Ratios, Rates and Proportions

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What is a ratio?

Back

A ratio is a comparison of two quantities expressed as a fraction, indicating how many times one value contains or is contained within the other.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

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How do you calculate a unit rate?

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A unit rate is calculated by dividing the quantity of one item by the quantity of another item, typically expressed as 'per one' (e.g., miles per gallon).

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

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If the ratio of boys to girls in a class is 6:5 and there are 18 boys, how many girls are there?

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To find the number of girls, set up the proportion: 6/5 = 18/x. Cross-multiply to find x, which equals 15.

Tags

CCSS.7.RP.A.3

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What is the relationship between ratios and proportions?

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

Tags

CCSS.6.RP.A.3A

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How do you scale a recipe using ratios?

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To scale a recipe, maintain the same ratio of ingredients while increasing or decreasing the total amount. For example, if a recipe calls for 2 cups of milk for every 3 cups of flour, doubling the milk to 4 cups requires doubling the flour to 6 cups.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal, often used to solve for an unknown quantity.

Tags

CCSS.7.RP.A.2A

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How do you find the total number of items when given a ratio and one quantity?

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To find the total number of items, add the parts of the ratio together and then use the known quantity to find the unknown quantities.

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What is the formula for calculating the total number of home runs based on games played?

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The formula is: Total Home Runs = (Home Runs per Game) x (Total Games). For example, if a player hits 3 home runs per game over 21 games, they would hit 63 home runs.

Tags

CCSS.7.RP.A.2C

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How do you convert a ratio to a percentage?

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To convert a ratio to a percentage, divide the first number by the total of both numbers in the ratio and multiply by 100.

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

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Unit rates help compare different quantities and make informed decisions, such as determining the best price per item or efficiency of fuel consumption.

Tags

CCSS.6.RP.A.3B