Ratio word problems require interpreting a comparison between quantities as a multiplicative relationship, distinguishing part-to-part from part-to-whole ratios and identifying what each number represents. Solutions determine unknown amounts, totals, or scale factors by generating equivalent ratios and using tables, double number lines, bar models, or equations, rather than applying additive differences. The scope is familiar contexts with positive whole-number or simple rational quantities, not complex compound ratios, formal proportional functions, or proof-based generalizations.
A ratio compares quantities by showing how many equal-sized parts each quantity has. For example, a ratio of means:
The numbers are not an additive difference. They show a multiplicative relationship.
Example:
The ratio of almonds to raisins in a trail mix is . If there are cups of raisins, how many cups of trail mix are there altogether?
First, match each number in the ratio to its quantity:
The parts of raisins equal cups. Find the amount in part:
So each part represents cups. The almonds have parts:
There are cups of almonds. Add the two quantities to find the total:
Check the ratio:
So the answer matches the original ratio.
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