5.2: Ratios and Equivalence

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What is a ratio?

Back

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

Front

What is the ratio of 6 to 5 expressed in simplest form?

Back

The ratio 6:5 is already in simplest form.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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If the ratio of boys to girls in a class is 3:4, how many boys are there if there are 28 students in total?

Back

There are 12 boys. (3 parts boys out of 7 total parts: 3/7 * 28 = 12)

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What is the equivalent ratio of 5:4 when both terms are multiplied by 5?

Back

The equivalent ratio is 25:20.

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CCSS.6.RP.A.3A

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If you have a ratio of 12:20, what is its simplest form?

Back

The simplest form of 12:20 is 3:5.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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How do you write the ratio of 4 nickels to a total of 12 coins?

Back

The ratio is written as 4:12.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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What is the relationship between the ratios 3:4 and 6:8?

Back

The ratios 3:4 and 6:8 are equivalent because both can be simplified to the same fraction.

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CCSS.6.RP.A.3A

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If a recipe calls for a ratio of 2 cups of flour to 3 cups of sugar, how much sugar is needed for 4 cups of flour?

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You would need 6 cups of sugar. (The ratio 2:3 means for every 2 cups of flour, 3 cups of sugar are needed.)