Unit 7 Review: Proportions and Percentages

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What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. It expresses how much of one quantity corresponds to one unit of another quantity, often expressed as 'per' something (e.g., laps per minute).

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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 Alicia runs 4 laps in 7.41 minutes, the unit rate is 4 laps ÷ 7.41 minutes = 0.54 laps/min.

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What is percent change?

Back

Percent change is a way to express the change in a quantity as a percentage of the original amount. It is calculated using the formula: ((new value - old value) / old value) × 100%.

Front

How do you calculate percent increase?

Back

To calculate percent increase, subtract the old value from the new value, divide by the old value, and multiply by 100%. For example, if the number of teachers increased from 24 to 30, the percent increase is ((30 - 24) / 24) × 100% = 25%.

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How do you calculate percent decrease?

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To calculate percent decrease, subtract the new value from the old value, divide by the old value, and multiply by 100%. For example, if a bottle size decreased from 22.5 fl oz to 18 fl oz, the percent decrease is ((22.5 - 18) / 22.5) × 100%.

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What is the formula for finding the total amount based on unit rate?

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The formula is: Total Amount = Unit Rate × Time. For example, if Cora jars 3 liters of jam per day, in 6 days she will jar 3 liters × 6 days = 18 liters.

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How do you find the number of items needed to reach a total score?

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To find the number of items needed, divide the total score by the score per item. For example, if Nora scores 216 points with 2 coins, to find how many coins are needed for 540 points, calculate 540 points ÷ (216 points / 2 coins) = 5 coins.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if 4 laps take 7.41 minutes, the proportion can be set up as 4/7.41 = x/minutes.

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How do you solve a proportion?

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To solve a proportion, cross-multiply and then divide. For example, if you have 4/7.41 = x/1, then 4 × 1 = 7.41 × x, leading to x = 4/7.41.

Front

What is the relationship between fractions and percentages?

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Fractions can be converted to percentages by multiplying the fraction by 100%. For example, 1/4 = 0.25 × 100% = 25%.