5
Mathematics
Quarter 1 – Module 6:
Multiplication of Fractions
Mathematics
Alternative Delivery Mode
Quarter 1 – Module 6: Multiplication of Fractions
First Edition, 2020
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5
Mathematics
Quarter 1 – Module 6:
Multiplication of Fractions
Introductory Message
For the facilitator:
Welcome to the
Mathematics 5
Multiplication of Fractions!
Alternative Delivery Mode (ADM) Module on
This module was collaboratively designed, developed and reviewed by educators both
from public and private institutions to assist you, the teacher or facilitator in helping
the learners meet the standards set by the K to 12 Curriculum while overcoming
their personal, social, and economic constraints in schooling.
This learning resource hopes to engage the learners into guided and independent
learning activities at their own pace and time. Furthermore, this also aims to help
learners acquire the needed 21st century skills while taking into consideration their
needs and circumstances.
In addition to the material in the main text, you will also see this box in the body of
the module:
Notes to the Teacher
This contains helpful tips or strategies that
will help you in guiding the learners.
As a facilitator you are expected to orient the learners on how to use this module.
You also need to keep track of the learners' progress while allowing them to manage
their own learning. Furthermore, you are expected to encourage and assist the
learners as they do the tasks included in the module.
2
For the learner:
Welcome to the Mathematics 5 Alternative Delivery Mode (ADM) Module on
Multiplication of Fractions!
This module was designed to provide you with fun and meaningful opportunities for
guided and independent learning at your own pace and time. You will be enabled to
process the contents of the learning resource while being an active learner.
This module has the following parts and corresponding icons:
What I Need to Know
This will give you an idea of the skills or
competencies you are expected to learn in the
module.
What I Know
This part includes an activity that aims to
check what you already know about the
lesson to take. If you get all the answers
correct (100%), you may decide to skip this
module.
What’s In
This is a brief drill or review to help you link
the current lesson with the previous one.
What’s New
In this portion, the new lesson will be
introduced to you in various ways; a story, a
song, a poem, a problem opener, an activity
or a situation.
What is It
This section provides a brief discussion of the
lesson. This aims to help you discover and
understand new concepts and skills.
What’s More
This comprises activities for independent
practice to solidify your understanding and
skills of the topic. You may check the answers
to the exercises using the Answer Key at the
end of the module.
What I Have Learned
This
includes
questions
or
blank
sentence/paragraph to be filled in to process
what you learned from the lesson.
What I Can Do
This section provides an activity which will
help you transfer your new knowledge or skill
into real life situations or concerns.
Assessment
This is a task which aims to evaluate your
level of mastery in achieving the learning
competency.
3
Additional Activities
In this portion, another activity will be given
to you to enrich your knowledge or skill of the
lesson learned.
Answer Key
This contains answers to all activities in the
module.
At the end of this module, you will also find:
References
This is a list of all sources used in developing
this module.
The following are some reminders in using this module:
1. Use the module with care. Do not put unnecessary mark/s on any part of the
module. Use a separate sheet of paper in answering the exercises.
2. Don’t forget to answer What I Know before moving on to the other activities
included in the module.
3. Read the instruction carefully before doing each task.
4. Observe honesty and integrity in doing the tasks and checking your answers.
5. Finish the task at hand before proceeding to the next.
6. Return this module to your teacher/facilitator once you are through with it.
If you encounter any difficulty in answering the tasks in this module, do not
hesitate to consult your teacher or facilitator. Always bear in mind that you are
not alone.
We hope that through this material, you will experience meaningful learning and
gain deep understanding of the relevant competencies. You can do it!
4
What I Need to Know
This module was designed and written with you in mind. It is here to help you master
multiplication of fractions. The scope of this module permits it to be used in many
different learning situations. The language used recognizes the diverse vocabulary
level of students. The lessons are arranged to follow the standard sequence of the
course. But the order in which you read them can be changed to correspond with
the textbook you are now using.
The module is divided into three lessons, namely:



Lesson 1 – Visualizing Multiplication of Fractions Using Models
Lesson 2 – Multiplying a Fraction and a Whole Number and Another
Fraction
Lesson 3 – Multiplying Mentally Proper Fractions with Denominators up to
10
After going through this module, you are expected to:
1. visualize multiplication of fractions using models
2. multiply a fraction and a whole number and another fraction
3. multiply mentally proper fractions with denominators up to 10
What I Know
Choose the letter of the best answer. Write the chosen letter on the blank before each
number.
