Order of Operations
Learn the correct order for working out a calculation
1. Why Does Order Matter?
Consider This Problem:
6 + 8 × 3 = ?
Wrong Way:
6 + 8 = 14
14 × 3 = 42 ✗
Correct Way:
8 × 3 = 24
6 + 24 = 30 ✓
The order in which we do operations matters! Without rules, different people would get different answers to the same problem.
2. The Order of Operations Rule
When there are NO brackets:
- First: Work from left to right doing all multiplication and division
- Then: Work from left to right doing all addition and subtraction
Remember It This Way:
× and ÷ are stronger than + and −
Multiplication and Division come BEFORE Addition and Subtraction
3. Worked Examples
Example 1: 6 + 8 × 3
Do multiplication first: 8 × 3 = 24
Then do addition: 6 + 24 = 30
Example 2: 15 − 9 ÷ 3
Do division first: 9 ÷ 3 = 3
Then do subtraction: 15 − 3 = 12
Example 3: 20 + 16 ÷ 4 × 2
Division and multiplication from left to right:
16 ÷ 4 = 4
4 × 2 = 8
Then do addition: 20 + 8 = 28
Example 4: 48 ÷ 8 + 5 × 9 − 27
Division and multiplication (left to right):
48 ÷ 8 = 6
5 × 9 = 45
Expression becomes: 6 + 45 − 27
Addition and subtraction (left to right):
6 + 45 = 51
51 − 27 = 24
Practice Problems
1. Find the value of each (no brackets):
a) 5 + 4 × 3 = ?
b) 20 − 12 ÷ 4 = ?
c) 8 × 6 + 10 = ?
d) 36 ÷ 6 − 2 = ?
ShowHide solutions
a) 5 + 4 × 3 = 5 + 12 = 17
b) 20 − 12 ÷ 4 = 20 − 3 = 17
c) 8 × 6 + 10 = 48 + 10 = 58
d) 36 ÷ 6 − 2 = 6 − 2 = 4
2. Find the value of each (multiple operations):
a) 10 + 6 × 5 − 8 = ?
b) 45 ÷ 9 + 7 × 3 = ?
c) 100 − 25 × 2 + 30 = ?
d) 8 × 7 − 42 ÷ 6 = ?
ShowHide solutions
a) 10 + 6 × 5 − 8 = 10 + 30 − 8 = 40 − 8 = 32
b) 45 ÷ 9 + 7 × 3 = 5 + 21 = 26
c) 100 − 25 × 2 + 30 = 100 − 50 + 30 = 50 + 30 = 80
d) 8 × 7 − 42 ÷ 6 = 56 − 7 = 49
Key Takeaways
- Multiplication (×) and Division (÷) come FIRST
- Addition (+) and Subtraction (−) come SECOND
- When you have multiple × and ÷, work from left to right
- When you have multiple + and −, work from left to right
- This rule ensures everyone gets the same answer!