Ratios and Equivalent Ratios

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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.1

CCSS.6.RP.A.2

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How do you write a ratio?

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A ratio can be written in three ways: using a colon (e.g., 2:3), as a fraction (e.g., \(\frac{2}{3}\)), or in words (e.g., '2 to 3').

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CCSS.6.RP.A.2

CCSS.6.RP.A.1

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What does it mean for two ratios to be equivalent?

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Two ratios are equivalent if they represent the same relationship between quantities, meaning they can be simplified to the same fraction.

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CCSS.6.RP.A.3A

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How do you simplify a ratio?

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To simplify a ratio, divide both terms by their greatest common divisor (GCD).

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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What is the ratio of 16 boys to 32 girls in simplest form?

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The ratio of boys to girls is \(\frac{1}{2}\) or 1:2.

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CCSS.6.RP.A.2

CCSS.6.RP.A.1

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If a recipe calls for 3 cups of flour and 2 cups of chocolate chips, what is the ratio of chocolate chips to flour?

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The ratio of chocolate chips to flour is 2:3.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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Are the ratios 1:2 and 2:4 equivalent?

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Yes, they are equivalent because both simplify to \(\frac{1}{2}\).

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CCSS.6.RP.A.3A

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What is an equivalent ratio for 10:45?

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An equivalent ratio for 10:45 is 2:9.

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CCSS.6.RP.A.3A

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How do you find an equivalent ratio?

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To find an equivalent ratio, multiply or divide both terms of the ratio by the same non-zero number.

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CCSS.6.RP.A.3A

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What is the ratio of 28 to 70 in simplest form?

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The ratio of 28 to 70 in simplest form is 2:5.

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CCSS.6.RP.A.2

CCSS.6.RP.A.1