This is a self-learning module for Mathematics Grade 5, Quarter 1, Module 11: “Fun in Multiplying Fractions and a Whole Number and Another Fraction.” It is an Alternative Delivery Mode (ADM) module from DepEd Region VIII for learners studying at home or in class. After working through it, learners will be able to multiply a fraction by a whole number and a fraction by another fraction, and write the product in lowest terms.
What learners will learn
The module has one learning competency:
- Multiply a fraction and a whole number and another fraction (M5NS-Ig-90.1)
Lesson in this module
The module has one lesson, Lesson 1: Fun in Multiplying Fractions. It opens with a short review of multiplying fractions using shaded grids. Then it works through a word problem and explains the steps for both kinds of multiplication. Practice sets follow, with an answer key for every part.
Key ideas: multiplying fractions
Multiplying a whole number by a fraction
The module starts with this problem: Robert has 3 gallons of paint. He used 3/4 of the paint. How many gallons did he use?
- What is asked: the gallons of paint Robert used
- Facts given: 3 gallons of paint, 3/4 of the paint
- Operation: multiplication
- Rewrite the problem: “What is 3/4 of 3?” becomes the number sentence 3/4 x 3 = N
A drawing of three groups of three-fourths shows nine-fourths in all. So 3/4 x 3 = (3 x 3)/4 = 9/4. Robert used 9/4 gallons, or 2 1/4 gallons, of paint.
The word “of” means multiply. For example, 1/4 of 24 means 1/4 x 24. Write 24 as 24/1, then multiply: 24/4 = 6.
Steps for a whole number times a fraction:
- Multiply the whole number by the numerator of the fraction to get the numerator of the product.
- Copy the denominator of the fraction to get the denominator of the product.
- Express the product in lowest terms.
Multiplying a fraction by a fraction
To multiply fractions, multiply numerator by numerator and denominator by denominator. If the product is not in lowest terms, simplify it.
Example from the module: 2/3 x 4/5 = (2 x 4)/(3 x 5) = 8/15
More worked answers from the module’s activities:
| Problem | Product |
|---|---|
| 2/5 x 3/6 | 1/5 |
| 4/7 x 5/6 | 10/21 |
| 2/3 of 3/5 | 2/5 |
| 4/5 of 40 | 32 |
| 2/5 x 3/4 x 4/5 | 6/25 |
The last example shows that the same rule works for three fractions: multiply all the numerators, then all the denominators.
Parts of the module
- What I Need to Know: the learning objective
- What I Know: a 10-item multiple-choice pretest
- What’s In: a review using shaded-grid drawings of fraction products
- What’s New: the paint word problem with guide questions
- What Is It: the explanation and worked examples
- What’s More: 10 practice items with answers to choose from a box
- What I Have Learned: fill in the missing words in the steps for multiplying
- What I Can Do: 10 items to answer on your own, in lowest terms
- Assessment: a 10-item post-test
- Additional Activities: 5 more practice items
- Answer Key: answers for every part
How to use this module
- Learners: Answer the pretest first to see what you already know. Then go through the parts in order. Write all your answers in your Activity Notebook or on a separate sheet, not on the module. Check your work with the answer key only after you finish each part, and be honest with yourself.
- Parents and guardians: Help your child read the word problem and the guide questions in What’s New. Ask them to explain each step aloud, especially why “of” means multiply.
- Teachers: Use the pretest to spot learners who need help before they start. The Assessment works as a post-test, and the Additional Activities give extra practice for learners who need it.
If you have questions or have trouble with the tasks, ask your teacher or facilitator.
Frequently asked questions
What grade and quarter is this module for?
It is for Grade 5 Mathematics, Quarter 1. It is Module 11 of the quarter.
What competency does the module cover?
It covers multiplying a fraction and a whole number and another fraction, competency code M5NS-Ig-90.1.
How do you multiply a fraction by a fraction?
