Equivalent ratios describe the same multiplicative relationship between two quantities: multiplying or dividing both terms by the same positive scale factor produces a new ratio with the same value, as in and . The understanding includes generating and checking equivalent ratios with whole-number or rational quantities using ratio tables, pairs, or double-number lines, while distinguishing multiplicative scaling from adding the same amount; more advanced abstract or algebraic generalizations are outside this scope.
Equivalent ratios are made by multiplying or dividing both parts of a ratio by the same positive number.
For example, suppose you need to find a ratio equivalent to with a first term of .
So, the scale factor is .
Since both terms were multiplied by , the ratios are equivalent.
Remember, you must multiply or divide both terms by the same number. Adding the same amount does not usually make an equivalent ratio. For example, and are not equivalent because the parts were changed by adding , not by using the same multiplicative scale factor.
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