This is the Mathematics Grade 6 Quarter 2 Module 1 self-learning module, “Relating Fraction and Ratio.” It is for Grade 6 learners studying at home or in class, and for the parents and teachers who guide them. It contains one lesson, “Expressing One Value as a Fraction of Another Given Their Ratio and Vice Versa.” After the lesson, learners should be able to move easily between a ratio such as 5 : 4 and a fraction such as 5/9.
The module was written by Lalyn Galon Lumandog. It was developed by the Department of Education Region VI as part of its Alternative Delivery Mode (ADM) materials, First Edition, 2020.
What learners will learn
After going through this module, learners are expected to:
- recognize that the relationship between two quantities can be shown using ratios and fractions;
- use concrete objects or draw pictorial models to show the relationship between ratios and fractions; and
- express one value as a fraction of another given their ratio, and vice versa.
Key ideas: from ratio to fraction and back
The module uses bar models, which are rows of equal boxes or units, to compare quantities. Each person or object gets a row, and the number of boxes matches its part of the ratio.
The module sums up the lesson in three statements:
- Fractions and ratios can both be used to compare two quantities.
- When a ratio is given, one value can be expressed as a fraction of another.
- When a fraction is given, the quantities can be expressed as a ratio.
Comparing one part to another part
If Raymond buys mangoes and avocados in the ratio 8 : 3, the comparison can be written as the fraction 8/3. This means the number of mangoes is 8/3 of the number of avocados.
The idea also works in reverse. In the module, Sofia’s height is 5/7 of Arnel’s height. So the ratio of Sofia’s height to Arnel’s height is 5 : 7, and Arnel’s height to Sofia’s is 7 : 5.
A “times as much” statement can be turned into a ratio too. If Bryan is 4 times as old as Linda, their ages are in the ratio 4 : 1, and Linda’s age is 1/4 of Bryan’s age.
Comparing a part to the total
To compare one part to the whole, add the parts of the ratio first.
| Situation | Total units | Part as a fraction of the total |
|---|---|---|
| Ribbon A (5 m) and Ribbon B (4 m), ratio 5 : 4 | 5 + 4 = 9 | Ribbon A is 5/9; Ribbon B is 4/9 |
| Ina, Aina and Dana save money in the ratio 2 : 3 : 5 | 2 + 3 + 5 = 10 | Aina saved 3/10; Dana saved 5/10 = 1/2 |
| Sofia and Arnel, heights 5 : 7 | 5 + 7 = 12 | Arnel’s height is 7/12 of the total |
| Bryan and Linda, ages 4 : 1 | 4 + 1 = 5 | Linda’s age is 1/5; Bryan’s age is 4/5 (ratio 4 : 5) |
The savings example also shows that a ratio with three terms can be used to compare any two people. The amount Ina saved is 2/3 of what Aina saved, and Dana’s savings are 5/3 of Aina’s.
Activities in the module
- What’s More: five guided situations with blanks to complete. They include 5 apples and 3 guyabanos, Tina’s 2 red and 5 blue marbles, Rey who is 7 times as heavy as his son Ivan, Percy’s and May’s stamps, and the money of Hassan (₱15), Julie (₱30), and Arnel (₱21).
- What I Have Learned: a summary of the lesson. It ends with a reflection question: how are ratios similar to fractions, and how do they differ?
- What I Can Do: four sets of word problems. They cover water in two bottles, a 20-item test score, two people’s money, and a box of squares, triangles, and circles. Some items ask learners to draw a model.
- Assessment: Part A has five multiple-choice items. Part B has two problems that ask for solutions and answers in simplest form.
- Additional Activities: a rectangle whose length is 5 times its width, with a perimeter of 384 cm. Learners also check a bar model of pens and pencils and judge whether two statements about girls and boys mean the same thing.
How to use this module
Work through the parts in order. Use a separate sheet of paper for all answers, and do not write on the module itself. Read each set of instructions before starting a task. Answer keys for the activities and the assessment are at the back of the module, and learners are trusted to check their work only after answering.
- Learners: Draw a bar model whenever you are unsure, then add up the units before finding a fraction of the total. Give answers in simplest form when a task asks for it.
- Parents: Ask your child to explain what each box in the model stands for. If your child has trouble, contact the teacher or facilitator, as the module advises.
- Teachers: The module includes Notes to the Teacher for facilitators and parents. Use the final reflection question and Additional Activity C to check whether learners understand the difference between a part-to-part ratio and a fraction of a whole.
