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MathidiaMathematics Academy
Integers, powers and roots
Lesson 2 of 75
Easy practice

Order of operations

Objective. Evaluate expressions containing brackets, powers and directed numbers.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Order of operations is the agreed sequence for evaluating expressions so everyone gets the same answer: brackets, then powers, then multiplication and division left to right, then addition and subtraction left to right (BIDMAS). In an expression like 3 + 4 × 2², the power is worked out first (2² = 4), then the multiplication (4 × 4 = 16), and finally the addition (3 + 16 = 19). Brackets override the usual order, so (3 + 4) × 2 means add before multiplying. Always scan for brackets first, then powers, before touching the remaining operations.

Worked example

Use the correct order of operations to evaluate 5 + (6 − 2)² ÷ 4.

-1023467−2
Number line from -1 to 7 with a jump of 2 backwards from 6
  1. 1Work out the bracket: 6 − 2 = 4
  2. 2Apply the power: 4² = 16
  3. 3Divide: 16 ÷ 4 = 4
  4. 4Add: 5 + 4 = 9

Answer: 9

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Common mistake. A common error is working strictly left to right, so 2 + 3 × 4 is wrongly calculated as 5 × 4 = 20 instead of doing the multiplication first to get 2 + 12 = 14. Always apply BIDMAS, not reading order.

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