Ratios, Rates, and Equivalent Ratios

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What is a ratio?

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A ratio is a comparison of two quantities, showing how many times one value contains or is contained within the other.

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What is an equivalent ratio?

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Equivalent ratios are ratios that express the same relationship between numbers, even if the numbers themselves are different.

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CCSS.6.RP.A.3A

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How do you simplify a ratio?

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To simplify a ratio, divide both terms by their greatest common factor (GCF).

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What is a rate?

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A rate is a specific kind of ratio that compares two different units, such as speed (miles per hour) or price per item.

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CCSS.6.RP.A.1

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If the ratio of cats to dogs is 3:4, how many cats are there if there are 12 dogs?

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There are 9 cats. (3/4 = x/12; x = 9)

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What is the ratio of 18 to 54?

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The ratio of 18 to 54 simplifies to 1:3.

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How can you find an equivalent ratio to 12:20?

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Multiply or divide both terms of the ratio by the same non-zero number. For example, 12:20 is equivalent to 3:5.

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CCSS.6.RP.A.3A

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What is the missing number in the ratio 6:x = 3:12?

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The missing number is 8. (Cross-multiply: 6*12 = 3*x; x = 24/3 = 8)

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What is the ratio of red marbles to yellow marbles if there are 2 red and 5 yellow?

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The ratio is 2:5.

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CCSS.6.RP.A.1

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If a table shows the ratio of 4:8, what are the next two equivalent ratios?

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The next two equivalent ratios are 1:2 and 2:4.

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