Ratios & Equivalent Ratios

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What is a ratio?

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A ratio is a comparison of two quantities that shows the relative size of one quantity to another, often expressed as 'a:b'.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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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 simplify to the same fraction.

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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, you can 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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If the cost of 1 bag of chips is $1.50, how much do 7 bags cost?

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$10.50 (1.50 x 7 = 10.50).

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CCSS.6.NS.B.3

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What is the equivalent ratio of 5:4 when both terms are multiplied by 4?

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20:16 (5 x 4 = 20 and 4 x 4 = 16).

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CCSS.6.RP.A.3A

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What is the simplest form of the ratio 8:12?

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2:3 (dividing both terms by 4).

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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Which ratio is equivalent to 2:6?

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6:18 (2 x 3 = 6 and 6 x 3 = 18).

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CCSS.6.RP.A.3A

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How do you express the ratio of 40 to 12 in simplest form?

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The simplest form is 10:3 (dividing both terms by 4).

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CCSS.6.RP.A.2

CCSS.6.RP.A.1

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What is the relationship between the ratios 16:24 and 2:3?

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They are equivalent ratios because both simplify to the same fraction (2:3).

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CCSS.6.RP.A.3A

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If a recipe calls for a ratio of 3:2 for sugar to flour, how much sugar is needed for 10 cups of flour?

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15 cups of sugar (3/2 = x/10, so x = 15).