Rates, Ratio, and unit conversions

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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 one unit. For example, if you can type 408 words in 4 minutes, the unit rate is 102 words 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 by the number of units. For example, if you spend $40 on 5 pounds of concrete, the unit rate is $40 ÷ 5 = $8 per pound.

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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. For example, if a baseball team won 5 games and lost 9, the ratio of games won to games lost is 5:9.

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How do you express a ratio?

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A ratio can be expressed in three ways: using a colon (e.g., 5:9), as a fraction (e.g., 5/14), or in words (e.g., '5 to 9').

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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, 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 and then divide. For example, if 2/3 = x/6, then 2*6 = 3*x, leading to x = 4.

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What is the formula for finding the unit price?

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The unit price is found by dividing the total price by the total quantity. For example, if 5 pounds of concrete cost $40, the unit price is $40 ÷ 5 = $8 per pound.

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What does it mean to find the ratio of games won to games lost?

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Finding the ratio of games won to games lost means comparing the number of games won to the number of games lost to understand the team's performance.

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If a person earns $200 for 8 hours of work, how do you find their hourly wage?

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To find the hourly wage, divide the total earnings by the total hours worked. In this case, $200 ÷ 8 hours = $25 per hour.

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

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Unit rates help compare prices, speeds, and other quantities in real-life situations, making it easier to make informed decisions.