5-2 Identifying and Writing Proportions
Learn to find equivalent ratios and to
identify proportions.
Course 2
5-2 Identifying and Writing Proportions
Vocabulary
equivalent ratios
proportion
Course 2
5-2 Identifying and Writing Proportions
Students in Mr. Howell’s math
class are measuring the width
w and the length l of their
heads. The ratio of l to w is 10
inches to 6 inches for Jean and
25 centimeters to 15
centimeters for Pat.
Course 2
5-2 Identifying and Writing Proportions
These ratios can be written as the
fractions 10 and 25 . Since both simplify
6
15
to 5 , they are equivalent. Equivalent
3
ratios are ratios that name the same
comparison.
Course 2
5-2 Identifying and Writing Proportions
An equation stating that two ratios are
equivalent is called a proportion. The
equation, or proportion, below states that
the ratios 10 and 25 are equivalent.
6
15
10 = 25
15
6
Reading Math
Read the proportion 10 = 25 by saying “ten is to six
6
15
as twenty-five is to fifteen.”
Course 2
5-2 Identifying and Writing Proportions
If two ratios are equivalent, they are
said to be proportional to each other,
or in proportion.
Course 2
5-2 Identifying and Writing Proportions
Additional Example 1A: Comparing Ratios in
Simplest Forms
Determine whether the ratios are proportional.
A. 24 , 72
51 128
8
24 ÷ 3
=
17
51 ÷ 3
Simplify 24 .
51
72 ÷ 8
9
=
16
128 ÷ 8
Simplify 72 .
128
Since
Course 2
9
8
=
, the ratios are not proportional.
17 16
5-2 Identifying and Writing Proportions
Additional Example 1B: Comparing Ratios in
Simplest Forms
Determine whether the ratios are proportional.
B. 150 , 90
105 63
150 ÷ 15 10
=
7
105 ÷ 15
90 ÷ 9
10
=
7
63 ÷ 9
Since
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Simplify 150 .
105
Simplify
90
.
63
10 10
=
, the ratios are proportional.
7
7
5-2 Identifying and Writing Proportions
Try This: Example 1A
Determine whether the ratios are proportional.
A. 54 , 72
63 144
6
54 ÷ 9
=
7
63 ÷ 9
Simplify 54 .
63
72 ÷ 72
1
=
144 ÷ 72 2
Simplify 72 .
144
Since
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1
6
= , the ratios are not proportional.
2
7
5-2 Identifying and Writing Proportions
Try This: Example 1B
Determine whether the ratios are proportional.
B. 135 , 81
75 45
9
135 ÷ 15
=
5
75 ÷ 15
81 ÷ 9
9
=
5
45 ÷ 9
Since
Course 2
Simplify 135 .
75
Simplify
81
.
45
9
9
=
, the ratios are proportional.
5
5
5-2 Identifying and Writing Proportions
Additional Example 2: Comparing Ratios Using a
Common Denominator
Use the data in the table to determine whether the ratios
of rice to water are proportional for both servings of rice.
Servings of Rice
Cups of Rice
Cups of Water
12
3
6
40
10
19
Write the ratios of rice to water for 12 servings and for 40 servings.
3
Ratio of rice to water, 12 servings: 6
10
Ratio of rice to water, 40 servings:
19
3 = 3 · 19 = 57
6
6 · 19
114
10 = 10 · 6 = 60
19 19 · 6 114
Write the ratio as a fraction.
Write the ratio as a fraction
Write the ratios with a
common denominator,
such as 114.
Since 57 = 60 , the two ratios are not proportional.
114
Course 2
114
5-2 Identifying and Writing Proportions
Try This: Example 2
Use the data in the table to determine whether the ratios of
beans to water are proportional for both servings of beans.
Servings of Beans
Cups of Beans
Cups of Water
8
4
3
35
13
9
Write the ratios of beans to water for 8 servings and for 35 servings.
4
Write the ratio as a fraction.
Ratio of beans to water, 8 servings: 3
13
Write the ratio as a fraction
Ratio of beans to water, 35 servings:
9
4 = 4 · 9 = 36
Write the ratios with a
3
3·9
27
common denominator,
13 = 13 · 3 = 39
such as 27.
9
27
9·3
Since 36 = 39 , the two ratios are not proportional.
27
Course 2
27
5-2 Identifying and Writing Proportions
You can find an equivalent ratio by
multiplying or dividing the numerator
and the denominator of a ratio by
the same number.
Course 2
5-2 Insert
Lesson
Here
Identifying
andTitle
Writing
Proportions
Additional Example 3: Finding Equivalent Ratios and
Writing Proportions
Find a ratio equivalent to each ratio. Then use
the ratios to find a proportion.
A. 3
5
3 = 3 · 2 =6
5
5 · 2 10
3 = 6
10
5
B. 28
16
28 = 28 ÷ 4 7
=
16 16 ÷ 4 4
28 = 7
16 4
Course 2
Multiply both the numerator and
denominator by any number such as 2.
Write a proportion.
Divide both the numerator and
denominator by any number such as 4.
Write a proportion.
5-2 Insert
Lesson
Here
Identifying
andTitle
Writing
Proportions
Try This: Example 3
Find a ratio equivalent to each ratio. Then use
the ratios to find a proportion.
A. 2
3
2 = 2 · 3 =6
3
3·3 9
2 = 6
9
3
B. 16
12
16 = 16 ÷ 4 = 4
3
12 12 ÷ 4
16 = 4
12 3
Course 2
Multiply both the numerator and
denominator by any number such as 3.
Write a proportion.
Divide both the numerator and
denominator by any number such as 4.
Write a proportion.
5-2 Identifying
Insert Lesson
andTitle
Writing
Here
Proportions
Lesson Quiz
Determine whether the rates are proportional
by writing them in simplest form and
comparing them.
9
12
1. 30 , 40
3 , 3 ; proportional
10 10
12 10
2. 21 , 15
4 , 2 ; not proportional
7 3
Determine if the ratios are proportional
by finding a common denominator.
3 2
3. 8 , 5
15 , 16 ; not proportional
40 40
Course 2
4. 3 , 9
7 21
9 , 9 ; proportional
21 21
5-2 Identifying
Insert Lesson
andTitle
Writing
Here
Proportions
Lesson Quiz
5. In a local pre-school, there are 5 children for every
teacher. Write an equivalent ratio to show how
many children there would be if there were 4
teachers.
5 , 20
1 4
Course 2
Homework
• 5-2 Worksheet