Multiply the numerators to get the numerator of the product, multiply the denominators to get the denominator, then reduce the answer to lowest terms. For example, 2/3 x 4/5 = 8/15.
What does “of” mean in a problem like 1/4 of 24?
“Of” means multiply. So 1/4 of 24 is 1/4 x 24, which equals 24/4 or 6.
Does the module have an answer key?
Yes. It includes answers for the pretest, all the activities, the assessment, and the additional activities.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 1 – Module 11: Fun in Multiplying Fractions and a Whole Number and Another Fraction
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CO_Q1_Math5_Module11
Mathematics – Grade 5 Alternative Delivery Mode Quarter 1 – Module 11: Fun in Multiplying Fractions and a Whole Numbers and Another Fractions. First Edition, 2020
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Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this book are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them.
Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio
Printed in the Philippines by ________________________
Department of Education – Region VIII Office Address: Government Center, Candahug, Palo, Leyte Telefax: 053 – 832-2997 E-mail Address: region8@deped.gov.ph
Development Team of the Module
Writers: Elena Danduan Editors: Zosimo M. Miñozo Jr., Josephine L. Gallardo Jim Anthony C. Morfe, Ramil R. Magdua, Joseph Randolp Palattao, Lilia Martinez, Bernadeth Daran Reviewers: Renato S. Cagomoc, Rolando Lacbo, Joshua Sherwin T. Lim, Normel John A. Manuales Illustrator: Edgar B. Castillo Layout Artist: Modesto Y. Sapinit Management Team: Ramir B. Uytico, Arnulfo M. Balane, Rosemarie M. Guino, Joy B. Bihag, Ryan R. Tiu, Sarah S. Cabaluna, Thelma Cabadsan-Quitalig, Elena S. De Luna, Renato S. Cagomoc, Noel E. Sagayap, Geraldine P. Sumbise, Joshua Sherwin T. Lim
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Mathematics
Quarter 1 – Module 11: Fun in Multiplying Fractions and a Whole Number and Another Fraction
Introductory Message
This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.
In addition to the material in the main text, Notes to the Teacher are also provided to our facilitators and parents for strategies and reminders on how they can best help you on your home-based learning.
Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests, and read the instructions carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.
Good luck and happy learning!
Hi, Mathletes!
In this module, you will be dealing with multiplication of a fraction by a fraction and a whole number.
At the end of this module, you will be able to:
- multiply a fraction and a whole number and another fraction. M5NS-Ig-90.1
What I Need to Know
Hi, Mathletes!
In this module, you will be dealing with multiplication of a fraction by a fraction and a whole number.
At the end of this module, you will be able to:
- multiply a fraction and a whole number and another fraction.
M5NS-Ig-90.1
What I Know
Now, answer the questions below:
Directions: Choose the letter of the correct answers and write them in your Activity Notebook.
If $\frac{2}{3}$ x $\frac{1}{2}$ = N, what is the value of N?
a. A. $\frac{1}{4}$ B. $\frac{1}{3}$ C. $\frac{1}{2}$ D. $\frac{1}{5}$If you multiply $\frac{1}{4}$ by $\frac{2}{3}$, what will be the product?
a. A. $\frac{1}{5}$ B. $\frac{1}{6}$ C. $\frac{1}{7}$ D. $\frac{1}{12}$What is $\frac{3}{4}$ of 20?
a. A. 5 B. 10 C. 15 D. 25In a class of 40, $\frac{4}{5}$ are boys. How many are boys?
a. A. 40 B. 32 C. 45 D. 35What is $\frac{3}{7}$ of 35?
a. A. 5 B. 15 C. 25 D. 30Find the product of 3 and $\frac{5}{8}$.
a. A. $2\frac{7}{8}$ B. $\frac{7}{8}$ C. $1\frac{7}{8}$ D. $\frac{8}{8}$If you multiply 10 by $\frac{6}{10}$, the product is _____.
a. A. 6 B. $10\frac{6}{8}$ C. $\frac{6}{100}$ D. $\frac{60}{100}$What is $\frac{3}{10}$ multiplied by 5?