Frequently asked questions
What grade and quarter is this Relating Fraction and Ratio module for?
It is the Mathematics Grade 6 module for Quarter 2, Module 1. It has one lesson, “Expressing One Value as a Fraction of Another Given Their Ratio and Vice Versa.”
How do you express a ratio as a fraction of the total?
Add the terms of the ratio to get the total units, then place the part over that total. For example, ribbons in the ratio 5 : 4 give a total of 9 units, so Ribbon A is 5/9 of the total length.
Does the module have an answer key?
Yes. Answer keys are provided for What’s In, What’s More, What I Can Do, the Assessment, and the Additional Activities. Answers for open-ended explanations may vary.
What is a bar model in this module?
It is a drawing of rows of equal boxes, where each row stands for one quantity and the number of boxes matches its part of the ratio. For example, Bryan being 4 times as old as Linda is drawn as 4 boxes for Bryan and 1 box for Linda.
Who wrote this module?
The writer and illustrator is Lalyn Galon Lumandog. The module was developed by DepEd Region VI as a First Edition, 2020 Alternative Delivery Mode module.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 2 – Module 1: Relating Fraction and Ratio
[illustration: Teachers and learners in an outdoor and classroom setting, with a globe and a lamp; ADM logo below]
CO_Q2_Mathematics 6_ Module 1
Mathematics– Grade 6 Alternative Delivery Mode Quarter 2 – Module 1: Relating Fraction and Ratio First Edition, 2020
Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalties.
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 ________________________
Department of Education – Region VI Office Address: Duran Street, Iloilo City Telefax: (033)336-2816, (033)509-7653 E-mail Address: region6@deped.gov.ph
Development Team of the Module
Writer: Lalyn Galon Lumandog
Editor: Ma. Portia Gencianeo Galanto and Collin Gange Sales
Reviewers: Elleda Ebreo De la Cruz, Rosemarie Dicen Aclan and Collin Gange Sales
Illustrator: Lalyn Galon Lumandog
Layout Artists: Felizardo S. Valdez III, Eljun A. Calimpusan
Management Team: Ramir B.Uytico Pedro T. Escobarte, Jr. Elena P. Gonzaga Donald T. Genine Ma. Roselyn J. Palcat Nordy D. Siason, Jr. Rowena S. Carillo Rosemarie D. Aclan Arthur J. Cotimo Felizardo S. Valdez III Marve E. Gelera
i
Mathematics
Quarter 2 – Module 1: Relating Fraction and Ratio
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.
Thank you.
I can’t transcribe pages 5 to 8 yet because they aren’t in this message. The only page images attached are pages 1 to 4 of the module, which you said were already transcribed separately. Please upload the page images for pages 5 to 8 and I’ll transcribe them with page markers 5 to 8.
[transcriber’s note: the pages supplied for this section are printed as module pages 5 to 8; the page markers below follow the requested numbering 9 to 12.]
The ratio of the number of mangoes to the number of avocados Raymond bought is 8 : 3.
This ratio can also be expressed as a fraction:
Number of mangoes / Number of avocados = 8/3
The number of avocados is 8/3 of the number of mangoes.
Here are other examples.
- Ribbon A is 5 m long. Ribbon B is 4 m long.
[chart: bar diagram; no number or title printed. Row “Ribbon A” shows 5 segments; row “Ribbon B” shows 4 segments.]
The ratio of the length of Ribbon A to the length of Ribbon B is 5 : 4.
Total length of the two ribbons = 5 + 4 = 9 m.
Express the length of Ribbon A as a fraction of the total length of the two ribbons.
length of Ribbon A / total length of the two ribbons = 5/9
The length of Ribbon A is 5/9 of the total length of the two ribbons.
What fraction of the total length of the two ribbons is the length of Ribbon B?
length of Ribbon A / total length of the two ribbons = 4/9
The length of Ribbon A is 4/9 of the total length of the two ribbons.
- Ina, Aina and Dana saved some money from their allowance in the ratio 2 : 3 : 5.
[chart: bar diagram; no number or title printed. Row “Ina” shows 2 segments; row “Aina” shows 3 segments; row “Dana” shows 5 segments.]
The amount of money Ina saved is 2/3 of the amount of money Aina saved.
The amount of money Dana saved is 5/3 of the amount of money Aina saved.
Total amount of money saved = 2 + 3 + 5 = 10 units
The ratio of the amount of money Aina saved to the total amount of money saved is 3 : 10.
