Solving Ratios and Proportions

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What is a ratio?

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A ratio is a comparison of two quantities by division. It shows 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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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 determine if two ratios are equivalent?

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Two ratios are equivalent if they simplify to the same fraction or if their cross products are equal.

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CCSS.6.RP.A.3A

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CCSS.6.RP.A.3A

Front

Solve the ratio: 4 to 10 and x to 50. What is x?

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x = 20.

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Back

x = 9.

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CCSS.3.NF.A.3A

CCSS.3.NF.A.3B

CCSS.4.NF.A.1

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What is the relationship between ratios and fractions?

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Ratios can be expressed as fractions, where the first quantity is the numerator and the second quantity is the denominator.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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How can you simplify the ratio 12:16?

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By dividing both terms by their greatest common divisor, which is 4, the simplified ratio is 3:4.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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What is an example of a real-world application of ratios?

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Ratios are used in recipes to compare the amount of ingredients, such as 2 cups of flour to 1 cup of sugar.

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What does it mean if two ratios are in direct proportion?

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If two ratios are in direct proportion, as one quantity increases, the other quantity increases at the same rate.

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CCSS.7.RP.A.2D