WHOLE BRAIN LEARNING SYSTEM
OUTCOME-BASED EDUCATION
GRADE
MATHEMATICS
LEARNING
MODULE
QUARTER
WEEK
6
2
1
1
MODULE IN
MATHEMATICS 6
QUARTER 2
WEEK 1
Expressing One Value as a Fraction of Another
Ratio and Proportion
Development Team
Writers:
Nelia T. Obrero
Gemma B. Jose
Editors/Reviewers:
Josephine Gloria S. Tudlong
Ma. Mercedes G. Colobong
Donna Hazel G. Palafox
Illustrators:
Jeshimon C. Patoc
Ronie P. Fiesta
Layout Artists:
Nelia T. Obrero
Gemma B. Jose
Management Team:
Vilma D. Eda
Arnel S. Bandiola
Lourdes B. Arucan
Juanito V. Labao
Marlyn S. Ventura
2
What I Need to Know
This module was designed to help you understand the concept of ratio and
proportion. Through this concept, we can apply it accurately in our day to day lives like
in budgeting, cooking, baking and in business.
As you go through the different activities, you will learn the importance of ratio
and proportion in real-life situations.
MELC:
1. Visualizes the ratio of two given numbers.
2. Expresses one value as a fraction of another given their ratio and vice versa.
3. Defines and illustrates the meaning of ratio and proportion using concrete or
pictorial models.
OBJECTIVES:
At the end of this module, you should be able to:
1.visualize the ratio of two given numbers;
2. express one value as a fraction of another given their ratio and vice versa; and
3. define and illustrate the meaning of ratio and proportion using concrete or pictorial
models.
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What I Know
Directions: Read and analyze each item carefully. Write the letter of the correct
answer in a separate sheet of paper.
1. Which ratio is different from the others?
A. 3 to 7
B. 7:3
C. 3:7
3
D. 7
2. Express 4:12 into fraction form.
A.
12
4
4
B. 4 = 12
C. 12
D. 12 over 4
B. 1:5
C. 3 : 6 = 4 : 8
D. 7 over 10
3. Which is a proportion?
2
A. 3
4. There are 4 boys and 3 girls in a family. What is the ratio of the boys to girls?
A. 3:4
B. 4:3
C. 7:3
D. 3:7
5. Which of the following is the ratio of leaves to flowers?
A. 3 to 4
B. 4 to 5
C. 4 to 3
D. 5 to 4
6. What is the ratio of books to pupils if the teacher distributed 45 books to 45 ?
pupils?
A. 1:45
B. 1:12
C. 45:45
D. 45:1
7. What is the lowest term of the ratio 20 to 25?
A. 4:5
B. 8:10
C. 10:15
D. 10:12
For numbers 8-10, refer to the figure below:
8. What is the ratio of triangles to squares?
A. 2:3
B. 3:4
C. 3:3
D. 3:2
9. What is the ratio of circles to all of the shapes?
A. 3:12
B. 1:3
C. 3:8
D. 1:1
10. What is the ratio of stars to all of the shapes?
A. 4:3
B. 4:2
C. 4:12
D. 3:2
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Lesson
1
Expressing One Value as a
Fraction of Another Given
Their Ratio and Vice Versa
What’s In
In a sheet of paper, do the following activities:
A. Solve for N
2
1. 3 ÷ 6 = N
2.
2
3.
1
1
2
÷8=N
3
÷6=N
3
4. 6 ÷ 5 = N
B. Give the fractional part of the shaded portion.
1.
4.
2.
3.
5.
Lesson Guide in Elementary Mathematics Grade 6, Ateneo de Manila University, Book Media Press, Inc.,2010, p.29
5
What’s New
Let us read and analyze the problem.
In Ms. Trinidad’s Grade 6 Online Class in Mathematics, there are 17 girls and 15 boys.
Compare the number of girls to the number of boys and vice versa.
Study the illustrations:
Guide Questions:
What does the problem ask for? ____________________________________
How will you compare the number of girls to the number of boys? __________
How will you compare the number of boys to the number of girls? _________
What is It
To compare, let us use the concept of ratio. Ratio is defined as a comparison
of two quantities.
Given that there are 17 girls and 15 boys, we can say that 17 to 15 in comparing
girls to boys. Other ways to express such comparison is by writing them using a colon,
𝟏𝟕
17:15 or writing them in fraction form, 𝟏𝟓 . 17 is the 1st term which refers to the girls,
15 is the 2nd term which refers to the boys.
