Ratios, Rates and Unit Rates

Front

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 in the form 'a to b' or a:b.

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How do you calculate a unit rate?

Back

To calculate a unit rate, divide the quantity by the number of units. For example, if you have 60 miles in 3 hours, the unit rate is 60 miles ÷ 3 hours = 20 miles per hour.

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What is the difference between a rate and a ratio?

Back

A rate is a specific type of ratio that compares two quantities with different units, while a ratio compares two quantities with the same unit.

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How do you simplify a ratio?

Back

To simplify a ratio, divide both terms of the ratio by their greatest common divisor (GCD). For example, to simplify 8:12, divide both by 4 to get 2:3.

Front

What is a rate?

Back

A rate is a ratio that compares two different kinds of quantities, often expressed as a quantity per unit of another quantity, such as miles per hour or price per item.

Front

If 4 tickets cost $124, what is the cost of 1 ticket?

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To find the cost of 1 ticket, divide the total cost by the number of tickets: $124 ÷ 4 = $31 per ticket.

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What is the ratio of girls to boys if there are 9 girls and 7 boys?

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The ratio of girls to boys is 9:7.

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How do you convert a rate to a different unit?

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To convert a rate to a different unit, multiply or divide by the appropriate conversion factor. For example, to convert 15 miles per hour to miles per 30 minutes, divide by 2 to get 7.5 miles.

Front

What is the unit rate of 9 candy bars for $13.50?

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The unit rate is $13.50 ÷ 9 candy bars = $1.50 per candy bar.

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How do you find an equivalent rate?

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To find an equivalent rate, multiply or divide both the numerator and denominator of the rate by the same number. For example, 15 miles per hour is equivalent to 30 miles in 2 hours.