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Chapter 4 · Ratios · page 21 of 68

Proportions and cross multiplying

levelPre-algebra
standard7.RP.A.2
practiceProportions

A proportion is two equal ratios. If a/b = c/d, then a times d equals b times c, because you can multiply both sides by b and by d. That turns a proportion with an unknown into a one-step equation.

How to use it

  1. Set up the proportion with the same kind of thing on top of each fraction.
  2. Multiply along the two diagonals and set the products equal.
  3. Divide to find the unknown.
  4. Check that both fractions reduce to the same thing.

Example

x4=68⇒8x=24⇒x=3\frac{x}{4} = \frac{6}{8} \Rightarrow 8x = 24 \Rightarrow x = 3
35=12n⇒3n=60⇒n=20\frac{3}{5} = \frac{12}{n} \Rightarrow 3n = 60 \Rightarrow n = 20
x+25=610⇒10(x+2)=30⇒x=1\frac{x+2}{5} = \frac{6}{10} \Rightarrow 10(x+2) = 30 \Rightarrow x = 1

Where it goes wrong

  • Mixing the units: miles on top of one fraction and hours on top of the other.
  • Multiplying across instead of along the diagonals.
  • Forgetting the whole top is one unit when it is an expression like x + 2.

Related

Ratios and simplest formUnit ratesUndo in reverse orderPercent of a number
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