Ratio and Proportion: Direct, Inverse or Shares?
Write ratios in the order asked and in simplest form, solve proportions by cross products, and decide first whether a problem is direct, inverse or a sharing (partitive) problem.
What it is
A ratio compares two quantities: "3 clerks for every 2 computers" is the ratio 3 : 2 (read "3 to 2"), also written 3/2.
A proportion says that two ratios are equal: 3 : 2 = 9 : 6. If one number in a proportion is missing, you can find it.
Word problems come in three kinds: direct (more of one, more of the other), inverse (more of one, less of the other) and partitive (a total is shared in a given ratio).
Why it matters on the exam
Ratio and proportion items appear in both exam levels: simplifying ratios, finding a missing term, and word problems about costs, workers, supplies, speed and sharing. The most common trap is solving an inverse problem as if it were direct, or stopping at the value of one share.
At work, proportions help you scale a budget, estimate supplies for more people, or divide funds fairly.
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