Holt CA Course 1 5-3 Identifying and Writing Proportions An equation stating that two ratios are...
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Transcript of Holt CA Course 1 5-3 Identifying and Writing Proportions An equation stating that two ratios are...
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.