This document provides a summary of Module 8 on ratios from a mathematics curriculum. It contains 3 lessons: expressing ratios using colon and fraction form, expressing ratios in simplest form, and identifying and writing equivalent ratios. The module is designed to help students master ratios and be able to express them in different ways. It includes examples and activities for students to practice the concepts. The learning objectives are to express ratios using colons and fractions, express ratios in simplest form, identify equivalent ratios, and write equivalent ratios.
2. 1
This Self Learning Module (SLM) was designed and written with you in mind to help you master
the lesson on Identifying and Writing Equivalent Ratios and Expressing Ratios in their Simplest
Forms. The scope of this learning material focuses on the many different learning situations.
Moreover, the language used recognizes the diverse vocabulary level of learners. The lessons
are also arranged following the standard sequence of the course. Hence, the order in which
you read them can be changed to correspond with the textbook you are now using.
The module contains:
Lesson 8.1: Expressing Ratios Using Colon (:) and Fraction Form
Lesson 8.2: Expressing Ratios in Simplest Form
Lesson 8.3: Identifying and Writing Equivalent Ratios
After going through this module, you are expected to:
1. express ratio using a colon (:) and fraction;
2. express ratios in their simplest form;
3. identify equivalent ratios; and
4. write equivalent ratios.
3. 2
Pretest
Directions: Read and analyze each item carefully. Write the letter of the correct answer on a
separate sheet of paper.
1. Which of the following is the simplest form of 25:150?
A.
1
6
B.
5
6
C. 5:30 D. 25:15
2. What is the simplest form of
48
72
?
A.
1
2
B. 2:3 C.
4
8
D. 4:12
3. Express ten boys to three girls as a ratio in a fraction form.
A. 3:10 B.
3
10
C. 10:3 D.
10
3
4. What is the lowest term of 32:48?
A.
2
3
B. 4:6 C.
4
8
D. 6:8
5. Which of the following is an equivalent ratio of 30:180?
A.
1
6
B. 5:6 C.
5
30
D. 15:25
6. Write an equivalent ratio of 40:60.
A.
1
2
B. 2:3 C.
2
6
D. 4:8
7. The following are equivalent ratios of
3
5
EXCEPT
A. 6:10 B.
6
12
C. 9:15 D.
12
20
8. What is the simplest form of 10:12?
A. 5:6 B.
20
24
C. 30:36 D.
40
48
9. In the launching of World Children’s Day, there are 40 girls and 25 boys participated
in the activity. What is the ratio of the girls to the boys in the lowest terms?
A. 2:3 B. 5:8 C. 6:8 D. 8:5
10. There were 35 seedlings planted. Ten of them died. What is the ratio of the seedlings
that survived to the seedlings died?
A. 10:35 B. 10:25 C. 25:10 D. 25:35
4. 3
Lesson 8.1 Expressing Ratio Using Colon (:) and Fraction Form
Compare the following quantities.
1. bags to books = 2 bags is to 4 books
2. boys to girls = 3 boys is to 9 girls
3. ducks to eggs = 4 ducks is to 16 eggs
A ratio is a comparison of two quantities or given sets of objects. It is also a pair of numbers
that compares two quantities in the same unit by division.
There are two ways of writing ratio:
We write using ratio in the colon (:) or a fraction form.
Word Phrase Colon Form Fraction Form
2 bags to 4 books 2:4
2
4
3 boys to 9 girls 3:9
3
9
4 ducks to 16 eggs 4:16
4
16
Remember:
The order of the terms of a certain ratio is the same as the order of the things being compared.
The ratio 2:4 means that there are 2 bags and 4 books, in which case the bags comes first
before the books.
Example 2:
Luis has 20 candies and 35 chocolates.
What is the ratio of the number of candies to the number of chocolates?
The ratio is 20 is to 35 where 20 are for the candies and 35 for chocolates.
As a fraction, it is written as
20
35
, using a colon the ratio is written as 20:35.
MATH
SCIENCE
ENGLISH
FILIPINO
5. 4
Lesson 8.2 Expressing Ratio in Simplest Form
Since ratios are fractions, we may also express them in the simplest form. The simplest form
of the three given ratios will answer the problem.
Simplifying ratios is just the same as simplifying fractions since ratios can also be written as
fractions. To reduce ratios in the simplest form, divide the numerator and the denominator of
each ratio by their greatest common factor (GCF).
Look at the table below:
Colon
Form
Fraction
Form
GCF of numerator and
denominator
Divide GCF to the numerator
and denominator
2:4
2
4
2
2
4
÷
2
2
=
1
2
or 1:2
3:9
3
9
3
3
9
÷
3
3
=
1
3
or 1:3
4:16
4
16
4
4
16
÷
4
4
=
1
4
or 1:4
Explain
We divide the numerator and the denominator by a common factor until the two numbers have
the number 1 as the only common factor.
