Equivalent ratios represent the same multiplicative relationship between two quantities: multiplying or dividing both terms by the same positive whole-number factor preserves the ratio, as shown in ratio tables, paired values, or double number lines. The reasoning distinguishes proportional scaling from adding the same amount to both terms and supports finding missing values in proportional situations; the focus is on positive whole-number quantities and scale factors, not generalized algebraic or more advanced fractional-ratio cases.
A ratio stays equivalent when you multiply or divide both terms by the same positive whole-number factor. This keeps the multiplicative relationship the same.
Example: A recipe uses cups of flour for every cups of oats. How much flour and oats are needed for an equivalent ratio using cups of oats?
Write the ratio:
Find the scale factor from to :
The scale factor is .
Multiply both parts of the ratio by :
The equivalent ratio is:
So, the recipe needs cups of flour for every cups of oats.
Remember, you must multiply or divide both terms by the same factor. Adding the same amount does not usually create an equivalent ratio: , which is not equivalent to .
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