Ratios & Equivalent Ratios

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What is a ratio?

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A ratio is a comparison of two quantities that shows the relative size of one quantity to another, often expressed as 'a:b'.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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What does it mean for two ratios to be equivalent?

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Two ratios are equivalent if they represent the same relationship between quantities, meaning they can be simplified to the same fraction.

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CCSS.6.RP.A.3A

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How do you find an equivalent ratio?

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To find an equivalent ratio, you can multiply or divide both terms of the ratio by the same non-zero number.

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CCSS.6.RP.A.3A

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What is the ratio of flour to water if 48 cups of flour are used with 12 pints of water?

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The ratio of flour to water is 48:12, which simplifies to 4:1.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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If the ratio of soup to pasta is 40:12, what is the equivalent ratio when both are divided by 4?

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The equivalent ratio is 10:3.

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CCSS.6.RP.A.3A

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Which of the following ratios is equivalent to 1:2? (Options: 3:6, 3:8, 4:12, 9:60)

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3:6 is equivalent to 1:2.

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CCSS.6.RP.A.3A

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If a recipe calls for a ratio of 5:4 for sugar to flour, how much sugar is needed for 20 cups of flour?

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To find the amount of sugar, set up the ratio: 5/4 = x/20. Solving gives x = 25 cups of sugar.

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What is the missing number in the ratio 3:8 if the first number is 6?

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The missing number is 16, because 3:8 is equivalent to 6:16.

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How can you express the ratio 20:16 in simplest form?

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The simplest form of 20:16 is 5:4.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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If you have a ratio of 2:5 and you want to find an equivalent ratio with a total of 70 parts, what are the two quantities?

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The two quantities are 28 and 42, because 2 + 5 = 7, and (2/7)*70 = 20 and (5/7)*70 = 50.