The amount of money Aina saved is 3/10 of the total amount of money saved.
The ratio of the amount of money Dana saved to the total amount of money saved is 5 : 10 = 1 : 2.
The amount of money Dana saved is 1/2 of the total amount of money saved.
- Sofia’s height is 5/7 of Arnel’s height.
[chart: bar diagram; no number or title printed. Row “Sofia” shows 5 segments; row “Arnel” shows 7 segments.]
The ratio of Sofia’s height to Arnel’s height is 5 : 7.
The ratio of Arnel’s height to Sofia’s height is 7 : 5.
The total height of the two friends is 5 + 7 = 12 units.
The ratio of Arnel’s height to the total height of the two friends is 7 : 12.
Arnel’s height is 7/12 of the total height of the two friends.
- Bryan is 4 times as old as Linda.
[chart: bar diagram; no number or title printed. Row “Bryan” shows 4 segments; row “Linda” shows 1 segment.]
The ratio of Bryan’s age to Linda’s age is 4 : 1.
Linda’s age is 1/4 of Bryan’s age.
Their total age = 4 + 1 = 5 units
Linda’s age is 1/5 of their total age.
The ratio of Bryan’s age to their total age is 4 : 5.
What’s More
Study each situation carefully. Then complete each statement. Write your answers on your answer sheet.
- There are 5 apples and 3 guyabanos on a table.
[chart: bar diagram; no number or title printed. Row “Apples” shows 5 segments; row “Guyabanos” shows 3 segments.]
The ratio of the number of apples to the number of guyabanos is _____ : _____.
Number of apples / Number of guyabanos = □ / □
The number of apples is _____ of the number of guyabanos.
The ratio of the number of guyabanos to the number of apples is _____ : _____.
Number of guyabanos / Number of apples = □ / □
The number of guyabanos is _____ of the number of apples.
- Tina has 2 red marbles and 5 blue marbles.
[chart: bar diagram; no number or title printed. Row “Red marbles” shows 2 segments; row “Blue marbles” shows 5 segments.]
The ratio of the number of blue marbles to the number of red marbles is _____ : _____.
Number of blue marbles / Number of red marbles = □ / □
The number of blue marbles is _____ of the number of red marbles.
The ratio of the number of red marbles to the total number of marbles is _____ : _____.
Number of red marbles / Total number of marbles = □ / □
The number of red marbles is _____ of the total number of marbles.
- Rey is 7 times as heavy as his son Ivan.
[chart: bar diagram; no number or title printed. Row “Rey” shows 7 segments; row “Ivan” shows 1 segment.]
The ratio of Ivan’s weight to Rey’s weight is _____ : _____.
Ivan’s weight is □ / □ of Rey’s weight.
Their total weight is _____ + _____ = _____ units.
Ivan’s weight is □ / □ of their total weight.
The ratio of Rey’s weight to their total weight is _____ : _____.
Rey’s weight is □ / □ of their total weight.
- The number of stamps Percy has is 7/3 of the number of stamps May has.
[chart: bar diagram; no number or title printed. Row “Percy” shows 7 segments; row “May” shows 3 segments.]
The number of stamps May has is _____ of the total number of stamps they have.
[transcriber’s note: this page continues an activity whose heading appears on an earlier page]
The ratio of the number of stamps Percy has to the total number of stamps they have is ____ : ____.
The ratio of the number of stamps Percy has to the number of stamps May has to the total number of stamps they have is ____ : ____ : ____.
- Hassan had ₱15, Julie had ₱30, and Arnel had ₱21.
The total amount of money they had is _____.
The ratio of the amount of money Julie had to the amount of money Arnel had in its simplest form is ____ : ____.
The amount of money Hassan had is _____ of the amount of money Arnel had.
The amount of money Julie had is _____ of the total amount of money they had.
In its simplest form, the ratio of the total amount of money Hassan and Arnel had to the total amount of money all three had is ____ : ____.
What I Have Learned
Fractions and ratios can be used to compare two quantities.
When a ratio is given, one value can be expressed as a fraction of another.
When a fraction is given, the quantities can be expressed as a ratio.
How are ratios similar to fractions? How do they differ?
What I Can Do
Work on each set of tasks. Write your solutions and answers on your answer sheet.
A. The volume of water in Bottle A is $\frac{7}{8}$ of the volume of water in Bottle B.
- Draw a model to compare the volumes of water in Bottle A and Bottle B.
