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Order of operations

Decide what to calculate first, with and without parentheses.

Practice + answer key · 2 pages

Worksheet settings12 questions · 2 columns · A4
Base-number range

Every underlying positive base number is within the range; constructed products may be larger.

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Order of operationsOrder of operations. Practice. Calculate 5 + 8 × 4. Calculate (4 + 8) × 6. Calculate 24 ÷ 8 + 7. Calculate 4 + 8 × 4. Calculate (4 + 3) × 6. Calculate 18 ÷ 3 + 3. Calculate 8 + 6 × 2. Calculate (2 + 8) × 3. Calculate 21 ÷ 7 + 5. Calculate 2 + 2 × 7. Calculate (8 + 4) × 2. Calculate 64 ÷ 8 + 7.Name __________________________Date _______________Order of operationsCalculate each expression in the correct order.Worked exampleCalculate 4 + 3 × 6, then compare with (4 + 3) × 6. → 22; 42Without brackets, calculate 3 × 6 = 18, then 4 + 18 = 22.1.Calculate 5 + 8 × 4.2.Calculate (4 + 8) × 6.3.Calculate 24 ÷ 8 + 7.4.Calculate 4 + 8 × 4.5.Calculate (4 + 3) × 6.6.Calculate 18 ÷ 3 + 3.7.Calculate 8 + 6 × 2.8.Calculate (2 + 8) × 3.9.Calculate 21 ÷ 7 + 5.10.Calculate 2 + 2 × 7.11.Calculate (8 + 4) × 2.12.Calculate 64 ÷ 8 + 7.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · 4873ed5d
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Practice + answer key · 2 pages

Arithmetic

What you’ll practice

Evaluate short integer expressions using parentheses and multiplication/division before addition.

Compare 4 + 3 × 6 with (4 + 3) × 6. The numbers are the same, but the parentheses change which part you calculate first—and the answer.

How this skill works

Work inside parentheses first. Outside parentheses, multiplication and division take precedence over addition and subtraction.

These questions use short forms so the effect of the operation order stays visible. Rewriting the expression after its first calculation helps prevent left-to-right guessing.

Worked example

Calculate 4 + 3 × 6, then compare with (4 + 3) × 6.
  1. Without brackets, calculate 3 × 6 = 18, then 4 + 18 = 22.
  2. With brackets, calculate 4 + 3 = 7 first, then 7 × 6 = 42.

Answer: 22; 42

Teaching notes

  • Underline the part to calculate first.
  • Copy the unchanged part when rewriting an intermediate expression.
Practice questions
  1. Calculate 5 + 8 × 4.
  2. Calculate (4 + 8) × 6.
  3. Calculate 24 ÷ 8 + 7.
  4. Calculate 4 + 8 × 4.
  5. Calculate (4 + 3) × 6.
  6. Calculate 18 ÷ 3 + 3.
  7. Calculate 8 + 6 × 2.
  8. Calculate (2 + 8) × 3.
  9. Calculate 21 ÷ 7 + 5.
  10. Calculate 2 + 2 × 7.
  11. Calculate (8 + 4) × 2.
  12. Calculate 64 ÷ 8 + 7.
Answers and steps
  1. 37
    1. Multiply first: 8 × 4 = 32. Then 5 + 32 = 37.
  2. 72
    1. Work inside the brackets: 4 + 8 = 12. Then 12 × 6 = 72.
  3. 10
    1. Divide first: 24 ÷ 8 = 3. Then 3 + 7 = 10.
  4. 36
    1. Multiply first: 8 × 4 = 32. Then 4 + 32 = 36.
  5. 42
    1. Work inside the brackets: 4 + 3 = 7. Then 7 × 6 = 42.
  6. 9
    1. Divide first: 18 ÷ 3 = 6. Then 6 + 3 = 9.
  7. 20
    1. Multiply first: 6 × 2 = 12. Then 8 + 12 = 20.
  8. 30
    1. Work inside the brackets: 2 + 8 = 10. Then 10 × 3 = 30.
  9. 8
    1. Divide first: 21 ÷ 7 = 3. Then 3 + 5 = 8.
  10. 16
    1. Multiply first: 2 × 7 = 14. Then 2 + 14 = 16.
  11. 24
    1. Work inside the brackets: 8 + 4 = 12. Then 12 × 2 = 24.
  12. 15
    1. Divide first: 64 ÷ 8 = 8. Then 8 + 7 = 15.