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Chapter 9 · Questions · page 55 of 68

How do you set up a proportion from a word problem?

Short answerPut the same kind of thing on top of both fractions and the other kind on the bottom. A recipe with 3 cups for 4 eggs gives 3/4 = c/10 for 10 eggs.

levelPre-algebra
standard7.RP.A.3
practiceProportions

Most proportion mistakes happen in the setup, not the arithmetic. Label each fraction with its units. If the left fraction is cups over eggs, the right one has to be cups over eggs too.

How to use it

  1. Write the known pair as a fraction with its units.
  2. Write the second fraction with the same units in the same places, using a letter for the unknown.
  3. Cross multiply and solve.
  4. Ask whether the answer makes sense: more eggs should mean more cups.

Example

34=c10⇒4c=30⇒c=7.5\frac{3}{4} = \frac{c}{10} \Rightarrow 4c = 30 \Rightarrow c = 7.5
25=m30⇒5m=60⇒m=12\frac{2}{5} = \frac{m}{30} \Rightarrow 5m = 60 \Rightarrow m = 12

Where it goes wrong

  • Cups on top of one fraction and eggs on top of the other.
  • Adding the difference instead of scaling: 4 eggs to 10 eggs is not 3 cups to 9 cups.

Related

Proportions and cross multiplyingUnit rates
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