Fractional Linear Equations Worksheet for Grades 7 and 8

A fraction in every equation, like x/4 + 3 = 10 or 3/4x = 6, printed with its answer key.

20 problems. Letter over a number, plus or minus: x/4 + 3 = 10. Sheet AQSRD6, with its answer key.

Letter over a number, plus or minus: x/4 + 3 = 10

Name Date Score / 20

Solve each equation.

  1. 1.y2 + 14 = 24  y = _____
  2. 2.x3 − 6 = 0  x = _____
  3. 3.n8 + 15 = 27  n = _____
  4. 4.y3 − 1 = 11  y = _____
  5. 5.x7 + 13 = 14  x = _____
  6. 6.n3 − 2 = 0  n = _____
  7. 7.y5 + 13 = 23  y = _____
  8. 8.x5 − 9 = 3  x = _____
  9. 9.n6 + 9 = 11  n = _____
  10. 10.y7 − 7 = 1  y = _____
  11. 11.x9 + 9 = 20  x = _____
  12. 12.n7 − 5 = 6  n = _____
  13. 13.y4 + 15 = 20  y = _____
  14. 14.x9 − 10 = 2  x = ________
  15. 15.n3 + 6 = 12  n = _____
  16. 16.y6 − 7 = 0  y = _____
  17. 17.x2 + 9 = 17  x = _____
  18. 18.n6 − 8 = 0  n = _____
  19. 19.y3 + 10 = 13  y = _____
  20. 20.x5 − 2 = 5  x = _____

Sheet AQSRD6 · Made at homeroomtools.com

Answer key. Letter over a number, plus or minus: x/4 + 3 = 10

  1. 1.y2 + 14 = 24  y = 20 24 − 14 = 10 10 × 2 = 20 Check: 20 ÷ 2 + 14 = 24
  2. 2.x3 − 6 = 0  x = 18 0 + 6 = 6 6 × 3 = 18 Check: 18 ÷ 3 − 6 = 0
  3. 3.n8 + 15 = 27  n = 96 27 − 15 = 12 12 × 8 = 96 Check: 96 ÷ 8 + 15 = 27
  4. 4.y3 − 1 = 11  y = 36 11 + 1 = 12 12 × 3 = 36 Check: 36 ÷ 3 − 1 = 11
  5. 5.x7 + 13 = 14  x = 7 14 − 13 = 1 1 × 7 = 7 Check: 7 ÷ 7 + 13 = 14
  6. 6.n3 − 2 = 0  n = 6 0 + 2 = 2 2 × 3 = 6 Check: 6 ÷ 3 − 2 = 0
  7. 7.y5 + 13 = 23  y = 50 23 − 13 = 10 10 × 5 = 50 Check: 50 ÷ 5 + 13 = 23
  8. 8.x5 − 9 = 3  x = 60 3 + 9 = 12 12 × 5 = 60 Check: 60 ÷ 5 − 9 = 3
  9. 9.n6 + 9 = 11  n = 12 11 − 9 = 2 2 × 6 = 12 Check: 12 ÷ 6 + 9 = 11
  10. 10.y7 − 7 = 1  y = 56 1 + 7 = 8 8 × 7 = 56 Check: 56 ÷ 7 − 7 = 1
  11. 11.x9 + 9 = 20  x = 99 20 − 9 = 11 11 × 9 = 99 Check: 99 ÷ 9 + 9 = 20
  12. 12.n7 − 5 = 6  n = 77 6 + 5 = 11 11 × 7 = 77 Check: 77 ÷ 7 − 5 = 6
  13. 13.y4 + 15 = 20  y = 20 20 − 15 = 5 5 × 4 = 20 Check: 20 ÷ 4 + 15 = 20
  14. 14.x9 − 10 = 2  x = 108 2 + 10 = 12 12 × 9 = 108 Check: 108 ÷ 9 − 10 = 2
  15. 15.n3 + 6 = 12  n = 18 12 − 6 = 6 6 × 3 = 18 Check: 18 ÷ 3 + 6 = 12
  16. 16.y6 − 7 = 0  y = 42 0 + 7 = 7 7 × 6 = 42 Check: 42 ÷ 6 − 7 = 0
  17. 17.x2 + 9 = 17  x = 16 17 − 9 = 8 8 × 2 = 16 Check: 16 ÷ 2 + 9 = 17
  18. 18.n6 − 8 = 0  n = 48 0 + 8 = 8 8 × 6 = 48 Check: 48 ÷ 6 − 8 = 0
  19. 19.y3 + 10 = 13  y = 9 13 − 10 = 3 3 × 3 = 9 Check: 9 ÷ 3 + 10 = 13
  20. 20.x5 − 2 = 5  x = 35 5 + 2 = 7 7 × 5 = 35 Check: 35 ÷ 5 − 2 = 5

