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Operations and Calculations - Order of operations (BODMAS/BIDMAS)

Grade 5IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The order of operations is a standard rule used to clarify which procedures should be performed first in a mathematical expression.

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Operations inside Brackets always take top priority and must be solved first.

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Indices (or Orders) refer to powers and square roots, which are calculated after brackets.

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Multiplication and Division carry equal weight; if both appear, solve them from left to right.

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Addition and Subtraction carry equal weight; if both appear, solve them from left to right.

📐Formulae

BIDMAS: Brackets, Indices, Division, Multiplication, Addition, Subtraction

BODMAS: Brackets, Orders, Division, Multiplication, Addition, Subtraction

💡Examples

Problem 1:

7+3×57 + 3 \times 5

Solution:

2222

Explanation:

According to BIDMAS, Multiplication must be done before Addition. Calculate 3×5=153 \times 5 = 15, then 7+15=227 + 15 = 22.

Problem 2:

(10+2)÷3−1(10 + 2) \div 3 - 1

Solution:

33

Explanation:

Start with Brackets: 10+2=1210 + 2 = 12. Next, perform Division: 12÷3=412 \div 3 = 4. Finally, perform Subtraction: 4−1=34 - 1 = 3.

Problem 3:

42+8÷24^2 + 8 \div 2

Solution:

2020

Explanation:

First, solve the Indices (Order): 42=164^2 = 16. Next, perform Division: 8÷2=48 \div 2 = 4. Finally, add the results: 16+4=2016 + 4 = 20.

Problem 4:

20÷4×220 \div 4 \times 2

Solution:

1010

Explanation:

Division and Multiplication have equal priority. Solve from left to right: 20÷4=520 \div 4 = 5, then 5×2=105 \times 2 = 10.