a. A. $\frac{1}{2}$ B. $1\frac{1}{2}$ C. $1\frac{1}{4}$ D. $\frac{1}{5}$What is the value of N in the expression $\frac{4}{5}$ x $\frac{5}{8}$ = N?
a. A. $\frac{1}{2}$ B. $\frac{1}{5}$ C. $\frac{1}{4}$ D. $\frac{1}{3}$Multiplying $\frac{1}{3}$, $\frac{2}{5}$ and $\frac{1}{3}$ will give a product of _____.
a. A. $\frac{2}{15}$ B. $\frac{2}{35}$ C. $\frac{2}{45}$ D. $\frac{2}{11}$
Lesson 1: Fun in Multiplying Fractions
What’s In
Directions: Write your correct answers in your Math Activity notebook.
Which is the correct illustration of the product of the fraction $\frac{1}{3}$ of $\frac{1}{2}$?
a. A. [illustration: grid with shaded parts, option A]
b. B. [illustration: grid with shaded parts, option B]
c. C. [illustration: grid with shaded parts, option C]
d. D. [illustration: grid with shaded parts, option D]Which is the correct number sentence of the illustration below?
[illustration: three rectangles showing a multiplication of two fractions with a product shown as a shaded grid]
a. A. $\frac{1}{3}$ x $\frac{3}{4}$ = $\frac{3}{12}$ or $\frac{1}{4}$
b. B. $\frac{3}{5}$ x $\frac{5}{9}$ = $\frac{15}{45}$ or $\frac{1}{3}$
c. C. $\frac{1}{3}$ x $\frac{2}{5}$ = $\frac{2}{15}$
d. D. $\frac{2}{3}$ x $\frac{1}{4}$ = $\frac{2}{12}$ or $\frac{1}{6}$Illustrate the fraction $\frac{3}{5}$ x $\frac{1}{3}$.
a. A. [illustration: three rectangles showing $\frac{3}{5}$ x $\frac{1}{3}$ with the product shown as a shaded grid, option A]
b. B. [illustration: three rectangles showing $\frac{3}{5}$ x $\frac{1}{3}$ with the product shown as a shaded grid, option B]
c. C. [illustration: three rectangles showing $\frac{3}{5}$ x $\frac{1}{3}$ with the product shown as a shaded grid, option C]
d. D. [illustration: three rectangles showing $\frac{3}{5}$ x $\frac{1}{3}$ with the product shown as a shaded grid, option D]
What’s New
Are you ready for the next task? Let us read and analyze the problem below.
Robert has 3 gallons of paint. He used 3/4 of the paint. How many gallons of paint did he use?
What is asked in the problem? What facts are given? What operation are we going to use? How to solve the problem? What is the correct answer?
What Is It
Robert has 3 gallons of paint. He used 3/4 of the paint. How many gallons of paint did he use?
What is asked in the problem?
The gallons of paint Robert used.
What are the facts given?
3 gallons of paint, 3/4 of the paint
What operation are we going to use?
Multiplication
How to solve the problem?
One way to think and solve the problem is to rewrite the problem.
In words: What is 3/4 of 3?
As a number sentence: 3/4 x 3 = N
An illustration can help you to solve this problem:
[illustration: rectangles divided into fourths, with shaded parts showing three groups of three-fourths, set beside an equals sign and nine-fourths shaded]
How many fourths are there in total?
There are nine-fourths in total. So, 3/4 x 3 = (3 X 3)/4 = 9/4.
What is the correct answer?
Therefore, Robert used 9/4 gallons of paint or 2 1/4 gallons of paint.
To multiply fractions to fractions, simply multiply the numerator to numerator and denominator to denominator, then if the product is not in the lowest term, it is necessary to simplify to lowest or simplest term.
Consider the following examples.
