
If n=121, then 121+(121+1)= 243
121+122 =243
243 = 243
Review and check your answer: you cannot have a page
that is 121 r. 1

5. Mr. De Guzman and the boys spent P 567.75 for food and P 175.50 for transportation
during the Science Fair Camp. If they had P 800.00 to spend, how much money was
left?
Keep Moving
Analyze and sole the ff. Problems.
1) The diameter of the earth is 12 763.29 kilometers. If Mercury’s diameter is about
7 913.04 kilometers shorter than that of the earth, what is the diameter of Mercury?
2) Luz wants to buy a bag that costs 375.95. If she has saved 148.50 for it, how much
more does she need?
3) Martha bought 2.5 m of yellow ribbon, 3.4 m of red, 8.75 m of white, and 3.70 m of blue.
How many metres of ribbon did she buy altogether?
Apply Your Skills
Write the number sentence and solve.
1. Delia filled the container with 3.5 litres of water. Her mother used 0.75 litres of water for cooking
and 1.25 litres for palamig. How much water was left in the container?
2. Mang Caloy cut four pieces of bamboo. The first piece was 0.75 metre; the second was 2.278
metres, the third was 6.11 metres, and the fourth was 6.72 metres. How much longer were the
third and fourth pieces put together than the first and second pieces put together?

Lesson 37- Creating Problems (with reasonable answers)Involving Addition and Subtraction of
Decimal Numbers Including Money
Second Grading Period, Week 3
How do you create a word problem involving addition and subtraction of decimals including
money?
a. Familiarize yourself with the concept and their application to real life situation.
b. Think of the problem you want to create.
c. Read some problems and study their solutions
You also consider the following when creating a problem.
1. Characters
2. Situation/Setting
3. Data
4. Key Questions
Study the table below
Name Things bought Price
Shane T-shirt 250.75 kg.
Lito Shoes 1,999.99 kg.
Study the problem as an example for the data given.
Get Moving
Use the data below to create a two-step word problem involving addition and subtraction of
decimals.
Name Items bought Price
Carlo 10 note books P80.65
Lolit Bag P617.35
Jane Shoes P1,250.08
Shane and Lito went to the Department Store. Shane bought a T-shirt cost P 250.75. Lito bought a
shoes cost 1,999.99kg. How much more does Lito spend than Shane?

Keep Moving
Use the data below to create a two-step word problem involving addition and subtraction of
decimals.
Name Foods Ordered Price
Amie Spaghetti P50.75
Zet Palabok P48.25
Precy Regular Yum P30.75
Apply Your Skills
Use the data below to create a problem for each of the ff.
1. One- step word problem involving addition of fraction
2. One -step word problem involving subtraction of fraction
3. Two- step word problem involving addition and subtraction of fraction
Name Amount Deposited in the Bank
Allan P 2,978.88
Amiel P 4, 656.75
Raquel P 7, 665.50

Lesson 10: Visualizing Multiplication of Decimal Numbers Using Pictorial Models
Sophia’s rides the bus to and from school each day. A one-way trip is 8.12 kilometers.
How many kilometers does he travels in 5 days?
Can you visualize how far Sophia travels?
One way of visualizing how far Sophia travels is through number line.
Get Moving!
Show the following multiplication equations by using number lines.
1.) 0.3 x 0.6 =
2.) 0.5 x 0.8 =
3.) 0.7 x 0.4 =
4.) 0.2 x 0.9 =
5.) 0.8 x 0.3 =

Keep Moving!
Directions: Illustrate the given equation in a grid.
1. 0.7 x 0.6 = n 4. 0.2 x 0.3 = n
2. 0.4 x 0.8 = n 5. 0.3 x 0.5 = n
3. 0.6 x 0.6 = n
Use number lines to find the answer.
1.) Nichole needs 0.95 m of ribbon to trim a shirt. If the ribbon costs ₱ 0.75 per meter. How
much did she has to pay?
2.) JR can swim 12 meters in one minute. How far can he swim in 30 minutes?
Apply Your Skills!
Read and solve the following. Use your own pictorial model to answer the following.
1.) Looking after my baby cousins after classes, my Aunt Abing gives me ₱ 45.00 a day.
How can I save a week if I spend ₱ 100.00 for my snacks in school?
2.) Realyn bought 2.5 kg of meat at ₱ 100.00 per kg. she gave the seller a ₱ 500.00 bill.
How much change did she get?
3.) Each potted plant in a nursery costs ₱ 25.50. How much will be left on of my ₱ 400.00 if
I buy 10 potted plants.

Lesson 11: Multiplying decimals up to 2 decimal places by 1 to 2 digit whole numbers.
Look at this square.
What is its perimeter?
3.5 cm
How can you find the perimeter?
How many sides has a square?
What can you say about its side?
Because there are 4 equal sides and each measures 3.5 cm, we can compute this as 4 x 3.5 =
N. Here’s how this is done.
 Multiply as with whole numbers. Regroup if necessary.
3.5
X 4
140
 Count the number of decimal places in the factors.
3.5
X 4
140
 Place the decimal point in the product. The decimal place in the product is equal to the
total number of decimal places in the factors.
3.5
X 4
1.40 1 decimal place

K TO 12 GRADE 5 LEARNER’S MATERIAL IN MATHEMATICS (Q1-Q4)

K TO 12 GRADE 5 LEARNER’S MATERIAL IN MATHEMATICS (Q1-Q4)

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K TO 12 GRADE 5 LEARNER’S MATERIAL IN MATHEMATICS (Q1-Q4)