Scholars & Parents
ExplainerMathGrades 3–5

Order of Operations (PEMDAS)

What Is This?

When an expression contains more than one operation — addition, subtraction, multiplication, division, brackets, or exponents — there are rules that tell you which operation to perform first. These rules are called the order of operations. Without them, the same expression could give different answers depending on how it was read.

The order of operations is often remembered using the acronym PEMDAS:

Letter Stands for Do this…
P Parentheses (brackets) First — work inside all brackets
E Exponents (powers) Second
M Multiplication Third — left to right
D Division Third — left to right (same level as M)
A Addition Fourth — left to right
S Subtraction Fourth — left to right (same level as A)

Memory tip: "Please Excuse My Dear Aunt Sally"

Why Does It Matter?

Without an agreed order, 2 + 3 × 4 could mean (2 + 3) × 4 = 20 OR 2 + (3 × 4) = 14. The order of operations gives everyone the same answer: 14 (multiply first). This is essential for programming, spreadsheets, calculators, and all mathematical communication.

The Rules in Detail

Rule 1 — Parentheses First

Work out everything inside brackets (parentheses) before anything else.

Example: (3 + 5) × 2

  • Inside brackets: 3 + 5 = 8
  • Then multiply: 8 × 2 = 16 ✓

If there are nested brackets, start with the innermost set.

Example: 2 × (3 + (4 − 1))

  • Innermost: 4 − 1 = 3
  • Next brackets: 3 + 3 = 6
  • Multiply: 2 × 6 = 12 ✓

Rule 2 — Exponents (Powers)

After brackets, calculate any exponents.

Example: 3 + 2²

  • Exponent: 2² = 4
  • Then add: 3 + 4 = 7 ✓

Example: (2 + 1)² − 5

  • Brackets: 2 + 1 = 3
  • Exponent: 3² = 9
  • Subtract: 9 − 5 = 4 ✓

Rule 3 — Multiplication and Division (Left to Right)

Multiplication and division are at the same level. When both appear, work from left to right.

Example: 12 ÷ 4 × 3

  • Left to right: 12 ÷ 4 = 3, then 3 × 3 = 9 ✓
  • (Not 12 ÷ 12 = 1 — that would be doing multiplication before division)

Example: 5 × 6 ÷ 2

  • Left to right: 5 × 6 = 30, then 30 ÷ 2 = 15 ✓

Rule 4 — Addition and Subtraction (Left to Right)

Addition and subtraction are at the same level. When both appear, work from left to right.

Example: 10 − 3 + 2

  • Left to right: 10 − 3 = 7, then 7 + 2 = 9 ✓
  • (Not 10 − 5 = 5 — that would be doing addition before subtraction)

Putting It All Together

Example: 3 + 4 × 2

  • No brackets or exponents.
  • Multiplication before addition: 4 × 2 = 8
  • Then add: 3 + 8 = 11 ✓

Example: (3 + 4) × 2

  • Brackets first: 3 + 4 = 7
  • Multiply: 7 × 2 = 14 ✓

Notice how brackets completely change the answer.

Worked Examples

Worked Example 1

8 + 2 × 5 − 3

  1. Multiplication: 2 × 5 = 10
  2. Left to right: 8 + 10 = 18
  3. Subtract: 18 − 3 = 15 ✓

Worked Example 2

(8 + 2) × (5 − 3)

  1. Brackets: 8 + 2 = 10 and 5 − 3 = 2
  2. Multiply: 10 × 2 = 20 ✓

Worked Example 3

3² + 4 × (6 − 2)

  1. Brackets: 6 − 2 = 4
  2. Exponent: 3² = 9
  3. Multiply: 4 × 4 = 16
  4. Add: 9 + 16 = 25 ✓

Worked Example 4

20 ÷ 4 + 3 × 2 − 1

  1. Division: 20 ÷ 4 = 5
  2. Multiplication: 3 × 2 = 6
  3. Left to right: 5 + 6 = 11
  4. Subtract: 11 − 1 = 10 ✓

Worked Example 5

2 × (3 + 1)² ÷ 8

  1. Brackets: 3 + 1 = 4
  2. Exponent: 4² = 16
  3. Left to right: 2 × 16 = 32, then 32 ÷ 8 = 4 ✓

Using Brackets to Change the Answer

Brackets let you override the default order.

Expression Answer Why
5 + 3 × 4 17 Multiply first: 3×4=12, then 5+12
(5 + 3) × 4 32 Brackets first: 5+3=8, then 8×4
10 − 4 ÷ 2 8 Divide first: 4÷2=2, then 10−2
(10 − 4) ÷ 2 3 Brackets first: 10−4=6, then 6÷2

Common Mistakes

Mistake 1: Working strictly left to right without PEMDAS 2 + 3 × 4: computing left to right gives (2+3)×4 = 20. The correct answer is 2 + 12 = 14.

Mistake 2: Treating multiplication before division as a strict rule 12 ÷ 4 × 3 — division and multiplication are equal. Go left to right: (12÷4)×3 = 3×3 = 9, not 12÷12 = 1.

Mistake 3: Treating addition before subtraction as a strict rule 10 − 3 + 2 — go left to right: (10−3)+2 = 7+2 = 9, not 10−5 = 5.

Mistake 4: Forgetting the exponent before multiplication 3 + 2² × 4: exponent first (2²=4), then multiply (4×4=16), then add (3+16=19). Not (3+4)×4 = 28.

Key Takeaways

  • Parentheses → Exponents → Multiplication/Division (L→R) → Addition/Subtraction (L→R)
  • Multiplication and division are equal priority — go left to right
  • Addition and subtraction are equal priority — go left to right
  • Brackets always override the default order
  • When in doubt, evaluate step by step and show your working

Practice and Resources

Ready to practise? Try our Grade 3-5 Order of Operations Worksheet with problems covering each level of PEMDAS. Test yourself with the Grade 3-5 Math Practice Test.

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