_____1.) Which shows the visualization of the product
A.
x
x
?
B.
C.
D.
x
x
x
x
x
x
x
x
x
5
x
_____2.) Which visualization gives the product of
x
x
x
x
x
A.
x
x
x
B.
______3. )
x 10 = _______
_____4. )
x
A.
x
C.
D.
B.
C.
D. 3
B.
C.
D.
_____5.) What is the product when we multiply
A. 13
_____6.) What is
x
A.
by 16?
B. 14
C. 15
D. 16
B.
C.
D.
?
_____7.) The product of
x
A.
B.
is _____________.
C.
D.
x 10 will give you a product of ___________.
A. 5
_____9.)
x
= ________
A.
_____8.)
?
x
B.
x
A.
C. 15
D. 20
C.
D.
= _______
A.
_____10.)
B. 10
will give you a product of ____________.
B.
C.
6
D.
Lesson
1
Visualizing Multiplication of
Fractions
Hey kids! After learning addition and subtraction of fractions, this week we are going
to learn about multiplication of fractions. In this module, you will learn how to
visualize multiplication of fractions using models or illustrations. So, let’s get it on!
What’s In
Write the fraction for the shaded parts of the whole.
1. ____________________
3._________________
2. ______________________________
4. _________________________
5. __________________
Notes to the Teacher
As teachers, we need to teach fractions by using concrete materials, illustrations and
models for our pupils to visualize how a whole is divided into parts. In this way, they can easily
add, subtract, multiply and divide fractions. Moreover, they can master the lessons on fractions
by providing them various and differentiated activities.
7
What’s New
A face mask nowadays is very important because of the pandemic. So, don’t forget
to wear your face mask if you are with other people and when you go out. In order
to be safe, stay at home and enjoy our lesson!
Let’s read and analyze our story problem.
Rosemel had
meter of white cloth. She used
of it to make her face mask. What fractional part of the
white cloth did she use?
Let’s help Rosemel find out the fractional part of the white cloth she used for
her face mask!
What is It
Analysis of the Problem
1. Understand
What is asked? Fractional part of the white cloth she used for making her
face mask
What are given?
= meter of white cloth
= fractional part of the white cloth she used for making her face mask
2. Plan
Find the fractional part of the white cloth she used for making her face mask.
> We can use illustration or unit.
What operation to use? Multiplication
What is the number sentence?
x
8
=N
3. Solve
a. Visualization
Let’s say that the rectangle below represents 1 meter of cloth and it is divided into
9. The shaded part represents Rosemel’s cloth which is
meter. (Model A)
Model A
Then divide the shaded part into three. (Model B)
Model B
Color 1 of the 3 shaded parts to get
and put X mark.
of
Final Output
X
meter of the white cloth
b. Computation
x
4. Answer:
= Multiply first the numerators.
Multiply the denominators.
meter of cloth was used by Rosemel in making her face mask.
Let’s have more activities for you to visualize multiplication of fractions.
9
1. Get a piece of paper. Fold it horizontally into 2 and color
. Then fold
the paper vertically into 4 and color using the colored part of the first
fraction and put X mark. Open the folded paper for you to see the final
output.
a. Visualization
Model A
X
Model B
Final Output
=
X
b. Computation:
x
X
=
of it to your
2. If the Barangay gave you 6 kilograms of rice and you shared
best friend. What fractional part did you give to your best friend?
a. Visualization
Each box contains 1 kilo of rice.
Model A
1 Kilo
1 Kilo
1 Kilo
1 Kilo
1 Kilo
1 Kilo
1
1
You get ½ kilo from each box for your best friend.
Model B
1
1
2
2
1
1
2
2
2
2
Now, let’s combine all his share in one container for us to see the fractional
part you had given him.
Final Output
2
1
1 Kilo
2
b. Computation
2
1 Kilo
2
3
of 6 = 1 x 6 = 1x 6 = 6 = 3 kilos of rice
2
2x1 2
1
10
2
1
1 Kilo
2
3. If your brother had 9 marbles and he gave you
you get?
of it. How many marbles will
a. Visualization
We group the 9 marbles into 3 because we need to find
group will be given to you so you will get 3.
of it. The first
b. Computation:
3
of 9 = x 9 = 9 = 9 marbles ÷ 3 groups = 3 marbles per group
3
1
Answer: 3 marbles will be given to you.