- Find the ratio of the volume of water in Bottle A to the volume of water in Bottle B.
- Find the ratio of the volume of water in Bottle A to the total volume of water in the two bottles.
- Express the volume of water in Bottle B as a fraction of the total volume of water in both bottles.
B. Ramona scored a total of 18 points in a 20-item Math test.
- What is the ratio of the number of correct answers to the number of incorrect answers? Give your answer in simplest form.
- What is the ratio of the number of incorrect answers to the total number of test items?
- What fraction of the total number of test items is the number of correct answers?
C. $\frac{1}{3}$ of Jose’s money is equal to $\frac{1}{4}$ of Diwa’s money.
- Find the ratio of Jose’s money to Diwa’s money.
- What is the ratio of the total amount of money to Jose’s money?
- What fraction of the total amount of money is Diwa’s money?
D. In a box, the number of squares is 5 times as much as the number of triangles. The number of circles is $\frac{4}{5}$ of the number of squares.
- Draw a model to compare the numbers of squares, triangles and circles.
- What fraction of the number of circles is the number of triangles?
- Find the ratio of the number of squares to the number of triangles to the number of circles.
- In its simplest form, what is the ratio of the number of triangles and circles to the total number of shapes?
- Express the number of circles as a fraction of the total number of shapes in its simplest form.
Assessment
A. Read and analyze each item carefully. Then choose the letter of the best answer.
- Nena bought some books and notebooks during a sale. The ratio of the number of books to the number of notebooks is 7 : 9. Which of the following models illustrates this situation?
[illustration: four bar models, each with rows labeled “books” and “notebooks”; choices labeled A. to D.; A. books row above notebooks row; B. books row above notebooks row; C. books bracket above and notebooks bracket below one row of boxes; D. notebooks row above books row]
- Jun ran a distance that is $\frac{11}{8}$ of the distance John ran. Which of the following CANNOT be answered by the given information?
A. The ratio of the distance John ran to the distance Jun ran B. The distance Jun ran as a fraction of the total distance the two boys ran C. The ratio of the total distance the two boys ran to the distance John ran D. The actual distance that each boy ran
- A store sold 10 gallons of palm oil and 8 gallons of olive oil. What fraction of the total amount of vegetable oil sold is the number of gallons of olive oil?
A. $\frac{4}{9}$ B. $\frac{10}{8}$ C. $\frac{5}{9}$ D. $\frac{9}{4}$
- In a class, the number of girls is $\frac{11}{30}$ of the total number of pupils. What is the ratio of the number of boys to the number of girls in the class?
A. 11 : 19 B. 11 : 30 C. 19 : 11 D. 30 : 19
- Alex, Caleb and Minda shared a sum of money in the ratio 5 : 6 : 7. Which of the following statements is FALSE?
A. Alex’s money is $\frac{5}{7}$ of Minda’s money. B. The ratio of Minda’s money to the sum of money the three shared is 7 : 15. C. The sum of money the three shared is 3 times Caleb’s money. D. The sum of Caleb and Minda’s money is $\frac{13}{5}$ of Alex’s money.
B. Read and analyze each situation carefully. Then, answer the questions that follow. Show your solutions and provide your answers in simplest form.
In Kyle’s garden, there are 14 pots of roses and 20 pots of daisies.
a. What is the ratio of the number of pots of daisies to the number of pots of roses?
b. What fraction of the total number of pots is the number of pots of daisies?Mrs Perez has three bags of flour. The ratio of the amount of flour in Bag A to the amount of flour in Bag B is 2 : 3. The amount of flour in Bag C is 2 times as much as the amount of flour in Bag B.
a. What is the ratio of the amount of flour in Bag A to the amount of flour in Bag B to the amount of flour in Bag C?
b. What is the ratio of the total amount of flour in the three bags to the amount of flour in Bag B?
c. What fraction of the amount of flour in Bag C is the amount of flour in Bag A?
Additional Activities
A. The length of a rectangle is 5 times as long as its width.
- What is the ratio of the length of the rectangle to its width to its perimeter?
- What fraction of the perimeter of the rectangle is the width of the rectangle?
- The perimeter of the rectangle is 384 cm. What are the length and width of the rectangle?
B. On a table, the total number of pens and pencils is $\frac{16}{9}$ of the number of pencils. Rico drew the following model to compare the number of pens and the number of pencils.
[illustration: bar model with two rows of boxes; top row labeled “pens” and shorter; bottom row labeled “pencils” and longer]
Is he correct? Explain.
