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Reading Math. If two ratios are equivalent, they are said to be proportional to each other, or in proportion. 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 6. 25 15.

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10 6

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  1. Reading Math If two ratios are equivalent, they are said to be proportional to each other, or in proportion. 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 6 25 15 25 15 10 6 =

  2. 8 17 24 ÷ 3 51 ÷ 3 24 51 Simplify . = 72 ÷ 8 72 128 9 16 = Simplify . 128 ÷ 8 9 16 8 17 Since = , the ratios are notproportional. Example 1A: Comparing Ratios in Simplest Forms Determine whether the ratios are proportional. 24 51 72 128 ,

  3. 150 105 10 7 150 ÷ 15 105 ÷ 15 Simplify . = 90 ÷ 9 90 63 10 7 = Simplify . 63 ÷ 9 10 7 10 7 Since = , the ratios are proportional. Example 1B: Comparing Ratios in Simplest Forms Determine whether the ratios are proportional. 150 105 90 63 ,

  4. Since = , the two ratios are notproportional. Example 2: Comparing Ratios Using a Common Denominator 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. Write the ratios of rice to water for 12 servings and for 40 servings. 3 6 Ratio of rice to water, 12 servings: Write the ratio as a fraction. 10 19 Ratio of rice to water, 40 servings: Write the ratio as a fraction. Write the ratios with a common denominator, such as 114. 3 6 10 19 60 114 3 · 19 6 · 19 57 114 10 · 6 19 · 6 = = = = 57 114 60 114

  5. You can find an equivalent ratio by multiplying or dividing the numerator and the denominator of a ratio by the same number.

  6. Example 3: Finding Equivalent Ratios and Writing Proportions Find a ratio equivalent to each ratio. Then use the ratios to find a proportion. 3 5 A. 3 5 3 · 2 5 · 2 6 10 Multiply both the numerator and denominator by any number, such as 2. = = 6 10 3 5 = Write a proportion. 28 16 B. Divide both the numerator and denominator by any number, such as 4. 28 16 28 ÷ 4 16 ÷ 4 7 4 = = 7 4 28 16 = Write a proportion.

  7. 135 75 9 5 135 ÷ 15 75 ÷ 15 Simplify . = 9 4 9 4 is already in simplest form. 9 4 9 5 Since = , the ratios arenotproportional. Check It Out! Example 1 Determine whether the ratios are proportional. 135 75 9 4 ,

  8. Since = , the two ratios are notproportional. Check It Out! Example 2 Use the data in the table to determine whether the ratios of beans to water are proportional for both servings of beans. Write the ratios of beans to water for 8 servings and for 35 servings. 4 3 Write the ratio as a fraction. Ratio of beans to water, 8 servings: 13 9 Write the ratio as a fraction. Ratio of beans to water, 35 servings: Write the ratios with a common denominator, such as 9. 4 3 4 · 3 3 · 3 12 9 13 9 = = 12 9 13 9

  9. Check It Out! Example 3 Find a ratio equivalent to the ratio. Then use the ratios to find a proportion. Possible Answers: 16 12 Divide both the numerator and denominator by any number, such as 4. 16 12 16 ÷ 4 12 ÷ 4 4 3 = = 16 12 Write a proportion. 4 3 =

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