4. Mother bought 4 donuts. She gave you
of it. How many donuts will you
receive?
a. Visualization
To find
of the 4 donuts, we need to group the donuts into 2
based on the denominator of . The first group of donuts will be
given to you. Therefore, you will receive 2 donuts.
b. Computation:
of 4 = 1 x 4 = 4 donuts ÷ 2 groups = 2 donuts per group
11
Here are some ways to visualize multiplication of fractions:
1. You may use models or illustrations or grids and color
the part that represents the first fraction (Model A).
Then color the part that represents the 2nd fraction in
the problem (Model B) and put X mark to see the final
output.
2.
You may also use a piece of paper. Fold the paper
horizontally (pahiga) using the denominator of the first
fraction and color the part that represents it (Model A). Then
fold the paper vertically (patayo) using the denominator of
the second fraction then color the part that represents it and
put X mark (Model B). Open the folded paper for you to see
the final output.
3. In visualizing the fractional part of a whole, we use model A
to show the given item then we use model B as the fractional
part. Finally, we combine all the fractional parts in model B
for the final output.
4. To visualize the fractional part of objects, we group them
according to the denominator of the given fraction then we
box the group based from the numerator of the fraction.
Key Ideas to Remember in Multiplication of Fractions



In multiplying fractions, multiply first the numerators then
multiply the denominators. Common factors appearing in the
numerator and denominator can be cancelled. Get the lowest
term when possible.
In finding the fractional part of a whole number, we write 1
as the denominator of the whole number. Then, we multiply
the numerators and the denominators.
Another way is to multiply the numerators then divide its
product with the denominator. Ex. ¼ of 24 = 1 x 24 = 6
4
12
What’s More
Activity 1.1: Color Time
Color the final output of each visualization. Then write the multiplication equation.
1.)
_____
4.)
x
_____
=
____
_____ x
5.)
2.)
______ x
_____
=
______
____
3.)
_____
x
_____
=
_______
Activity 1.2: Combining Fractional Parts
Find the fractional part of a whole:
1.)
_____ = ____
x 4 = ______
13
x
____ =
____
2.)
x 5 = _______
3.)
x 2 = ______
Activity 1.3: Analyze and Solve using Illustration
If you have of a whole pizza and you gave of it to your friend. What fractional part
of your pizza did you give to her? Illustrate it using the circle below. Then write your
answer on the blank.
_________
Activity 1.4: Drawing Time
Illustrate and find the product.
1.)
x
= __________
2.)
x
= __________
3.)
x
= __________
4.)
x8
= __________
5.)
x3
= __________
14
What I Have Learned
What have you learned about visualization of multiplication of fractions?
What do we use to visualize multiplication of fractions?
For visualization of each fraction equation, we can use
_____________, _______________, and ________________.
What I Can Do
Analyze and solve the problem.
Romel has
meter of transparent acetate sheet. He used
of it in making
his “Do It Yourself” face shield for his protection. What fractional part of the
transparent acetate sheet did he use in making his face shield?
Assessment
Choose the best answer. Write the letter of your answer on the blank before each
number.
_____1. What is
x
=_____
A.
B.
C.
D.
X
X
X
X
X
X
X
X
15
X
X
______2. What fraction does this final output represent?
X
B.
A.
C.
D.
______3. What is the correct multiplication equation for this visualization?
x x x
A.
x
=N
B.
x
=N
C.
x
=N
D.
x
______4. What is the correct visualization for the product of
B.
C.
D.
X
X
X
X
A.
B.
x
x
x
x
x 3 = N?
C.
x
x
=N
= N?
A.
_____5. Which is the correct visualization for
x
x
x
D.
x
x
______6. What is the product of the equation in number 5?
A.
B.
C.
16
D.
x
______7. Which of the following visualizations shows the product of
A.
B.
X
C.
X
D.
X
X
______8. Which of the following visualizations gives the product of
A.
B.
x
C.
x
x
x
x 4?
