7th Grade Rates and Unit Rate

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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 a car travels 300 miles in 5 hours, the unit rate is 60 miles per hour.

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How do you calculate a unit rate?

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To calculate a unit rate, divide the quantity of one item by the quantity of another item. For example, if you have 150 apples for 3 baskets, the unit rate is 150 apples ÷ 3 baskets = 50 apples per basket.

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What is a ratio?

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A ratio is a relationship between two numbers indicating how many times the first number contains the second. 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, to simplify the ratio 8:12, divide both by 4 to get 2:3.

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What is the difference between a ratio and a rate?

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A ratio compares two quantities, while a rate compares two quantities with different units. For example, speed is a rate that compares distance to time.

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What does it mean to express a ratio in simplest form?

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Expressing a ratio in simplest form means reducing it to its lowest terms, where the two numbers have no common factors other than 1.

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How can you convert a ratio to a percentage?

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To convert a ratio to a percentage, divide the first number by the sum of both numbers in the ratio and then multiply by 100. For example, for the ratio 1:4, the percentage is (1/(1+4)) * 100 = 20%.

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What is a rate problem?

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A rate problem involves finding a unit rate or comparing quantities that have different units, such as speed, price per item, or density.

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How do you find the total from a unit rate?

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To find the total from a unit rate, multiply the unit rate by the number of units. For example, if the unit rate is $0.15 per item and you buy 10 items, the total cost is $0.15 * 10 = $1.50.

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What is the significance of unit rates in real-life applications?

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Unit rates help in making comparisons and informed decisions in real-life situations, such as shopping, travel, and budgeting.