Rates, Ratios and Unit Rates

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What is a ratio?

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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.2

CCSS.6.RP.A.1

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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., 3:5), as a fraction (e.g., 3/5), or in words (e.g., 3 to 5).

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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What is a unit rate?

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A unit rate is a ratio that compares a quantity to one unit of another quantity, often expressed as 'per' (e.g., miles per hour).

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CCSS.6.RP.A.2

CCSS.6.RP.A.1

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How do you find a unit rate?

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To find a unit rate, divide the first quantity by the second quantity to determine how much of the first quantity corresponds to one unit of the second.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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What is a proportion?

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A proportion is an equation that states that two ratios are equal.

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CCSS.7.RP.A.2A

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How do you solve a proportion?

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To solve a proportion, cross-multiply the terms and then solve for the unknown variable.

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CCSS.7.RP.A.2C

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What is the simplest form of a ratio?

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The simplest form of a ratio is when both quantities are divided by their greatest common factor.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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If the ratio of cats to dogs is 2:3 and there are 12 cats, how many dogs are there?

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18 dogs (since 12 cats corresponds to 18 dogs in the ratio 2:3).

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What is an equivalent ratio?

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An equivalent ratio is a ratio that expresses the same relationship between quantities, even if the numbers are different (e.g., 2:3 is equivalent to 4:6).

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CCSS.6.RP.A.3A

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How do you convert a ratio to a fraction?

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To convert a ratio to a fraction, place the first quantity as the numerator and the second quantity as the denominator.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2