Equivalent Ratios from Tape Diagrams and Double Number Lines

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What is an equivalent ratio?

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An equivalent ratio is a ratio that expresses the same relationship between two quantities, even if the numbers are different. For example, the ratios 4:6 and 2:3 are equivalent because they both represent the same proportion.

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How do you find equivalent ratios?

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To find equivalent ratios, you can multiply or divide both terms of the ratio by the same non-zero number. For example, to find an equivalent ratio for 2:3, you can multiply both terms by 2 to get 4:6.

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What is a tape diagram?

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A tape diagram is a visual representation of a ratio or a fraction. It uses rectangles to show the parts of a whole and helps in understanding the relationship between different quantities.

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What is a double number line?

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A double number line is a visual tool that shows two sets of numbers along parallel lines. It helps to illustrate the relationship between two quantities and can be used to find equivalent ratios.

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If the ratio of cats to dogs is 3:4, how many cats are there if there are 12 dogs?

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There are 9 cats. (Using the ratio 3:4, if 4 parts represent 12 dogs, then 3 parts represent 9 cats.)

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What is the ratio of 10 to 5 in simplest form?

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The simplest form of the ratio 10:5 is 2:1.

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How can you use a tape diagram to solve ratio problems?

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You can use a tape diagram to visually represent the parts of a ratio, making it easier to see how many of one quantity corresponds to another. For example, if a tape diagram shows 3 parts for apples and 2 parts for oranges, you can easily find how many oranges correspond to a given number of apples.

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What does it mean if two ratios are not equivalent?

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If two ratios are not equivalent, it means they do not represent the same relationship between the two quantities. For example, the ratios 2:3 and 4:5 are not equivalent.

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If a recipe calls for a ratio of 2 cups of flour to 3 cups of sugar, how much flour is needed for 9 cups of sugar?

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You need 6 cups of flour. (Using the ratio 2:3, if 3 parts represent 9 cups of sugar, then 2 parts represent 6 cups of flour.)

Front

What is the relationship between ratios and fractions?

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