Holt CA Course 1

5-3 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 and are equivalent. 10

62515

106

= 2515

If two ratios are equivalent, they are said to be proportional to each other, or in proportion.

Reading Math

Holt CA Course 1

5-3 Identifying and Writing Proportions

Determine whether the ratios are proportional.

Example 1A: Comparing Ratios in Simplest Forms

,2451

72128

72 ÷ 8128 ÷ 8

= 916

24 ÷ 351 ÷ 3

= 817

Simplify .2451

Simplify . 72128

817

Since = , the ratios are not proportional.9

16

Holt CA Course 1

5-3 Identifying and Writing Proportions

Determine whether the ratios are proportional.

Example 1B: Comparing Ratios in Simplest Forms

,150 105

9063

90 ÷ 9 63 ÷ 9

= 107

150 ÷ 15105 ÷ 15

= 10 7

Simplify .150105

Simplify . 90 63

107

Since = , the ratios are proportional.107

Holt CA Course 1

5-3 Identifying and Writing Proportions

Directions for making 12 servings of rice call for 3 cups of rice and 6 cups of water. For 40 servings, the directions call for 10 cups of rice and 19 cups of water. Determine whether the ratios of rice to water are proportional for both servings of rice.

Example 2: Comparing Ratios Using a Common Denominator

Write the ratios of rice to water for 12 servings and for 40 servings.

Ratio of rice to water, 12 servings:36

Ratio of rice to water, 40 servings: 1019

36

= 3 · 196 · 19

= 57114

1019

= 10 · 619 · 6

= 60114

57114

60114

Write the ratio as a fraction.

Write the ratio as a fraction.

Write the ratios with a common denominator, such as 114.

Since = , the two ratios are not proportional.

Servings of Rice

Cups of Rice

Cups of Water

12 3 6

40 10 19

Holt CA Course 1

5-3 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.

Holt CA Course 1

5-3 Identifying and Writing Proportions

Example 3: Finding Equivalent Ratios and Writing Proportions

Find a ratio equivalent to each ratio. Then use the ratios to find a proportion.

A. 3535

= 3 · 25 · 2

610

= Multiply both the numerator and denominator by any number, such as 2.

35

= 610

Write a proportion.

B. 28162816

= 28 ÷ 416 ÷ 4

2816

= 74

= 74

Divide both the numerator and denominator by any number, such as 4.

Write a proportion.

Holt CA Course 1

5-3 Identifying and Writing Proportions

Determine whether the ratios are proportional.

Check It Out! Example 1

, 135 75

94

9 4

135 ÷ 15 75 ÷ 15

= 9 5

Simplify .135 75

is already in simplest form. 9 4

95

Since = , the ratios are not proportional.94

Holt CA Course 1

5-3 Identifying and Writing Proportions

Use the data in the table to determine whether the ratios of beans to water are proportional for both servings of beans.

Check It Out! Example 2

Write the ratios of beans to water for 8 servings and for 35 servings.

Ratio of beans to water, 8 servings: 43

Ratio of beans to water, 35 servings: 13 9

43

= 4 · 33 · 3

= 129

13 9

129

139

Write the ratio as a fraction.

Write the ratio as a fraction.

Write the ratios with a common denominator, such as 9.

Servings of Beans Cups of Beans Cups of Water

8 4 3

35 13 9

Since = , the two ratios are not proportional.

Holt CA Course 1

5-3 Identifying and Writing ProportionsCheck It Out! Example 3

Find a ratio equivalent to the ratio. Then use the ratios to find a proportion. Possible Answers:

1612

1612

=16 ÷ 412 ÷ 4

1612

= 43

= 43

Divide both the numerator and denominator by any number, such as 4.

Write a proportion.