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Solving Proportions Worksheets

Solve ten algebraic proportions with five expression families, variable denominators, exact fraction or decimal answers and worked solutions.

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Solve for the variable and exclude values that make an original denominator zero.

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Keep each expression grouped

Cross multiply complete numerators and denominators, solve the resulting linear equation, and check the original denominator exclusions.

Learning objective

What this activity builds

Solve proportions by cross multiplication while respecting denominator restrictions.

Worked example

Solve 2/(x − 22) = 5/(x − 2).

x = 106/3.

First exclude x = 22 and x = 2. Cross multiply: 2(x − 2) = 5(x − 22), so 106 = 3x. The result is allowed by both original denominators.

Teaching notes

Make the practice count

  • State denominator exclusions before solving.
  • Cross multiply the complete numerator and denominator expressions.
  • Keep the exact fraction until the final decimal rounding step.

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Choose the expression families and the final-answer format. Every equation remains stacked as a proportion.

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Expression families
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Math SheetNameScoreTeacherDateSolving ProportionsCross multiply, solve, and check excluded denominator values in the original equation. Give the exact answer as a simplified fraction.1.Solve for x.26x+10=14Cross multiply and solve:2.Solve for z.8z-22=11z-2Cross multiply and solve:Diagrams are not to scale.math-sheet.comPage 1 of 5
Math SheetNameScoreTeacherDateSolving ProportionsCross multiply, solve, and check excluded denominator values in the original equation. Give the exact answer as a simplified fraction.3.Solve for c.c3=c-284Cross multiply and solve:4.Solve for k.298=5kCross multiply and solve:Diagrams are not to scale.math-sheet.comPage 2 of 5
Math SheetNameScoreTeacherDateSolving ProportionsCross multiply, solve, and check excluded denominator values in the original equation. Give the exact answer as a simplified fraction.5.Solve for r.79=6r-1919Cross multiply and solve:6.Solve for y.20y+5=13Cross multiply and solve:Diagrams are not to scale.math-sheet.comPage 3 of 5
Math SheetNameScoreTeacherDateSolving ProportionsCross multiply, solve, and check excluded denominator values in the original equation. Give the exact answer as a simplified fraction.7.Solve for t.58=4t-1313Cross multiply and solve:8.Solve for m.236=7mCross multiply and solve:Diagrams are not to scale.math-sheet.comPage 4 of 5
Math SheetNameScoreTeacherDateSolving ProportionsCross multiply, solve, and check excluded denominator values in the original equation. Give the exact answer as a simplified fraction.9.Solve for v.v5=v-186Cross multiply and solve:10.Solve for w.9w-10=10w+2Cross multiply and solve:Diagrams are not to scale.math-sheet.comPage 5 of 5

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