Ratios, Rates & Proportions

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What is a ratio?

Back

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

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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What is a rate?

Back

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

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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What is a unit rate?

Back

A unit rate is a rate in which the second quantity is one unit, such as 60 miles per hour or 5 dollars per item.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal, often written in the form a/b = c/d.

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CCSS.7.RP.A.2B

Front

How do you find the unit rate from a total distance and total gallons of gas?

Back

Divide the total distance by the total gallons of gas. For example, if you drive 92 miles using 4 gallons, the unit rate is 92 ÷ 4 = 23 miles per gallon.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

Front

If the ratio of dogs to cats is 5 to 3 and there are 25 dogs, how many cats are there?

Back

Set up the proportion 5/3 = 25/c. Cross-multiply to find c = 15.

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CCSS.7.RP.A.2C

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What is the formula to solve for a missing value in a proportion?

Back

If a/b = c/d, then ad = bc. You can solve for the missing value by cross-multiplying.

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CCSS.7.RP.A.2C

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How do you calculate the unit rate of calories per serving?

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Divide the total calories by the number of servings. For example, 624 calories in 3 servings gives 624 ÷ 3 = 208 calories per serving.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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What does it mean if two ratios are equivalent?

Back

It means that they represent the same relationship between quantities, and can be expressed as a proportion.

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CCSS.6.RP.A.3A

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What is the first step in solving a proportion?

Back

Identify the two ratios and set them equal to each other.

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CCSS.7.RP.A.3