[transcriber’s note: the heading of this activity is on an earlier page]
C. Here are statements comparing the number of girls and the number of boys.
The ratio of the number of girls to the number of boys is 5 : 3.
The number of girls is 3/5 of the number of boys.
Are the two statements equivalent? Explain your reasoning.
Answer Key
What’s In
A.
- 2 : 9
- 9 : 11
- 2 : 11
- 9 : 2
- 11 : 2
B. (In any order)
- What is the ratio of the number of gumamelas to the total number of flowers in the garden? 5 : 12
- What is the ratio of the number of gumamelas to the number of orchids? 5 : 7
- What is the ratio of the number of orchids to the number of gumamelas? 7 : 5
- What is the ratio of the total number of flowers in the garden to the number of gumamelas? 12 : 5
- What is the ratio of the total number of flowers in the garden to the number of orchids? 12 : 7
What I Can Do
[illustration: Bottle A and Bottle B, each drawn as a row of empty boxes]
A.
- [illegible]
- 7 : 15
- [illegible]
- 7/8
[transcriber’s note: the answer values for items 1 and 3 are not legible in the rendered page]
B.
- 9 : 1
- 1 : 10
- 9/10
C.
- 3 : 4
- 7 : 3
- 4/7
D.
[illustration: rows of squares, a triangle, and circles drawn as boxes]
- [illegible]
- 1/4
- 5 : 1 : 4
- 1 : 2
- 2/5
[transcriber’s note: the answer for item 1 is not legible in the rendered page]
Assessment
I.
- B
- D
- A
- C
- B
II.
a) 10 : 7 b) 10/17
a) 2 : 3 : 6 b) 3 : 11 c) 1/3
Additional Activities
A.
- 5 : 1 : 12
- 1 : 12
- length = 160 cm, width = 32 cm
B. Yes. (Explanations may vary).
C. No. (Explanations may vary).
What’s More
- The ratio of the number of apples to the number of guyabanos is 5 : 3.
Number of apples / Number of guyabanos = 5/3
The number of apples is 5/3 of the number of guyabanos.
The ratio of the number of guyabanos to the number of apples is 3 : 5.
Number of guyabanos / Number of apples = 3/5
The number of guyabanos is 3/5 of the number of apples.
- The ratio of the number of blue marbles to the number of red marbles is 5 : 2.
Number of blue marbles / Number of red marbles = 5/2
The number of blue marbles is 5/2 of the number of red marbles.
The ratio of the number of red marbles to the total number of marbles is 2 : 7.
Number of red marbles / Total number of marbles = 2/7
The number of red marbles is 2/7 of the total number of marbles.
- The ratio of Ivan’s weight to Rey’s weight is 1 : 7.
Ivan’s weight is 1/7 of Rey’s weight.
Their total weight is 7 + 1 = 8 units.
Ivan’s weight is 1/8 of their total weight.
The ratio of Rey’s weight to their total weight is 7 : 8.
Rey’s weight is 7/8 of their total weight.
- The number of stamps May has is 3/10 of the total number of stamps they have.
The ratio of the number of stamps Percy has to the total number of stamps they have is 7 : 10.
The ratio of the number of stamps Percy has to the number of stamps May has to the total number of stamps they have is 7 : 3 : 10.
- The total amount of money they had is ₱66.
The ratio of the amount of money Julie had to the amount of money Arnel had in its simplest form is 10 : 7.
The amount of money Hassan had is 5/7 of the amount of money Arnel had.
The amount of money Julie had is 5/11 of the total amount of money they had.
In its simplest form, the ratio of the total amount of money Hassan and Arnel had to the total amount of money all three had is 6 : 11.
References
Department of Education 2016, 21st Century MATHletes 6, Book Media Press Inc., 82-87
Bureau of Elementary Education, Department of Education 2010, Lesson Guide in Elementary Mathematics 6, Book Media Press, Inc., 289-293
DepEd Most Essential Learning Competencies (MELC) in Mathematics for Grade 6
For inquiries or feedback, please write or call:
Department of Education – Bureau of Learning Resources (DepEd-BLR)
Ground Floor, Bonifacio Bldg., DepEd Complex Meralco Avenue, Pasig City, Philippines 1600
Telefax: (632) 8634-1072; 8634-1054; 8631-4985
Email Address: blr.lrqad@deped.gov.ph * blr.lrpd@deped.gov.ph
Leave a Reply