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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How do you write a ratio?

Back

Ratios can be written in three ways: using a colon (3:2), as a fraction (3/2), or with the word 'to' (3 to 2).

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

Front

What is a rate?

Back

A rate is a specific kind of ratio that compares two quantities with different units, such as speed (miles per hour) or price 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, for example, 1/2 = 2/4.

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CCSS.7.RP.A.2A

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How do you solve a proportion?

Back

To solve a proportion, cross-multiply the terms and set the products equal to each other.

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CCSS.7.RP.A.2C

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What is the cross-multiplication method?

Back

The cross-multiplication method involves multiplying the numerator of one ratio by the denominator of the other ratio to find an unknown value.

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CCSS.6.RP.A.3A

Front

If 3/4 = x/12, what is x?

Back

x = 9, because 3 * 12 = 4 * x leads to 36 = 4x, so x = 36/4 = 9.

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CCSS.7.RP.A.2B

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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.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

Front

How do you find a unit rate?

Back

To find a unit rate, divide the first quantity by the second quantity to get the value per one unit.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

Front

If a car travels 150 miles in 3 hours, what is the unit rate?

Back

The unit rate is 50 miles per hour, calculated by dividing 150 miles by 3 hours.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2