Order of Operations with Brackets

Brackets always come first, and they can change the answer!

1. Brackets Can Change the Answer

Compare These Two Expressions:

6 + 8 × 3

8 × 3 = 24 (multiply first)

6 + 24 = 30

(6 + 8) × 3

6 + 8 = 14 (brackets first!)

14 × 3 = 42

The brackets made us do the addition first, giving us a different answer!

2. The Complete Order of Operations

When there are brackets:

BRACKETS FIRST

Work out everything inside the brackets

Then × and ÷

Multiplication and division, left to right

Then + and −

Addition and subtraction, left to right

Memory Tip: Think of brackets as a VIP section - they get served first!

3. Worked Examples

Example 1: (6 + 8) × 3

Step 1

Brackets first: (6 + 8) = 14

Step 2

Then multiply: 14 × 3 = 42

Example 2: 50 − (12 + 18) ÷ 6

Step 1

Brackets first: (12 + 18) = 30

Expression becomes: 50 − 30 ÷ 6

Step 2

Then division: 30 ÷ 6 = 5

Expression becomes: 50 − 5

Step 3

Finally subtraction: 50 − 5 = 45

Example 3: 8 × (15 − 6) ÷ 3

Step 1

Brackets first: (15 − 6) = 9

Expression becomes: 8 × 9 ÷ 3

Step 2

× and ÷ from left to right:

8 × 9 = 72

72 ÷ 3 = 24

Example 4: (4 + 6) × (15 − 7)

Step 1

Work out BOTH brackets:

(4 + 6) = 10

(15 − 7) = 8

Expression becomes: 10 × 8

Step 2

Multiply: 10 × 8 = 80

Example 5: 100 − (8 + 7) × 4 + 20

Step 1

Brackets first: (8 + 7) = 15

Expression becomes: 100 − 15 × 4 + 20

Step 2

Multiplication: 15 × 4 = 60

Expression becomes: 100 − 60 + 20

Step 3

+ and − from left to right:

100 − 60 = 40

40 + 20 = 60

Practice Problems

1. Find the value of each (with brackets):

a) (5 + 4) × 3 = ?

b) (20 − 12) ÷ 4 = ?

c) 8 × (6 + 4) = ?

d) 36 ÷ (9 − 3) = ?

ShowHide solutions

a) (5 + 4) × 3 = 9 × 3 = 27

b) (20 − 12) ÷ 4 = 8 ÷ 4 = 2

c) 8 × (6 + 4) = 8 × 10 = 80

d) 36 ÷ (9 − 3) = 36 ÷ 6 = 6

2. Find the value of each (more complex):

a) (10 + 5) × 2 − 8 = ?

b) 45 ÷ (3 + 6) + 7 = ?

c) (8 + 2) × (15 − 10) = ?

d) 100 − (25 + 15) × 2 = ?

ShowHide solutions

a) (10 + 5) × 2 − 8 = 15 × 2 − 8 = 30 − 8 = 22

b) 45 ÷ (3 + 6) + 7 = 45 ÷ 9 + 7 = 5 + 7 = 12

c) (8 + 2) × (15 − 10) = 10 × 5 = 50

d) 100 − (25 + 15) × 2 = 100 − 40 × 2 = 100 − 80 = 20

Key Takeaways

BRACKETS ( ) always come FIRST - they are the VIP!
Inside brackets, follow the normal rules (× and ÷ before + and −)
After brackets: × and ÷, then + and −
When there are multiple brackets, work out ALL of them before moving on
Brackets can completely change the answer to a problem!