A proportion expresses that two ratios represent the same multiplicative relationship; solving one involves determining an unknown term by identifying the scale factor or constructing equivalent ratios in a ratio table, diagram, or equation. The reasoning applies to positive whole-number and rational quantities, including an unknown in any position, and distinguishes multiplicative equivalence from adding the same amount to both terms; it does not extend to formal proofs or advanced cases involving zero or generalized algebraic structures.
A proportion says that two ratios are equivalent. To solve it, find the multiplicative scale factor that changes one ratio into the other, then apply the same factor to both parts.
Example:
Five notebooks cost $15. How much would eight notebooks cost?
Write the equivalent ratios in the same order:
Change 5 notebooks into 8 notebooks:
So, the scale factor is .
Therefore,
Answer: Eight notebooks cost $24.
You multiply both terms by the same factor. You do not add the same amount to both terms, because equivalent ratios are created by multiplication, not addition. Check the result:
The ratios are equal, so the answer is reasonable.
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