What is BIDMAS?
BIDMAS is an acronym that helps you remember the correct order to perform mathematical operations in an expression. Getting the order right is crucial for finding the correct answer!
B - Brackets
I - Indices (or Orders, like powers and square roots)
D - Division
M - Multiplication
A - Addition
S - Subtraction
Important Note:
- Division and Multiplication have equal priority. Work them out from left to right as they appear in the expression.
- Addition and Subtraction also have equal priority. Work them out from left to right as they appear.
- When dealing with fractions, treat the numerator and the denominator as if they are enclosed in brackets. Calculate them separately before performing the division indicated by the fraction line.
BIDMAS in Action: Worked Examples
Example 1: 3 + 5 × 2
- Multiplication first:
5 × 2 = 10
- Then Addition:
3 + 10 = 13
Answer: 13
Example 2: (7 - 2) × 3
- Brackets first:
7 - 2 = 5
- Then Multiplication:
5 × 3 = 15
Answer: 15
Example 3: 10 + 2² × 3
- Indices first:
2² = 4
- Then Multiplication:
4 × 3 = 12
- Finally Addition:
10 + 12 = 22
Answer: 22
Example 4 (Left to Right): 20 ÷ 4 × 2
- Division (left-most of D/M):
20 ÷ 4 = 5
- Then Multiplication:
5 × 2 = 10
Answer: 10
Example 5 (Complex): 6 + (10 - 4)² ÷ 3
- Brackets first:
(10 - 4) = 6
- Then Indices:
6² = 36
- Then Division:
36 ÷ 3 = 12
- Finally Addition:
6 + 12 = 18
Answer: 18
Example 6 (Fractions):
7 + 3 × 6
10 - (12 ÷ 4)
7 + 3 × 6
10 - (12 ÷ 4)
Note: The fraction line acts as a grouping symbol (like brackets) for both the numerator and the denominator. Solve the numerator and denominator separately before performing the final division.
- Numerator
(7 + 3 × 6)
:- Multiplication first:
3 × 6 = 18
- Then Addition:
7 + 18 = 25
- Multiplication first:
- Denominator
(10 - (12 ÷ 4))
:- Innermost Brackets (Division) first:
12 ÷ 4 = 3
- Then Subtraction:
10 - 3 = 7
- Innermost Brackets (Division) first:
- The expression becomes the fraction:
25
7
- Finally, Division:
25 ÷ 7
(or as an improper fraction25/7
)
Answer: 25/7
Test Your Knowledge: Quick Quiz!
1. What is 12 - 3 × 2
?
Answer: 6
Explanation: Multiplication first (3 × 2 = 6), then Subtraction (12 - 6 = 6).
2. What is (4 + 6) ÷ 2
?
Answer: 5
Explanation: Brackets first (4 + 6 = 10), then Division (10 ÷ 2 = 5).
3. What is 5 + 3² - 2
?
Answer: 12
Explanation: Indices first (3² = 9), then Addition (5 + 9 = 14), then Subtraction (14 - 2 = 12). (Or 5+9=14, then 14-2=12, A/S left to right)
4. What is 18 ÷ 3 × (1 + 2)
?
Answer: 18
Explanation: Brackets first (1 + 2 = 3). Expression becomes 18 ÷ 3 × 3. Then Division (18 ÷ 3 = 6). Then Multiplication (6 × 3 = 18).
5. What is
(5 + 3) × 2
10 - 6
?
Answer: 4
Explanation: Numerator: Brackets first (5 + 3 = 8), then Multiplication (8 × 2 = 16). Denominator: Subtraction (10 - 6 = 4). Finally, Division (16 ÷ 4 = 4).
6. What is 4² + 20 ÷ (4 + 1) - 3
?
Answer: 17
Explanation: Brackets first (4 + 1 = 5). Then Indices (4² = 16). Then Division (20 ÷ 5 = 4). Expression becomes 16 + 4 - 3. Then Addition (16 + 4 = 20). Finally, Subtraction (20 - 3 = 17).
