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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.

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Age band:Ages 13-15Ages 16-18

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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 + 46) ÷ 7 = 84 for x.

    LHS=RHS
    6(x + 46) ÷ 7 = 84 · x + 46 = 98 → x = ?

  2. 2. Solve the algebraic fraction equation 4(x + 6) ÷ 4 = 24 for x.

    LHS=RHS
    4(x + 6) ÷ 4 = 24 · x + 6 = 24 → x = ?

  3. 3. Solve the algebraic fraction equation 4(x + 13) ÷ 5 = 52 for x.

    LHS=RHS
    4(x + 13) ÷ 5 = 52 · x + 13 = 65 → x = ?

  4. 4. Solve the algebraic fraction equation 3(x + 5) ÷ 3 = 27 for x.

    LHS=RHS
    3(x + 5) ÷ 3 = 27 · x + 5 = 27 → x = ?

  5. 5. Solve the algebraic fraction equation 2(x + 7) ÷ 2 = 22 for x.

    LHS=RHS
    2(x + 7) ÷ 2 = 22 · x + 7 = 22 → x = ?

  6. 6. Solve the algebraic fraction equation 3(x + 12) ÷ 4 = 36 for x.

    LHS=RHS
    3(x + 12) ÷ 4 = 36 · x + 12 = 48 → x = ?

  7. 7. Solve the algebraic fraction equation 5(x + 13) ÷ 5 = 25 for x.

    LHS=RHS
    5(x + 13) ÷ 5 = 25 · x + 13 = 25 → x = ?

  8. 8. Solve the algebraic fraction equation 5(x + 28) ÷ 6 = 55 for x.

    LHS=RHS
    5(x + 28) ÷ 6 = 55 · x + 28 = 66 → x = ?

  9. 9. Solve the algebraic fraction equation 5(x + 16) ÷ 6 = 15 for x.

    LHS=RHS
    5(x + 16) ÷ 6 = 15 · x + 16 = 18 → x = ?

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

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

  11. 11. Solve the algebraic fraction equation 3(x + 24) ÷ 4 = 21 for x.

    LHS=RHS
    3(x + 24) ÷ 4 = 21 · x + 24 = 28 → x = ?

  12. 12. Solve the algebraic fraction equation 4(x + 23) ÷ 4 = 40 for x.

    LHS=RHS
    4(x + 23) ÷ 4 = 40 · x + 23 = 40 → x = ?
12 questions · Seed 46 · 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 + 46) ÷ 7 = 84 for x.

    52

    Multiply both sides by 7 to get 6(x + 46) = 588. Divide by 6 to get x + 46 = 98, so x = 52.

  2. 2. Solve the algebraic fraction equation 4(x + 6) ÷ 4 = 24 for x.

    18

    Multiply both sides by 4 to get 4(x + 6) = 96. Divide by 4 to get x + 6 = 24, so x = 18.

  3. 3. Solve the algebraic fraction equation 4(x + 13) ÷ 5 = 52 for x.

    52

    Multiply both sides by 5 to get 4(x + 13) = 260. Divide by 4 to get x + 13 = 65, so x = 52.

  4. 4. Solve the algebraic fraction equation 3(x + 5) ÷ 3 = 27 for x.

    22

    Multiply both sides by 3 to get 3(x + 5) = 81. Divide by 3 to get x + 5 = 27, so x = 22.

  5. 5. Solve the algebraic fraction equation 2(x + 7) ÷ 2 = 22 for x.

    15

    Multiply both sides by 2 to get 2(x + 7) = 44. Divide by 2 to get x + 7 = 22, so x = 15.

  6. 6. Solve the algebraic fraction equation 3(x + 12) ÷ 4 = 36 for x.

    36

    Multiply both sides by 4 to get 3(x + 12) = 144. Divide by 3 to get x + 12 = 48, so x = 36.

  7. 7. Solve the algebraic fraction equation 5(x + 13) ÷ 5 = 25 for x.

    12

    Multiply both sides by 5 to get 5(x + 13) = 125. Divide by 5 to get x + 13 = 25, so x = 12.

  8. 8. Solve the algebraic fraction equation 5(x + 28) ÷ 6 = 55 for x.

    38

    Multiply both sides by 6 to get 5(x + 28) = 330. Divide by 5 to get x + 28 = 66, so x = 38.

  9. 9. Solve the algebraic fraction equation 5(x + 16) ÷ 6 = 15 for x.

    2

    Multiply both sides by 6 to get 5(x + 16) = 90. Divide by 5 to get x + 16 = 18, so x = 2.

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

    2

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

  11. 11. Solve the algebraic fraction equation 3(x + 24) ÷ 4 = 21 for x.

    4

    Multiply both sides by 4 to get 3(x + 24) = 84. Divide by 3 to get x + 24 = 28, so x = 4.

  12. 12. Solve the algebraic fraction equation 4(x + 23) ÷ 4 = 40 for x.

    17

    Multiply both sides by 4 to get 4(x + 23) = 160. Divide by 4 to get x + 23 = 40, so x = 17.