Example 2: Simplifying ratio in fraction form.
.
Application
The ratio of chicken to goat in grandfather’s farm is 6:2. Write the ratio of the number of
chickens to the number of goats in the simplest form.
Solution:
GCF of 6:2 is 2.
6÷2=3;
2÷2=1
So, 3:1 is the simplest form of 6:2.
Lesson 8.3 Identifying and Writing Equivalent Ratios
Study and analyze the situation.
Lisa needs 2 eggs to make 7 pancakes. If she wants to make 28 pancakes, how many eggs
are needed?
Study the table.
eggs 2 4 6 8
pancakes 7 14 21 28
Explanation
To find the number of eggs needed to make 28 pancakes, we can use skip counting for both
numbers until the counting for pancakes reaches 28.
Therefore, Lisa needs 8 eggs to make 28 pancakes.
The table above shows the list of equivalent ratios of 2:7. Equivalent Ratios are ratios that
have the same value.
Divide the pair by the GCF.
10
18
÷
2
2
=
5
9
, GCF is 2
5
9
is the lowest term.
10
18
6. 5
Identifying Equivalent Ratios
A. Cross Multiplication Method.
Example 1: Are ratios 3:5 and 6:10 equivalent ratios?
Express the ratios in fractions. Do the cross multiplication.
numerator of first fraction x denominator of 2nd fraction – 3 x 10
denominator of 1st fraction x numerator of 2nd fraction – 5 x 6
Since the products are the same, the ratio 3:5 and 6:10 are equivalent ratios.
B. Multiplication of Means and Extremes.
Extremes
a : b = c : d
Means
Example 2: Are ratios 3:4 and 9:12 equivalent ratios?
Multiply the means and extremes.
Since the products are the same, the ratios are equivalent.
C. Finding the simplest form. If the simplest form of two or more ratios is the same or
equal, then the ratios are equivalent.
Example 3: Are 20:30 and 6:9 equivalent ratios?
Simplify the ratios:
For 20/30, the GCF is 10
20 ÷ 10 = _2_
30 ÷ 10 = 3
The simplest form of 20/30 is 2/3
For 6:9, the GCF is 3
6 ÷ 3 = _2_
9 ÷ 3 = 3
The simplest form of 6:9 is 2/3
Therefore, the given ratios are equivalent.
Writing Equivalent Ratios
A. Multiplying Both Quantities
Jane uses 4 cups of flour and 1 cup of sugar in her recipe of hotcake. She wants to
make 10 batches of the cake. How many cups of flour and sugar will she need?
Find the equivalent ratios by following the steps:
Step 1: Write the ratio in fraction form
Step 2: Multiply both numerator and denominator by 10 to find the equivalent ratio.
(10 for the batches)
The ratio above tells that Jane needs 40 cups of flour and 10 cups of sugar for her to
make 10 batches of hotcake. Therefore, 4:1 and 40:10 are equivalent ratios.
B. Dividing Both Quantities
Find the equivalent ratio of 50:15.
Write the ratio in a fraction form then look for a number that is divisible by both
quantities or find it GCF.
GCF for 50 and 15 is 5, so
50 ÷ 5 = 10;
15 ÷ 5 = 3
50:15 = 10:3
So, the equivalent ratio of 50:15 is 10:3.
3
5
=
6
10
3×10 = 5×6
30 = 30
The first and last terms are called “extremes”.
The middle terms are called “means”.
3:4 = 9:12
3×12 = 4×9
36 = 36
4
1 cups of sugar
cups of flour
4
1
×
10
10
=
40
10
𝑜𝑟 40: 10
Divide both pair by 5.
7. 6
General Directions: Copy and answer activities 1-3 on a separate sheet of paper.
Activity 1. Expressing Ratio Using Colon (:) and Fraction Form
Directions: Express the following ratios below using colon and fraction form.
Colon Form Fraction Form
1. 32 children to 12 parents __________ ___________
2. 35 books to 20 pupils __________ ___________
3. 20 orchids to 50 ladies __________ ___________
4. 15 ladies to 30 gentlemen __________ ___________
5. 48 girls to 32 boys __________ ___________
6. 45 teachers to 120 pupils __________ ___________
7. 10 parents to 20 teachers __________ ___________
8. 52 mangoes to 64 lanzones __________ ___________
9. 13 baskets to 52 strawberries __________ ___________
10. 10 dogs to 15 cats __________ ___________
Activity 2. Ratios in Simplest Form
A. Write () if the given ratio in each number is in simplest form, if not, give its simplest
form.