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Using colon
17:15
Using fraction form
17
15
In words
17 to 15
In comparing the number of boys to the number of girls, it can be expressed as:
𝟏𝟓
15 to 17, 15:17, or 𝟏𝟕 , 15 is the 1st term which refers to the boys, 17 is the 2nd term
which refers to the girls.
Using colon
15:17
Using fraction form
15
17
In words
15 to 17
Ratio is the spoken language of arithmetic. It is a way of comparing two or more
quantities having the same units - the quantities may be separate entities or they
may be different parts of a whole.
We can write the ratio of a and b in three ways:
Using colon
a:b
Using fraction form
𝑎
𝑏
In words
a to b
Let us have more examples on writing ratios:
1. What is the ratio of oblongs to triangles? Write the ratio in three forms.
Using colon
10 : 17
Using fraction form
10
17
In words
10 to 17
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2. What is the ratio of cupcakes to ice creams? Write the ratio in three forms.
Using colon
8 : 14
Using fraction form
8
14
In words
8 to 14
Ratio must be expressed in simplest form, which means that the terms are
relatively prime to each other.
If there are 20 boys and 16 girls in a class, then, the ratio of the boys to the
girls is 20 is to 16 and the ratio of the girls to the boys is 16 is to 20.
In a ratio, 20 to 16, the first term is 20 and the second term is 16. It may also
be written as 20:16 or
20
. Even if the ratio is in fractional form, we say twenty to
16
sixteen.
Now let us reduce the ratio in simplest form.
Step 1: Find the Greatest Common Factor (GCF) of 20 and 16 using prime
factorization.
20
10
5
16
2
8
2
4
2
2
2
2
20 = 5 X 2 X 2
16 =
2X2X2X2
GCF = 2 x 2
=4
Step 2: Divide the first term and the second term by the GCF.
20
20 ÷4
5
= 16 ÷ 4 = 4
16
Therefore, the simplest form of 20:16 is 5:4.
8
Let us have more examples:
Example 1: Reduce the ratio 81:24 to lowest term
Solution: The GCF of 81 and 24 is 3.
81
24
81
Answer: 24 =
=
81 ÷3
24 ÷3
=
27
8
27
8
Example 2: There are 20 teachers to 520 students. What is the ratio of teachers to
students? Express the ratio in lowest term.
Solution: The GCF of 20 and 520 is 20.
20
20 ÷20
1
= 520 ÷20 = 26
520
Answer:
20
520
1
= 26
The order in which the ratio is expressed is important. Therefore, the order of
the terms in a ratio must correspond to the order of objects being compared.
In a ratio, a part can be compared to its whole.
In the preceding example, the ratio of the number of boys to the total number
of the students is 20 is to 36 and the ratio of the number of girls to the number of
total students is 16 is to 36.
If we compare the part to the total, the ratio of the part to the total has the
same meaning as fraction.
Example: Compare the number of vowels to consonants and vice versa in the
following word using colon, fraction form and in words.
ADORABLE
Letters
Number of Letters
Vowels
A, O, and E
3
Consonants
D, R, B and L
4
Ratio of vowels to consonants:
Using colon
3:4
Using fraction form
3
4
In words
3 to 4
9
Ratio of consonants to vowels:
Using colon
4:3
Using fraction form
4
3
In words
4 to 3
Ratio of vowels and consonants to vowels:
Using colon
7:3
Using fraction form
7
3
In words
7 to 3
In ratio, we compare two numbers or quantities with the same unit of measure. If
these are in different units, they must be expressed in the same units.
Examples:
1. 7 days to 3 weeks. Express in days (7days = 1 week)
7 days: 21 days or 7:21 or 1:3 in lowest term
2. 1 year to 4 months. Express in months (12 months = 1 year)
12 months: 4 months or 12:4 or 3:1
What’s More
Use a sheet of paper in answering the following activities:
A. Write each of the following as ratio in three forms. Express your answers in simplest
form.
Word Form
Colon Form
Fraction Form
1. 15 vases to 75 roses
2. 22 boys to 33 girls
3. 25 dogs to 45 cats
4. 10 meters to 400 centimeters
5. 18 hammers to 24 nails
B. Read and answer the following problems.
1. Every quarter, each pupil submits 2 projects in Science. Give the ratio of projects
to quarters.
2. There are 20 buses at a station. If each bus has 6 wheels, what is the ratio of
buses to wheels?
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What I Have Learned
A ratio is a comparison of two values expressed as a word, a fraction or
colon form. A ratio has two terms. In the ratio 6:10, the first term 6, is the numerator
and is the number being compared. The second term 10 is the denominator and
is the number to which the first number is being compared.
