Small practice. Bright discoveries.Explore the free starter collection
worksheetstudio.
Sign in
Back to worksheets
MathsAges 13-15

Equations with brackets & fractions

Solve multi-step linear equations involving bracketed expressions and algebraic fractions by clearing the denominator. Review suitability for your learners before teaching.

New variationTry interactive challengeBrowse templates
Age band:Ages 13-15Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 13-15

Equations with brackets & fractions

Take your time. Show your thinking.

  1. 1. Solve the algebraic fraction equation 6(x + 15) ÷ 5 = 66 for x.

    LHS=RHS
    6(x + 15) ÷ 5 = 66 · x + 15 = 55 → x = ?

  2. 2. Solve the algebraic fraction equation 5(x + 8) ÷ 2 = 35 for x.

    LHS=RHS
    5(x + 8) ÷ 2 = 35 · x + 8 = 14 → x = ?

  3. 3. Solve the algebraic fraction equation 5(x + 17) ÷ 2 = 65 for x.

    LHS=RHS
    5(x + 17) ÷ 2 = 65 · x + 17 = 26 → x = ?

  4. 4. Solve the algebraic fraction equation 2(x + 11) ÷ 2 = 14 for x.

    LHS=RHS
    2(x + 11) ÷ 2 = 14 · x + 11 = 14 → x = ?

  5. 5. Solve the algebraic fraction equation 2(x + 19) ÷ 7 = 10 for x.

    LHS=RHS
    2(x + 19) ÷ 7 = 10 · x + 19 = 35 → x = ?

  6. 6. Solve the algebraic fraction equation 4(x + 33) ÷ 7 = 44 for x.

    LHS=RHS
    4(x + 33) ÷ 7 = 44 · x + 33 = 77 → x = ?

  7. 7. Solve the algebraic fraction equation 3(x + 62) ÷ 6 = 42 for x.

    LHS=RHS
    3(x + 62) ÷ 6 = 42 · x + 62 = 84 → x = ?

  8. 8. Solve the algebraic fraction equation 5(x + 42) ÷ 6 = 45 for x.

    LHS=RHS
    5(x + 42) ÷ 6 = 45 · x + 42 = 54 → x = ?

  9. 9. Solve the algebraic fraction equation 3(x + 13) ÷ 2 = 30 for x.

    LHS=RHS
    3(x + 13) ÷ 2 = 30 · x + 13 = 20 → x = ?

  10. 10. Solve the algebraic fraction equation 6(x + 2) ÷ 4 = 12 for x.

    LHS=RHS
    6(x + 2) ÷ 4 = 12 · x + 2 = 8 → x = ?

  11. 11. Solve the algebraic fraction equation 6(x + 13) ÷ 7 = 66 for x.

    LHS=RHS
    6(x + 13) ÷ 7 = 66 · x + 13 = 77 → x = ?

  12. 12. Solve the algebraic fraction equation 4(x + 1) ÷ 2 = 8 for x.

    LHS=RHS
    4(x + 1) ÷ 2 = 8 · x + 1 = 4 → x = ?
12 questions · Seed 47 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15

Equations with brackets & fractions

Answers and reasoning. Review before teaching.

  1. 1. Solve the algebraic fraction equation 6(x + 15) ÷ 5 = 66 for x.

    40

    Multiply both sides by 5 to get 6(x + 15) = 330. Divide by 6 to get x + 15 = 55, so x = 40.

  2. 2. Solve the algebraic fraction equation 5(x + 8) ÷ 2 = 35 for x.

    6

    Multiply both sides by 2 to get 5(x + 8) = 70. Divide by 5 to get x + 8 = 14, so x = 6.

  3. 3. Solve the algebraic fraction equation 5(x + 17) ÷ 2 = 65 for x.

    9

    Multiply both sides by 2 to get 5(x + 17) = 130. Divide by 5 to get x + 17 = 26, so x = 9.

  4. 4. Solve the algebraic fraction equation 2(x + 11) ÷ 2 = 14 for x.