12 questions · Seed 46 · 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 + 46) ÷ 7 = 84 for x.

    LHS=RHS
    6(x + 46) ÷ 7 = 84 · x + 46 = 98 → x = ?

  2. 2. Solve the algebraic fraction equation 4(x + 6) ÷ 4 = 24 for x.

    LHS=RHS
    4(x + 6) ÷ 4 = 24 · x + 6 = 24 → x = ?

  3. 3. Solve the algebraic fraction equation 4(x + 13) ÷ 5 = 52 for x.

    LHS=RHS
    4(x + 13) ÷ 5 = 52 · x + 13 = 65 → x = ?

  4. 4. Solve the algebraic fraction equation 3(x + 5) ÷ 3 = 27 for x.

    LHS=RHS
    3(x + 5) ÷ 3 = 27 · x + 5 = 27 → x = ?

  5. 5. Solve the algebraic fraction equation 2(x + 7) ÷ 2 = 22 for x.

    LHS=RHS
    2(x + 7) ÷ 2 = 22 · x + 7 = 22 → x = ?

  6. 6. Solve the algebraic fraction equation 3(x + 12) ÷ 4 = 36 for x.

    LHS=RHS
    3(x + 12) ÷ 4 = 36 · x + 12 = 48 → x = ?

  7. 7. Solve the algebraic fraction equation 5(x + 13) ÷ 5 = 25 for x.

    LHS=RHS
    5(x + 13) ÷ 5 = 25 · x + 13 = 25 → x = ?

  8. 8. Solve the algebraic fraction equation 5(x + 28) ÷ 6 = 55 for x.

    LHS=RHS
    5(x + 28) ÷ 6 = 55 · x + 28 = 66 → x = ?

  9. 9. Solve the algebraic fraction equation 5(x + 16) ÷ 6 = 15 for x.

    LHS=RHS
    5(x + 16) ÷ 6 = 15 · x + 16 = 18 → x = ?

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

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

  11. 11. Solve the algebraic fraction equation 3(x + 24) ÷ 4 = 21 for x.

    LHS=RHS
    3(x + 24) ÷ 4 = 21 · x + 24 = 28 → x = ?

  12. 12. Solve the algebraic fraction equation 4(x + 23) ÷ 4 = 40 for x.

    LHS=RHS
    4(x + 23) ÷ 4 = 40 · x + 23 = 40 → x = ?
12 questions · Seed 46 · 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 + 46) ÷ 7 = 84 for x.

    52

    Multiply both sides by 7 to get 6(x + 46) = 588. Divide by 6 to get x + 46 = 98, so x = 52.

  2. 2. Solve the algebraic fraction equation 4(x + 6) ÷ 4 = 24 for x.

    18

    Multiply both sides by 4 to get 4(x + 6) = 96. Divide by 4 to get x + 6 = 24, so x = 18.

  3. 3. Solve the algebraic fraction equation 4(x + 13) ÷ 5 = 52 for x.

    52

    Multiply both sides by 5 to get 4(x + 13) = 260. Divide by 4 to get x + 13 = 65, so x = 52.

  4. 4. Solve the algebraic fraction equation 3(x + 5) ÷ 3 = 27 for x.

    22

    Multiply both sides by 3 to get 3(x + 5) = 81. Divide by 3 to get x + 5 = 27, so x = 22.

  5. 5. Solve the algebraic fraction equation 2(x + 7) ÷ 2 = 22 for x.

    15

    Multiply both sides by 2 to get 2(x + 7) = 44. Divide by 2 to get x + 7 = 22, so x = 15.

  6. 6. Solve the algebraic fraction equation 3(x + 12) ÷ 4 = 36 for x.

    36

    Multiply both sides by 4 to get 3(x + 12) = 144. Divide by 3 to get x + 12 = 48, so x = 36.

  7. 7. Solve the algebraic fraction equation 5(x + 13) ÷ 5 = 25 for x.

    12

    Multiply both sides by 5 to get 5(x + 13) = 125. Divide by 5 to get x + 13 = 25, so x = 12.

  8. 8. Solve the algebraic fraction equation 5(x + 28) ÷ 6 = 55 for x.

    38

    Multiply both sides by 6 to get 5(x + 28) = 330. Divide by 5 to get x + 28 = 66, so x = 38.

  9. 9. Solve the algebraic fraction equation 5(x + 16) ÷ 6 = 15 for x.

    2

    Multiply both sides by 6 to get 5(x + 16) = 90. Divide by 5 to get x + 16 = 18, so x = 2.

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

    2

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

  11. 11. Solve the algebraic fraction equation 3(x + 24) ÷ 4 = 21 for x.

    4

    Multiply both sides by 4 to get 3(x + 24) = 84. Divide by 3 to get x + 24 = 28, so x = 4.

  12. 12. Solve the algebraic fraction equation 4(x + 23) ÷ 4 = 40 for x.

    17

    Multiply both sides by 4 to get 4(x + 23) = 160. Divide by 4 to get x + 23 = 40, so x = 17.

12 questions · Seed 46 · Age guidance, not curriculum certification