Solving Ratios and Proportions

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What is a ratio?

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A ratio is a comparison of two quantities expressed as a fraction, indicating 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 solve a proportion?

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To solve a proportion, cross-multiply the two ratios and set the products equal to each other, then solve for the unknown variable.

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CCSS.7.RP.A.2C

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What does it mean for two ratios to be proportional?

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Two ratios are proportional if they can be expressed as equivalent fractions.

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CCSS.7.RP.A.2D

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What is the cross-multiplication method?

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The cross-multiplication method involves multiplying the numerator of one ratio by the denominator of the other ratio to find a solution.

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CCSS.6.RP.A.3A

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If a:b = c:d, what is the relationship between a, b, c, and d?

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The relationship indicates that the ratio of a to b is equal to the ratio of c to d.

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CCSS.6.RP.A.3A

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What is the value of the ratio 3:4 in decimal form?

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The decimal form of the ratio 3:4 is 0.75.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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How can you determine if two ratios are proportional using a numerical example?

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You can determine if two ratios are proportional by checking if the cross-products are equal. For example, for ratios 1:2 and 2:4, check if 1*4 = 2*2.

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What is the first step in solving a ratio problem?

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The first step is to identify the quantities being compared and express them as a ratio.

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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 and proportions?

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A real-world application is in recipes, where ingredients must be scaled up or down based on the number of servings.