Ratio is expressed in lowest term by dividing its Greatest Common Factors
to the first term and second term such as:
6
10
3
or 5;
10
20
1
or 2;
12
36
1
or 3
In a ratio, the order in which the numbers or quantities is written is important.
Example, the ratio of 5 white roses to 10 red ones is 5:10. This ratio is different
from 10:5.
What I Can Do
Directions: Give the ratio of each of the following in three different ways. Reduce
your answer in lowest term, if necessary. Write your answers in a separate sheet of
paper.
1. atis to santol
Word
Form
Colon
Form
2. sipa ball to golf balls
Fraction
Form
Word
Form
Colon
Form
Fraction
Form
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3. buttons to gems
Word
Form
Colon
Form
4. ribbons to marbles
Fraction
Form
5. sandwiches to orange juice
Word
Form
Colon
Form
Fraction
Form
7. skirts to blouses
Word
Form
Colon
Form
Colon
Form
Colon
Form
Fraction
Form
6. pencils to erasers
Word
Form
Colon
Form
Fraction
Form
8. pair of shoes to pair of socks
Fraction
Form
9. laptops to cellphones
Word
Form
Word
Form
Word
Form
Colon
Form
Fraction
Form
10. notebooks and bags to bags
Fraction
Form
Word
Form
Colon
Form
Fraction
Form
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Lesson
2
Ratio and Proportion Using
Concrete or Pictorial Models
What’s In
Directions: In a sheet of paper, write the following ratio in colon form and express
your answers in simplest form.
Colon Form
1. 6 baskets to 24 fruits
2. 48 plates to 32 glasses
3. 15 rooms to 480 pupils
4. 18 apples to 12 oranges
5. 9 pencils to 21 paper
What’s New
Read the word problem below and answer the questions that follow. Write your
answers on a separate sheet of paper.
Jane bought 5 pens for PhP60.00 and Jia bought 10 pens at PhP120.00
at Jahnel’s School Supplies Store. Give the ratio of pens to the amount of each
child paid.
PhP60.00
PhP120.00
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Answer the following questions:
1. What did Jane and Jia buy? __________________________________________
2. How many pens did each of them buy? ________________________________
3. How much did each of them pay? ______________________________________
4. What are being compared in the problem? _______________________________
What is It
Let us go back to the word problem given.
What are being compared? The number of pens and the amount each
child paid.
How can we show it?
Number of pen
Amount paid
Jane
5 pens
PhP60.00
Jia
10 pencils
PhP120.00
We can write the two ratios in two ways: using colon form and fraction form.
colon form
5:60 = 10:120
fraction form
5
10
= 120
60
5 is called the first term
60 and 10 are called means
60 is called the second term
5 and 120 are called extremes
10 is called the 3rd term
means
120 is called the 4th term
5:60 = 10:120
extremes
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What do you call two equal ratios? Two equal ratios form a proportion.
In a proportion, the product of the means and the extremes are equal.
In the previous example, 5:60 = 10:120
Means:
60 x 10 = 600
Extremes:
5 x 120 = 600
The products are the same so, 5:60 = 10:120 is a proportion.
Here are more examples. The following pair of ratios form a proportion.
1. 3: 4= 15:20
means
3:4 = 15:20
3
15
= 20
4
extremes
Means:
Extremes:
4 x 15= 60
3 x 20 = 60
4 x 15 = 60
3 x 20 = 60
The products are the same so, 3: 4 = 15:20 is a proportion.
2. 5: 25= 10:30
means
5:25 = 10:30
5
25
10
= 30
extremes
Means:
Extremes:
25 x 10 = 250
5 x 30 = 150
25 x 10 = 250
5 x 30 = 150
The products are not the same so, 5: 25= 10:30 is not a proportion.
If a given proportion, a term is missing, it can be solved using cross
multiplication.
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Examples:
1.
3:2 = 9:n
3
9
=𝑛
2
3xn=2x9
3𝑛
18
= 3
3
n= 6
means: 2 x 9 = 18
extremes: 3 x 6 = 18
2.
n: 1 = 30:2
𝑛
30
= 2
1
n x 2 = 1 x 30
2𝑛
30
= 2
2
n = 15
means: 1 x 30 = 30
extremes: 15 x 2 = 30
Remember:
If two ratios are equal, the two ratios form a proportion.
A proportion is formed if the cross products of the two ratios are equal.
What’s More
Directions: In a sheet of paper, write Yes if each of the following forms a proportion
and write No if it’s not.