D.
x
x
______9. The product of
A.
x
B.
x 5 is ____________.
x
C.
x
x
D.
x
x
x
x
x
x
17
?
_____10. If you had 4 apples and you gave
of them to your mother, how many
apples did she receive? Which of the following visualizations shows the correct
answer for the problem?
A.
B.
C.
D.
Additional Activities
Illustrate and give the product
1.
x
= _______________
2.
x
= _______________
3.
x
= _______________
4.
x 10
= _______________
5.
x6
= ______________
18
Lesson
2
Multiplying a Fraction and a
Whole Number and Another
Fraction
Hi Kids! You have learned the visualization of fractions in Lesson 1 of this module.
This time, you will learn about multiplying a fraction and a whole number and
another fraction. So, come on let’s learn about this.
What’s In
A. Choose the letter of the correct answer.
_____1. What fraction does this final output represent?
X
X
B.
𝐴.
C.
D.
_____2. What is the correct multiplication equation for this visualization?
x x x x
A.
x
=N
B.
x
x
=N
C.
X
=N
_____3. Which of the following visualizations shows
A.
X
B.
X
X
D.
x
?
C.
D.
X
X
X
X
X
X
X
19
X
=N
_____4. Which of the following visualizations gives the product of
A.
x
B.
x
C.
x
x
x
x
_____5. What is
of 6?
A.
B.
C.
D.
20
D.
x 5?
What’s New
Story Problem
Ana helped her mother prepare their family
breakfast. She prepared Spanish chocolate drinks by
boiling
of the 5 liters of fresh milk with
liters of native
chocolate with coco sugar. How many liters of ingredients
did she use in all?
What is It
Analysis of the Problem:
1. Understand:
Asked: Fractional part of liters of milk was used.
Given: = fractional part of the fresh milk that Ana used
5 = liters of fresh milk
2. Find:
What operation to use? Multiplication
What is the number sentence?
3. Solve:
x5=N
of 5 liters pack of fresh milk
1
3 x 5 = 3 liters
5
1
4. Answer: 3 liters of 5 liters of fresh milk was used.
21
Let’s have more activities for you to understand multiplication of fractions.
1. Romar received of a banana cake. He ate
of the banana cake did he eat?
x
Step 1
of it. What fractional part
=N
Multiply the numerators, 3 x 1 = 3.
Step 2
Multiply the denominators,
4 x 3 = 12.
Step 3
Reduce the product in lowest term,
x
=
= 3÷3 =
12 ÷ 3
Get the GCF of the numerator and denominator and use it to divide them.
3= 3x1
12 = 3 x 4
GCF = 3
Answer : Romar ate
2. Find the product of
Step 1
of the banana cake.
x
= N.
Check which of the numerators and denominators have the same
factors so that we can cancel them.
1
3=3x1
9=3x3
x
=
3
GCF =3
Step 2
Multiply the numerators and the denominators.
1x1 = 1
4x3
12
Answer :
Remember:


In multiplying fractions, we multiply first the numerators then we
multiply the denominators. We simplify if necessary.
We can also use the cancellation method for us to simplify the
fractions before multiplying.
22
What’s More
Activity 1.1
Find the product. Cancel the common factors if possible. Express all answers in
simplest forms.
1.
x
= 3 x 5 = _____
8x6
2. 18 x
= 18 x 9 = _____
9
3.
x
= 7x3
9 x 28
4. 35 x
5.
x
Activity 1.2
= _____
= 35 x 5 =_____
7
= 5 x 9__ = _____
12 x 10
Encircle the correct product.
1.) 35 of
=N
( 28
15
21 )
2.) 42 of
=N
( 30
35
45 )
of 18 = N
( 2
3
4)
4.) of 28 = N
( 15
21
12 )
5.)
( 15
21
30 )
3.)
of 35 = N
23
Activity 1.3
Match column A with column B. Write the letter of the correct answer on the blank
before each number.
A
B
_____1.
x 20 = N
A.
_____2.
x
B.
_____3.
x 36 = N
C. 16
_____4.
x
=N
D.
_____5.
x
=N
E.
F. 20
=N
What I Have Learned
What did you learn today?
How do we multiply fractions?


In multiplying fractions, we multiply first the _______ then we
multiply the ___________. We simplify if necessary.