Example a.
8
13
= Example b. 9:3 = 3:1
1. 7:11 = 4.
10
11
=
2.
26
65
= 5. 24:15 =
3. 19:57 =
B. Complete the table below.
Ratio GCF
Divide numerator and
denominator by the GCF
Simplest Form
Ex. 40:64 8
40 ÷ 8 = 5
64 ÷ 8 = 8
5:8
1. 18:9 ?
18 ÷ 9 = 2
9 ÷ 9 = 1
?
2. 12:72 ?
12 ÷ 12 = 1
72 ÷ 12 = 6
1:6
3. 36:48 12 ? ?
4. 11:110 ? ? 1:10
5. 54:18 18
54 ÷ 18 = 3
18 ÷ 18 = 1
?
8. 7
Activity 3. Identifying and Writing Equivalent Ratios
A. Match column A to column B to make the pair of ratio equivalent.
B. Complete the equal ratios.
1.
2
3
=
6
2.
4
5
=
15
3. 3: = 9:21
4. :21=8:3
5.
24
12
=
12
A
1.
6
21
2. 8:6
3.
2
5
4. 3:4
5. 6:36
B
A. 36:216
B. 2:7
C. 12:15
D.
4
10
E.
21
28
F.
16
12
9. 8
Directions: Complete the 3-2-1 Chart about your discoveries in expressing ratios in the colon
(:) and fraction form, and in simplest forms; and identifying and writing equivalent
ratios. Write your answers on a separate sheet of paper.
10. 9
Directions: Choose the letter of the correct answer. Write the chosen letter on a
separate sheet of paper.
1. Express 40 pupils to 12 teachers in a fraction form of a ratio.
A. 12:40 B.
12
40
C. 40:12 D.
40
12
2. What is the lowest term of 24:64?
A.
3
8
B.
3
12
C. 4:8 D. 4:1
3. The following are equivalent ratios of 4/5 EXCEPT
A. 4:10 B.
8
10
C. 12:15 D.
20
25
4. Which of the following is an equivalent ratio of 10:6?
A. 5:6 B.
10
6
C. 20:12 D.
30
36
5. Which of the following is an equivalent ratio of 50:180?
A. 5:16 B.
6
18
C.
80
150
D. 100:360
6. Write an equivalent ratio of 50:60.
A. 1:2 B. 2:3 C.
4
6
D.
5
6
7. Which of the following is the simplest form of 45:180?
A. 1:4 B.
1
6
C.
5
36
D. 9:45
8. What is the simplest form of
36
66
?
A. 3:11 B.
6
11
C. 6:18 D.
6
36
9. If 12 pencils are bought for Php 60.00, how much will you pay for 25 pencils at the
same rate?
A. Php125.00 B. Php128.00 C. Php130.00 D. Php135.00
10. There were 40 falcata seedlings planted in a farm. Five of them died. What is the
ratio of the seedlings that survived to the total number of seedlings planted from the
beginning?
A. 5:35 B. 5:40 C. 35:5 D. 35:40
Posttest
12. Books:
Lumbre, Angelina P., Alvin C. Ursua, Donnel P. Placer, Jaime R. Burgos, and Reynaldo A. Sy. 2016. 21st
Century MATHletes 5. Quezon City, Philippines: DepEd. Pages 152-165 (Textbook)
Borromeo, Melody G., Rosaline B. Abang, Dante D. Delas Alas, Bengie C. Osita, Joel E. Artista, Melanie
H. Rivera, Darrel C. Dueňas, Walner A. Saturno, Madison M. Mendoza, Junlor C. Dacsa, Anne
Kathleen B. Afan, Napoleon A. Montero III. 2016. 21st
Century MATHletes 5. Quezon City,
Philippines: DepEd. Pages 65 - 71 (Teacher’s Manual)
Published by the Department of Education, Caraga Region
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Schools Division Superintendent: Karen L. Galanida
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Office Address : M. Ortiz Street, Barangay Washington
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Telephone : (086) 826-1268; (086) 826-3075; (086) 826-8931
E-mail Address : surigao.city@deped.gov.ph
Development Team of the Self-Learning Module (SLM)
Writers : Leland Noel C. Lisondra
Editor : Ezel G. Jainar
Evaluators : Noemi D. Lim, Marissa A. Cantutay, Leslie Anne S. Bajan
Lay-out Artist : Leslie Anne S. Bajan
Management Team : Karen L. Galanida
Florence E. Almaden
Carlo P. Tantoy
Elizabeth S. Larase
Noemi D. Lim
