Ratios, Rates, & Proportions

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What is a ratio?

Back

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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How do you write a ratio?

Back

Ratios can be written in three ways: using a colon (3:2), as a fraction (3/2), or with the word 'to' (3 to 2).

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What is a rate?

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A rate is a specific kind of ratio that compares two quantities with different units, such as speed (miles per hour) or price per item.

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What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if a/b = c/d, then a, b, c, and d are in proportion.

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How do you solve a proportion?

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To solve a proportion, cross-multiply the terms and set the products equal to each other. For example, if a/b = c/d, then ad = bc.

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What is the relationship between ratios and fractions?

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Ratios can be expressed as fractions, and vice versa. For example, the ratio 3:4 can be written as the fraction 3/4.

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What is a unit rate?

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A unit rate is a rate in which the second quantity is one unit. For example, if a car travels 300 miles in 5 hours, the unit rate is 60 miles per hour.

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How do you find a missing value in a proportion?

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To find a missing value in a proportion, set up the proportion and cross-multiply to solve for the unknown.

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What is an example of a real-life ratio?

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An example of a real-life ratio is the ratio of boys to girls in a classroom, such as 10 boys to 15 girls, which can be simplified to 2:3.

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What does it mean to simplify a ratio?

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To simplify a ratio means to reduce it to its lowest terms by dividing both quantities by their greatest common factor.