Ratios and Equivalent Ratios

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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.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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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., 1:2), as a fraction (e.g., 1/2), or in words (e.g., '1 to 2').

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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What is an equivalent ratio?

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Equivalent ratios are ratios that express the same relationship between two quantities, even if the numbers are different (e.g., 1:2 is equivalent to 2:4).

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CCSS.6.RP.A.3A

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How can you find equivalent ratios?

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You can find equivalent ratios by multiplying or dividing both terms of the ratio by the same non-zero number.

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CCSS.6.RP.A.3A

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What is the ratio of red apples to green apples if there are 4 red apples and 3 green apples?

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The ratio of red apples to green apples is 4:3.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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If a recipe calls for 4 meatballs for every 1 cup of sauce, what is the ratio of meatballs to sauce?

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The ratio of meatballs to sauce is 4:1.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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How do you simplify a ratio?

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To simplify a ratio, divide both terms by their greatest common divisor (GCD).

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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What is the total number of toy cars if Patrick has 2 black, 3 red, and 5 white toy cars?

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Patrick has a total of 10 toy cars (2 + 3 + 5 = 10).

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CCSS.2.OA.A.1

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What is the ratio of red toy cars to all toy cars if Patrick has 3 red toy cars out of 10 total?

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The ratio of red toy cars to all toy cars is 3:10.

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CCSS.6.RP.A.1

CCSS.6.RP.A.2

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What does a ratio table represent?

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A ratio table is a tool used to show equivalent ratios in a structured format, making it easier to see relationships between quantities.