Sheet AQSRD6 · Made at homeroomtools.com

Next step Two-step equations with whole numbersAll equation worksheets

How it works

Every problem has a fraction in it. A free sheet has 20 like x/4 + 3 = 10 and y/8 − 3 = 6; Sheet type adds fraction coefficients, a fraction outside a bracket, fraction constants and fraction answers.

Read the full guide

Two ways to clear a fraction

Divide by the fraction or multiply by the number under it. 3/4x = 6: dividing by 3/4 is multiplying by 4/3, so x = 8. x/4 + 3 = 10: take 3 away, then multiply by 4, so x = 28. The key uses these steps.

Which sheet to print first

Start with Letter over a number, plus or minus: x/4 + 3 = 10, where the answers are whole. Then A fraction times the letter: 3/4x = 6. Whole numbers in, fraction answers out comes last: every answer, such as 10/3, is a fraction in lowest terms.

  • Ask pupils to say 3/4x as three quarters of x before they solve it.
  • A pupil who writes x = 4.5 for 3/4x = 6 has multiplied by 3/4 instead of dividing.

Questions and answers

Why is dividing by 3/4 the same as multiplying by 4/3?

Because 3/4 × 4/3 = 1. Dividing both sides of 3/4x = 6 by 3/4 leaves x, and multiplying 6 by 4/3 gives 24/3 = 8. Check: 3/4 × 8 = 6.

Are the answers fractions?

On two sheet types. Fraction constants has about one whole answer in four, and Whole numbers in, fraction answers out has none. The other six keep the answers whole.

How do I save a fractional linear equations worksheet as a PDF?

Press Print and choose Save as PDF as the printer. The answer key prints on its own page after the sheet; untick Answer key to leave it out.

All 8 sheet types

The letter over a number 2

  • Letter over a number with negatives: x/3 + 6 = 4 x/3 + 6 = 4: take 6 away (−2), then multiply by 3: x = −6.
  • Letter over a number, plus or minus: x/4 + 3 = 10 x/4 + 3 = 10: take 3 away (7), then multiply by 4: x = 28. Half the sheet subtracts, as in x/7 − 2 = 4.

A fraction times the letter 4

  • A fraction outside a bracket: 3/5(x − 2) = 3 3/5(x − 2) = 3: divide by 3/5 (5), then add 2: x = 7.
  • A fraction times the letter: 3/4x = 6 3/4x = 6: divide by 3/4, which is multiplying by 4/3, so x = 8. Halves to eighths.
  • Fraction coefficient, two steps: 2/5x + 16 = 18 2/5x + 16 = 18: take 16 away (2), then divide by 2/5: x = 5. Every answer is whole.
  • Fraction coefficients with negatives: 5 − 7/4y = 12 5 − 7/4y = 12: take 5 away (7), then divide by −7/4: y = −4. About half the coefficients and answers are negative, and some equations start with their answer side.

Fraction constants and fraction answers 2

  • Fraction constants: x − 9/8 = 1/8 x − 9/8 = 1/8: add 9/8, x = 10/8 = 5/4. Denominators from 2 to 10; about one answer in four is whole.
  • Whole numbers in, fraction answers out 6x − 11 = 3x − 1 gives 3x = 10, so x = 10/3. Every answer is a fraction in lowest terms.

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