__________ 1. 2:3 = 4:6
__________ 6. 12:5 = 4:5
__________ 2. 4:5 = 8:9
__________ 7. 2:6 = 4:10
__________ 3. 3:7 = 4:9
__________ 8. 8:10 = 4:6
__________ 4. 6:7 = 24:28
__________ 9. 15:20 = 5:6
__________ 5. 2:5 = 4:12
__________ 10. 28:42 = 2:3
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What I Have Learned
A proportion is an equation stating that two ratios are equal. It can be
written in fraction form or in colon form.
12
Example: fraction form
colon form
14
6
=7
12:14= 6:7
12 is called the first term
14 and 6 are called means
14 is called the second term
12 and 7 are called extremes
6 is called the 3rd term
means
7 is called the 4th term
12:14 = 6:7
extremes
In a proportion, the first and last terms are called the extremes while the
second and the third terms are called the means.
What I Can Do
Directions: Solve for the value of n in each proportion.
__________ 1. n : 6 = 8 : 4
__________ 2. 6 : n = 3 : 10
__________ 3. 12 : 15 = 20 : n
__________ 4.
__________ 5.
4
2
𝑛
=8
𝑛
12
4
=3
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II. Read and solve.
1. At the Bookstore, 5 pieces of Oslo paper cost PhP2.50. What is the cost of 30
pieces of Oslo paper?
2. Mrs. Juan’s family can consume 10 kilograms of rice in 5 days. How many
kilograms of rice can they consume in 20 days?
3. Four pencils cost PhP32.00. What is the cost of 12 pencils?
4. Two kilograms of avocados cost PhP80.00. What is the cost of 6 kilograms of
avocado?
5. Mariel saves PhP80.00 in 4 weeks. At this rate, how long will it take her to save
PhP160.00?
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Assessment
Directions: Read each item carefully. Choose the best answer among the choices
given and write the letter of the correct answer on your answer sheet.
1. What is the equivalent ratio of
A. 1 to 5
1
5
in words?
B. 2 to 5
C. 3 to 5
D. 4 to 5
C. 5 : 1
D. 4 : 3
2. What is the lowest term of the ratio 3 to 15?
A. 3 : 4
B. 1 : 5
3. Write the ratio of
A. 5 to 6
to
B. 10 to 12
C. 6 to 5
D. 12 to 10
4. Which of the following is a correct proportion?
A. 4:5 = 12:15
B. 1:2 = 3:4
C. 4: 6 = 7 : 8
D. 5: 9 = 10:12
5. What is the ratio of books to pupils if the teacher distributed 50 books to 25
pupils?
A. 25 : 50
B. 1 : 5
C. 1 : 2
D. 2 : 1
6. What ratio can you form from the following pictures?
A. 5 : 8
B. 8 : 5
C.10 : 16
D. 3 : 16
7. What proportion can you form from the following shapes?
A. 6 : 2 = 2 : 1
B. 6 : 2 = 3 : 1
C. 2 : 6 = 1 : 2
D. 1 : 2 = 2 : 1
8. Each day Alaisa saves PhP20.00 and spends Php15.00. What is the ratio of her
savings to her expenses?
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A. 15 : 20
B. 5 : 20
C. 20 : 15
D. 1 :15
For numbers 9-10, refer to the following situation:
There are 40 men, 25 women, and 30 children in a room.
9. What is the ratio of women to men?
A. 30 : 25
B. 40 : 25
C. 25: 40
D. 25 : 30
C. 25 : 40
D. 30 : 25
10. What is the ratio of children to men?
A. 30 : 40
B. 40 : 30
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Answer Key
21
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References
Books:
Adoracion M. Acuńa, Mathematics for Everyday Life Textbook for Grade Six, Quezon
City, JTW Corporation
Apistar, Elmer M. et.al, Soaring 21st Century Mathematics Grade 6, Second Edition,
Quezon City,Philippines, Phoenix Publishing House, Inc.
Frialde, Maysee B., Toward Excellence in Mathematics 6, pp.184-193
Lesson Guide in Elementary Mathematics Grade 6, Ateneo de Manila University, Book
Media Press, Inc.,2010, pp .289-301
New Ways in Numbers, Teacher’s Edition
Perez, M. et. al (2016). 21st Century Mathletes Textbook. Vibal Group Inc., pp. 82-91
Youtube /Youtube Pictures:
https://www.dreamstime.com/set-five-multi-colored-pens-vector-illustration-set-fivemulti-colored-pens-image116318566
https://clipartix.com/ice-cream-cone-clipart-image-38168/
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