Ratios, Rates & Unit Rates

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What is a ratio?

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

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How do you express a ratio?

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A ratio can be expressed in three ways: using a colon (e.g., 3:2), as a fraction (e.g., 3/2), or in words (e.g., '3 to 2').

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What is a rate?

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

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What is a unit rate?

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A unit rate is a rate in which the second quantity is one unit, such as 60 miles per hour (60 miles for 1 hour).

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How do you find 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 to 7.

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If a car travels 231 miles using 7 gallons of gas, how do you calculate the mileage in miles per gallon?

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To calculate mileage, divide the total miles by the gallons of gas: 231 miles ÷ 7 gallons = 33 miles per gallon.

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CCSS.6.RP.A.1

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What is the ratio of blue and yellow marbles to red marbles if there are 3 blue and 2 yellow marbles and 7 red marbles?

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The ratio of blue and yellow marbles (3 + 2 = 5) to red marbles is 5 to 7.

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CCSS.6.RP.A.1

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How do you express the ratio of blue marbles to green and red marbles if there are 3 blue, 8 green, and 7 red marbles?

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The ratio of blue marbles (3) to green and red marbles (8 + 7 = 15) is 1 to 5.

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CCSS.6.RP.A.1

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What is the ratio of quarters to dimes if there are 8 quarters and 10 dimes?

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The ratio of quarters to dimes is 8 to 10, which simplifies to 4 to 5.

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What is the importance of simplifying ratios?

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Simplifying ratios makes them easier to understand and compare, allowing for clearer communication of relationships between quantities.

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