    3

    Multiply both sides by 2 to get 2(x + 11) = 28. Divide by 2 to get x + 11 = 14, so x = 3.

  5. 5. Solve the algebraic fraction equation 2(x + 19) ÷ 7 = 10 for x.

    16

    Multiply both sides by 7 to get 2(x + 19) = 70. Divide by 2 to get x + 19 = 35, so x = 16.

  6. 6. Solve the algebraic fraction equation 4(x + 33) ÷ 7 = 44 for x.

    44

    Multiply both sides by 7 to get 4(x + 33) = 308. Divide by 4 to get x + 33 = 77, so x = 44.

  7. 7. Solve the algebraic fraction equation 3(x + 62) ÷ 6 = 42 for x.

    22

    Multiply both sides by 6 to get 3(x + 62) = 252. Divide by 3 to get x + 62 = 84, so x = 22.

  8. 8. Solve the algebraic fraction equation 5(x + 42) ÷ 6 = 45 for x.

    12

    Multiply both sides by 6 to get 5(x + 42) = 270. Divide by 5 to get x + 42 = 54, so x = 12.

  9. 9. Solve the algebraic fraction equation 3(x + 13) ÷ 2 = 30 for x.

    7

    Multiply both sides by 2 to get 3(x + 13) = 60. Divide by 3 to get x + 13 = 20, so x = 7.

  10. 10. Solve the algebraic fraction equation 6(x + 2) ÷ 4 = 12 for x.

    6

    Multiply both sides by 4 to get 6(x + 2) = 48. Divide by 6 to get x + 2 = 8, so x = 6.

  11. 11. Solve the algebraic fraction equation 6(x + 13) ÷ 7 = 66 for x.

    64

    Multiply both sides by 7 to get 6(x + 13) = 462. Divide by 6 to get x + 13 = 77, so x = 64.

  12. 12. Solve the algebraic fraction equation 4(x + 1) ÷ 2 = 8 for x.

    3

    Multiply both sides by 2 to get 4(x + 1) = 16. Divide by 4 to get x + 1 = 4, so x = 3.

12 questions · Seed 47 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Equations with brackets & fractions

Take your time. Show your thinking.

  1. 1. Solve the algebraic fraction equation 6(x + 15) ÷ 5 = 66 for x.

    LHS=RHS
    6(x + 15) ÷ 5 = 66 · x + 15 = 55 → x = ?

  2. 2. Solve the algebraic fraction equation 5(x + 8) ÷ 2 = 35 for x.

    LHS=RHS
    5(x + 8) ÷ 2 = 35 · x + 8 = 14 → x = ?

  3. 3. Solve the algebraic fraction equation 5(x + 17) ÷ 2 = 65 for x.

    LHS=RHS
    5(x + 17) ÷ 2 = 65 · x + 17 = 26 → x = ?

  4. 4. Solve the algebraic fraction equation 2(x + 11) ÷ 2 = 14 for x.

    LHS=RHS
    2(x + 11) ÷ 2 = 14 · x + 11 = 14 → x = ?

  5. 5. Solve the algebraic fraction equation 2(x + 19) ÷ 7 = 10 for x.

    LHS=RHS
    2(x + 19) ÷ 7 = 10 · x + 19 = 35 → x = ?

  6. 6. Solve the algebraic fraction equation 4(x + 33) ÷ 7 = 44 for x.

    LHS=RHS
    4(x + 33) ÷ 7 = 44 · x + 33 = 77 → x = ?

  7. 7. Solve the algebraic fraction equation 3(x + 62) ÷ 6 = 42 for x.

    LHS=RHS
    3(x + 62) ÷ 6 = 42 · x + 62 = 84 → x = ?

  8. 8. Solve the algebraic fraction equation 5(x + 42) ÷ 6 = 45 for x.

    LHS=RHS
    5(x + 42) ÷ 6 = 45 · x + 42 = 54 → x = ?

