Unit Rate, Ratios, and Proportions

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What is a unit rate?

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A unit rate is a comparison of two different quantities where one of the quantities is expressed as a quantity of one. For example, if you spend $40 on 5 pounds of concrete, the unit rate is $8 per pound.

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How do you calculate a unit rate?

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To calculate a unit rate, divide the total quantity of one item by the total quantity of the other item. For example, if you have 14 inches of snow in 5 hours, the unit rate is 14 inches ÷ 5 hours = 2.8 inches per hour.

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What is a ratio?

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A ratio is a relationship between two quantities, showing how many times one value contains or is contained within the other. It can be expressed in various forms, such as a fraction, with a colon, or with the word 'to'.

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How do you simplify a ratio?

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To simplify a ratio, divide both terms of the ratio by their greatest common divisor (GCD). For example, the ratio 8:12 can be simplified to 2:3 by dividing both terms by 4.

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What does it mean for ratios to be equivalent?

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Equivalent ratios are ratios that express the same relationship between quantities, even if the numbers are different. For example, 1:2, 2:4, and 3:6 are all equivalent ratios.

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How can you determine if two ratios are equivalent?

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To determine if two ratios are equivalent, cross-multiply the terms and compare the products. If the products are equal, the ratios are equivalent.

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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. For example, the ratio 3:4 can be expressed as the fraction 3/4.

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What is a proportion?

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

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How do you solve a proportion?

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To solve a proportion, you can use cross-multiplication. If a/b = c/d, then ad = bc. You can then solve for the unknown variable.

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What is the unit rate of a speed?

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The unit rate of speed is the distance traveled per unit of time, often expressed in miles per hour (mph) or kilometers per hour (km/h). For example, if a car travels 120 miles in 2 hours, the unit rate is 60 mph.