We can also use the ____________ for us to simplify the fractions
before multiplying.
What I Can Do
Solve each problem. Express all the answers in simplest forms.
1. A box has twenty-seven toys. If
of the toys are for girls, how many
toys are for girls?
2. A can of corned beef weighed 500 grams. If
of the can was served
at breakfast, how many grams were served?
3. Grace used of pad paper with 100 sheets. How many sheets of pad
paper were used?
24
of a class of grade 5 joined the Math Club. If there are 40 pupils
4.
in the class, how many joined the Math Club?
5. A leaking faucet wastes
liters of water per hour. How many liters
of water are wasted in a day?
Assessment
Find the product of the following fractions and whole numbers. Write the letter of the
best answer on the blank before each number.
_____1.)
of 6 = _________
A. 2
_____2.)
B. 3
of
C.
D.
C. 8
D. 9
C.
D.
C.
D.
C. 18
D. 19
C.
D.
of 10 = ________
_______3. )
A. 6
______4. )
x
_____5.)
x
B. 7
= _______
B.
A.
A.
= ________
B.
______6. )
of 20= _______
______7. )
x
A. 16
A.
D. 5
= _________
B.
A.
C. 4
B. 17
= _______
B.
25
x 36 = ______
______8. )
A. 5
x
_____9. )
B. 10
C. 15
D. 20
B.
C.
D. 1
C.
D.
= ______
A.
_____10.)
x
= ________
A.
B.
Additional Activities
Multiply and express the product in simplest form if possible.
x
= _________
2.
x3x
= _________
3.
x 5 = _________
4.
x 2 = ________
1. 1 x
= _________
5. 3 x
6.
x
= _________
7.
x
= __________
8.
x
= ___________
9.
x 5 = ___________
10.
x
= ___________
26
Multiplying a Fraction and a
Whole Number and Another
Fraction
Lesson
3
Hello Kids! We are now on our third lesson on multiplication of fractions. Today, you
are going to learn how to multiply fractions mentally. Are you ready?
What’s In
A. Give the product of the following numbers.
1.) 6 x 2 = _____
2.) 7 x 4 = ______
3.) 8 x 5 = ______
4.) 9 x 6 = ______
5.) 10 x 7 = ______
B. Multiply the following fractions.
6.)
x
= ______
7.)
x
= ______
8.)
x
= _______
9.)
x
= _______
10.)
x
= ________
What’s New
Story Problem:
Lea had
kilograms of cheese. She used
of the
cheese for baked macaroni. How many kilograms of
cheese were used?
27
What is It
Let us analyze the word problem:
1. Understand:
kg of cheese
Given:
part of the cheese she used for the baked macaroni
Asked: kg. of cheese used for the baked macaroni
2. Find:
What operation to use? Multiplication
x
What is the number sentence?
=N
3. Solve:
1 x 3 = 1 kg of cheese was used
3
4
4
4. Answer:
kg. of cheese was used for the baked macaroni.
Let’s have another activity:
x
=N
Step 1
Multiply the numerators,
Step 2
Multiply the denominators, 4 x 2 = 8.
1 x 1 = 1.
Answer:
To multiply fractions mentally, multiply the numerators and the
denominators separately.
28
What’s More
Activity 1.1
Find the product of the following fractions by using cancelation.
1.)
x
= ______
2.)
x
= _______
3.)
x
= _______
4.)
x
= ________
5.)
x
= ________
Activity 1.2
Multiply the following fractions. Express the product in lowest
terms.
1.)
x
= ______
2.)
x
= ______
3.)
x
= _______
4.)
x
= _______
5.)
x
= _______
Activity 1.3
Find the product of the following fractions orally.
x
1.
B.
A.
2.
x
x
A.
10
C.
D.
C.
D.
C.
D.
= _________
B.
A.
3.
= _________
= _______
B.
29
x
4.
A.
5.
20
x
= _______
B.
C.
D.
C.
D.
= ________
A.
B.
Activity 1.4
Multiply the following factions orally. Match column A with
column B. Write the letter of the correct answer on the space
provided.
A
B
_____1.
x
=N
A.
_____2.
x
=N
B.
_____3.
x
=N
C.
_____4.
x
=N
D.
_____5.
x
=N
E.
F.