A. Multiply: 2/3 x 4/5
Solution:
2/3 x 4/5 = (2 x 4)/(3 x 5) = 8/15
B. What is 1/4 of 24?
Solution:
1/4 of 24 means 1/4 x 24.
1/4 x 24 = 1/4 x 24/1 = 1/4 x 24/1 = 24/4 = 6
What’s More
Let us practice!
Directions: Multiply the following fractions. Choose the answer from the box.
- 4/5 x 30 = ____
- 3/5 of 15 = ____
- 3 x 2/12 = ____
- 2/8 x 40 = ____
- 4/5 of 20 = ____
- 2/5 x 3/6 = ____
- 4/7 x 5/6 = ____
- 2/3 of 3/5 = ____
- 5/12 x 3/4 = ____
- 6/20 x 5/7 = ____
24 16 2/5 3/14 5/16 9 1/2 10 1/5 10/21
What I Have Learned
Directions: Supply the missing term:
In multiplying a whole number by a fraction: Multiply the whole number by the (1) _______ of the fraction to get the numerator of the (2) _________. Copy the (3) _______ of the fraction to get the denominator of the product. Express the obtained product in (4) ______.
In multiplying fraction by a fraction: (5) _____ the numerators of the fraction to get the numerator of the product. Multiply the denominators of the (6) ______ to get the denominator of the product (7) ______ the answer in lowest terms.
What I Can Do
Now you can do this independently. Good luck!
Directions: Find the product of the following fractions in lowest terms.
- 3/4 x 60 = ______
- 1/4 x 80 = ______
- 5/6 x 120 = ______
- 4/7 x 3/4 = ______
- 9/10 x 2/15 = ______
- 14 x 5/6 = ______
- 25 x 3/5 = ______
- 4/5 x 2/3 = ______
- 3/8 of 5/6 = ______
- 7/8 x 2/3 = ______
Assessment
Time to find out what you have learned.
Directions: Read and understand the items carefully. Then write your answers in Activity Notebook.
If you multiply 1/4 and 2/3, what will be the product?
What is 2/7 of 3/5?
What is the value of N in 4/7 x 7/8 = N?
Multiply 5/6 by 4/5. What will be the product?
What is 4/5 of 40?
Find the product of 6 and 5/8. The answer is ______.
If you multiply 12 and 6/10, the answer would be _____.
What is 3/7 multiplied by 5.
What is the value of N? 4/7 x 7/8 = N
When you multiply 2/5, 3/4 and 4/5. It will give a product of _____.
Additional Activities
Practice more!
Directions: Multiply. Write each answer in lowest term if possible.
- What is 1/4 of 80?
- Find 5/6 of 15.
- How many is 2/7 of 12?
- Get 3/7 of 35.
- Show the 45 is 3/4 of 60
Answer Key
[transcriber’s note: this page is printed upside down; the sections below were read after rotating it to upright]
What I Know
- B
- B
- C
- B
- B
- C
- A
- B
- A
- C
What’s In
- A
- A
- A
What’s More
- 24
- 9
- 1/1
- 10
- 16
- 1/5
- 10/21
- 2/5
- 5/16
- 3/14
What’s New
- The gallons of paint Robert use.
- 3 gallons, 3/4 of paint
- Multiplication
- 3 x 3/4 = 3 x 3 = 9 or 2 1/4
- 2 1/4 gallons of paint used
What I Can Do
- 45
- 20
- 100
- 3/7
- 3/25
- 35/3
- 15
- 8/15
- 5/16
- 7/12
Assessment
- 2/12 or 1/6
- 6/35
- N= 4/8 or 1/2
- 2/3
- 32
- 3 3/4
- 7 1/5
- 2 1/7
- 1/2
- 6/25
Additional Activities
- 20
- 12 1/2
- 3 3/7
- 15
- 60 x 3/4 = 45
What I Have Learned
- Numerator
- Product
- Denominator
- Lowest Term
- Multiply
- Fraction
- reduce
Reference
DepEd Bureau of Elementary Education. 2010. Lesson Guide in Mathematics
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