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Solving rational proportions worksheets Grades 9–10

Cross multiply, distribute and solve for x.

The front of the free solving rational proportions worksheet
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Free · Worked example · 20 problems · Answer key · US Letter

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How to do it

Cross-multiply, distribute, and solve for x.

3x+2=12x+8x=0\dfrac{3}{x + 2} = \dfrac{12}{x + 8}\quad x = 0
3(x+8)=12(x+2)3(x + 8) = 12(x + 2)cross-multiply
3x+24=12x+243x + 24 = 12x + 24distribute
−9x=0-9x = 0get the x terms on one side
x=0x = 0divide by −9

Example problems

  1. x−1x−12=−29\dfrac{x - 1}{x - 12} = \dfrac{-2}{9}
  2. x+2x+13=−38\dfrac{x + 2}{x + 13} = \dfrac{-3}{8}
  3. x+312=x−22\dfrac{x + 3}{12} = \dfrac{x - 2}{2}
  4. x−12=x+47\dfrac{x - 1}{2} = \dfrac{x + 4}{7}

Rational expressions and equations

  1. Adding and subtracting rational expressions with like denominators
  2. Least common denominator of rational expressions
  3. Adding rational expressions with unlike denominators
  4. Subtracting rational expressions with unlike denominators
  5. Adding and subtracting rational expressions by factoring
  6. Simplifying complex fractions
  7. Solving rational proportions
  8. Solving rational equations