  9. 9. Solve the algebraic fraction equation 3(x + 13) ÷ 2 = 30 for x.

    LHS=RHS
    3(x + 13) ÷ 2 = 30 · x + 13 = 20 → x = ?

  10. 10. Solve the algebraic fraction equation 6(x + 2) ÷ 4 = 12 for x.

    LHS=RHS
    6(x + 2) ÷ 4 = 12 · x + 2 = 8 → x = ?

  11. 11. Solve the algebraic fraction equation 6(x + 13) ÷ 7 = 66 for x.

    LHS=RHS
    6(x + 13) ÷ 7 = 66 · x + 13 = 77 → x = ?

  12. 12. Solve the algebraic fraction equation 4(x + 1) ÷ 2 = 8 for x.

    LHS=RHS
    4(x + 1) ÷ 2 = 8 · x + 1 = 4 → x = ?
12 questions · Seed 47 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Equations with brackets & fractions

Answers and reasoning. Review before teaching.

  1. 1. Solve the algebraic fraction equation 6(x + 15) ÷ 5 = 66 for x.

    40

    Multiply both sides by 5 to get 6(x + 15) = 330. Divide by 6 to get x + 15 = 55, so x = 40.

  2. 2. Solve the algebraic fraction equation 5(x + 8) ÷ 2 = 35 for x.

    6

    Multiply both sides by 2 to get 5(x + 8) = 70. Divide by 5 to get x + 8 = 14, so x = 6.

  3. 3. Solve the algebraic fraction equation 5(x + 17) ÷ 2 = 65 for x.

    9

    Multiply both sides by 2 to get 5(x + 17) = 130. Divide by 5 to get x + 17 = 26, so x = 9.

  4. 4. Solve the algebraic fraction equation 2(x + 11) ÷ 2 = 14 for x.

    3

    Multiply both sides by 2 to get 2(x + 11) = 28. Divide by 2 to get x + 11 = 14, so x = 3.

  5. 5. Solve the algebraic fraction equation 2(x + 19) ÷ 7 = 10 for x.

    16

    Multiply both sides by 7 to get 2(x + 19) = 70. Divide by 2 to get x + 19 = 35, so x = 16.

  6. 6. Solve the algebraic fraction equation 4(x + 33) ÷ 7 = 44 for x.

    44

    Multiply both sides by 7 to get 4(x + 33) = 308. Divide by 4 to get x + 33 = 77, so x = 44.

  7. 7. Solve the algebraic fraction equation 3(x + 62) ÷ 6 = 42 for x.

    22

    Multiply both sides by 6 to get 3(x + 62) = 252. Divide by 3 to get x + 62 = 84, so x = 22.

  8. 8. Solve the algebraic fraction equation 5(x + 42) ÷ 6 = 45 for x.

    12

    Multiply both sides by 6 to get 5(x + 42) = 270. Divide by 5 to get x + 42 = 54, so x = 12.

  9. 9. Solve the algebraic fraction equation 3(x + 13) ÷ 2 = 30 for x.

    7

    Multiply both sides by 2 to get 3(x + 13) = 60. Divide by 3 to get x + 13 = 20, so x = 7.

  10. 10. Solve the algebraic fraction equation 6(x + 2) ÷ 4 = 12 for x.

    6

    Multiply both sides by 4 to get 6(x + 2) = 48. Divide by 6 to get x + 2 = 8, so x = 6.

  11. 11. Solve the algebraic fraction equation 6(x + 13) ÷ 7 = 66 for x.

    64

    Multiply both sides by 7 to get 6(x + 13) = 462. Divide by 6 to get x + 13 = 77, so x = 64.

  12. 12. Solve the algebraic fraction equation 4(x + 1) ÷ 2 = 8 for x.

    3

    Multiply both sides by 2 to get 4(x + 1) = 16. Divide by 4 to get x + 1 = 4, so x = 3.

12 questions · Seed 47 · Age guidance, not curriculum certification