7. What is 100 - [2 × (5 + 3)²] ÷ 8
?
Answer: 84
Explanation: Innermost Brackets (5 + 3 = 8). Then Indices within outer brackets (8² = 64). Then Multiplication within outer brackets (2 × 64 = 128). Expression becomes 100 - 128 ÷ 8. Then Division (128 ÷ 8 = 16). Finally, Subtraction (100 - 16 = 84).
8. What is 3 × 8 ÷ 2 + 10 - 4 ÷ 2
?
Answer: 20
Explanation: Left to right for D/M: Multiplication (3 × 8 = 24), then Division (24 ÷ 2 = 12). Rightmost Division (4 ÷ 2 = 2). Expression becomes 12 + 10 - 2. Left to right for A/S: Addition (12 + 10 = 22), then Subtraction (22 - 2 = 20).
9. What is
3² + (10 - 6)
2 × (4 - 1)
?
Answer: 13/6
Explanation: Numerator: Brackets (10 - 6 = 4), then Indices (3² = 9), then Addition (9 + 4 = 13). Denominator: Brackets (4 - 1 = 3), then Multiplication (2 × 3 = 6). Finally, Division (13 ÷ 6 = 13/6).
10. What is 5 × 3 - (4² + 9) ÷ 5
?
Answer: 10
Explanation: Brackets: Indices (4² = 16), then Addition (16 + 9 = 25). Expression becomes 5 × 3 - 25 ÷ 5. Then Multiplication (5 × 3 = 15). Then Division (25 ÷ 5 = 5). Finally, Subtraction (15 - 5 = 10).
Interactive BIDMAS Tool: What's Next?
For the given expression, click the button that represents the first operation you should perform according to BIDMAS.
Loading expression...
Exam-Style BIDMAS Problems
1. A shop sells pens for £2 each and notebooks for £5 each. Sarah buys 3 pens and 2 notebooks. She pays with a £20 note. How much change does she receive?
Answer: £4
Explanation:
- Calculate the cost of the pens:
3 × £2 = £6
(Multiplication) - Calculate the cost of the notebooks:
2 × £5 = £10
(Multiplication) - Calculate the total cost of items:
£6 + £10 = £16
(Addition - M comes before A in BIDMAS) - Calculate the change:
£20 - £16 = £4
(Subtraction)
2. A cinema ticket costs £8 for an adult and £5 for a child. A family of 2 adults and 3 children go to the cinema. They also buy a large popcorn for £6. What is the total cost of their cinema trip?
Answer: £37
Explanation:
- Calculate the cost of adult tickets:
2 × £8 = £16
(Multiplication) - Calculate the cost of child tickets:
3 × £5 = £15
(Multiplication) - Calculate the total cost of all tickets:
£16 + £15 = £31
(Addition - M comes before A in BIDMAS) - Add the cost of the popcorn:
£31 + £6 = £37
(Addition)
3. A school trip costs £150 in total for 10 students. On the day of the trip, 2 students are ill and cannot go. The school decides to split the total cost equally among the students who do go. How much does each student who goes on the trip pay?
Answer: £18.75
Explanation:
The calculation can be written as: £150 ÷ (10 - 2)
- First, calculate the number of students who go on the trip (operation inside the Brackets):
10 - 2 = 8
students. - Then, divide the total cost by the number of students attending:
£150 ÷ 8 = £18.75
(Division)
Key Takeaways
- Always follow BIDMAS: Brackets, Indices, Division/Multiplication, Addition/Subtraction.
- Work from left to right for Division/Multiplication.
- Work from left to right for Addition/Subtraction.
- When dealing with fractions, solve the numerator and denominator separately (as if they are in brackets) before the final division.
- Practice makes perfect! The more you use BIDMAS, the easier it becomes.