All skills Math

Learn Index · Arithmetic and Operations Grade 6–8

Order of operations

The agreed order for evaluating: brackets, exponents, ×÷, then +−.

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Why we need rules

What is 3 + 4 × 5? If you add first you get 35. If you multiply first you get 23. Without an agreed order of operations, the same expression would give different answers. Mathematicians agree on one order, so everyone gets 23.

BEDMAS

In Canada, students learn BEDMAS:

Step Letters Operation
1 B Brackets
2 E Exponents (powers and roots)
3 D M Division and Multiplication, left to right
4 A S Addition and Subtraction, left to right

(Elsewhere you may see PEMDAS or BODMAS. They mean the same thing.)

The important detail

Division and multiplication are a tie: do whichever comes first from left to right. The same goes for addition and subtraction.

  • 20 ÷ 4 × 5 = 5 × 5 = 25 (not 20 ÷ 20 = 1)
  • 10 − 3 + 2 = 7 + 2 = 9 (not 10 − 5 = 5)

Step-by-step example

Evaluate: 6 + 2 × (8 − 3)² ÷ 10

  1. Brackets: 8 − 3 = 5 → 6 + 2 × 5² ÷ 10
  2. Exponents: 5² = 25 → 6 + 2 × 25 ÷ 10
  3. × and ÷ left to right: 2 × 25 = 50; 50 ÷ 10 = 5 → 6 + 5
  4. Addition: 11

Write a new line after each step. It helps you avoid mistakes.

Hidden brackets

  • Fraction bars group: (12 + 8) ÷ (7 − 2) is the same as 20 over 5 → 4.
  • Square roots group: √(9 + 16) = √25 = 5.
  • Nested brackets: do the innermost first. 2 × [3 + (4 − 1)] = 2 × [3 + 3] = 2 × 6 = 12.

Negatives and exponents

  • −3² = −(3²) = −9 (the exponent comes before the negative)
  • (−3)² = 9

Calculators

Most scientific calculators follow BEDMAS, but simple ones may not. Test yours with 3 + 4 × 5. If it shows 35, it calculates left to right, so you’ll need brackets.

Worked examples

Example 1: 18 − 6 ÷ 3

Divide first: 6 ÷ 3 = 2 → 18 − 2 = 16.

Example 2: (4 + 5) × 2²

Brackets: 9; exponent: 4 → 9 × 4 = 36.

Example 3: 48 ÷ 6 × 2 + 1

48 ÷ 6 = 8; 8 × 2 = 16; 16 + 1 = 17.

Common mistakes

  • Doing multiplication before division every time. They’re done left to right.
  • Working strictly left to right and ignoring BEDMAS.
  • Squaring a negative without brackets incorrectly.

Try it yourself

  1. 5 + 3 × 4
  2. (5 + 3) × 4
  3. 36 ÷ 4 × 3
  4. 2³ + 10 ÷ 2
  5. 50 − 2 × (3 + 4)²

Answers: 1) 17 2) 32 3) 27 4) 13 5) −48

Quick recap

  • Follow BEDMAS: brackets, exponents, ÷ and ×, + and −.
  • Ties are done left to right.
  • Fraction bars and roots act like brackets.