What I Have Learned
How do we multiply fractions mentally with denominators up to 10?
To multiply fractions mentally, multiply the ___________
and the ______________ separately.
30
What I Can Do
Read and solve the problem. Reduce the answers to simplest form.
kg. of mango. She gave
1. Maresfel had
of it to her friend. What part
of the mango was given to her friend?
2. Jhia consumed
of her milk. She had
can of milk. What part of her
milk was consumed?
1
3. Nicole ate 2 of her food. She had
box of food. What part of the food
did she eat?
Assessment
Find the product of the following fractions. Write the letter of the best answer on the
blank before each number.
x
= ______
A.
B.
x
= ______
_____ 1.)
_____ 2.)
B.
A.
_____3.)
x
x
A.
D.
C.
D.
= _______
A.
_____4.)
C.
B.
C.
D.
= ______
B.
C.
31
D.
x
_____5.)
= ______
A.
B.
x
= _________
A.
B.
_____ 6.)
C.
D.
C.
D.
C.
D.
4
____ 7.)
A.
_____ 8.)
x 5 = _________
B.
x
= _____
A.
_____9.)
x
C.
D.
B.
C.
D.
B.
C.
D.
= ______
A.
_____10.)
B.
x
= ______
A.
Additional Activities
Multiply the following fractions. Write the answer on the space provided.
1.)
x
= ______
2.)
x
= _______
3.)
x
= ______
4.)
x
= ______
5.)
x
= ______
32
Math 5 Q1 Module 6 Lesson 1
Answer Key
What I Know
1. A
2. D
3. D
4. A
5. B
6. C
7. A
8. A
9. A
10. C
What's In
What’s More
Activity 1.1
1.
2.
3.
4.
5.
6.
1.
x
=
2.
x
=
3.
x
=
4.
x
=
5.
x
=
Activity 1.2
1. 2
2. 2
What’s More
What I Can Do
Activity 1. 3
x
x
=
Activity 1.4
(Drawing Varies)
1.
x
=
2.
x
=
3.
x
=
4.
x8=4
5.
x3=
=
or
Additional
Activities
(Drawing Varies)
Assessment
1.
2.
3.
4.
5.
3.
A
D
C
D
B
6. B
7. D
8. A
9. B
10. C
or
33
1.
2.
3.
4. 8
5. 5
Math 5 Q1 Module 6 Lesson 2
Answer Key
What’s In
1. B
2. D
3. A
4. A
5. C
What's More
Activity 1.1
1.
2. 10
3.
4. 25
5.
1. B
2. B
3. A
4. C
5. C
6. A
7. B
8. D
9. B
10. C
1. C
2. E
3. F
4. B
5. A
What I Can Do
Activity 1.2
1. 15
2. 35
3. 2
4. 12
5. 15
Assessment
Activity 1.3
1. 12 toys for girls
2. 375 grams
3. 40 sheets
4. 16 pupils
5. 3 Liters
Additional
Activities
1.
2.
3. 3
4. 1
5. 2
6.
7.
8.
9.3
10.
34
Math 5 Module 6 Lesson 3
Answer Key
What's More
Activity 1.1
What’s In
2. 12
3. 28
4. 40
5. 54
6. 70
7.
1.
What’s More
2.
Activity 1.3
3.
1. A
2. B
3. D
4. A
5. C
4.
5.
Activity 1.2
8.
1.
Activity 1.4
9.
2.
10.
3.
11.
4.
1. F
2. E
3. B
4. D
5. C
5.
What I Can Do
1.
2.
3.
Kg of mango
can of her
milk
of the box of
food
Assessment
1. A
2. C
3. A
4. B
5. A
6. A
7. B
8. D
9. A
10. C
Additional
Activities
1.
2.
3.
4.
5.
35
References
De Leon, Irminda (2017), et al, Math in a Challenging World 5. Instructional
Coverage System Publishing, Inc. pp.220
Most Essential Learning Competency Grade 5
Ecaldre, Felix G. (2004) . Skillbuilders in Math 5. Book Craft Publishing Co., Inc.
pp. 81 – 86
Ursua, Alvin C.,et al. (2016) . 21st Century Mathletes 5. Vibal Group, Inc. pp. 78-83
Villamayor, Adela C., et. Al. (2016) Math for Life 5. Rex Publishing
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