Simulic
English

Order of operations – brackets, powers, × ÷ and + −, step by step

MathematicsNumbers & ArithmeticAges 11–12

Loading…

Use with my class

Step through an expression with brackets, powers, ×, ÷, + and − while its expression tree fills in from the bottom, and compare the correct order with common mistakes: working strictly from left to right, doing × before ÷ or + before −, reading −3² as (−3)², and the implied product in 6 ÷ 2(1 + 2). Move one pair of brackets to see how the value changes, check the commutative, associative and distributive laws on number-line and area models, undo a chain of operations with inverse operations, and practise in a quiz that names your mistake.

Lesson: Order of operations (BIDMAS, BODMAS, PEMDAS)

What it shows

Every expression has one value because everyone follows the same order of operations: brackets first, then powers, then multiplication and division from left to right, then addition and subtraction from left to right. This simulation works an expression out one step at a time, highlights the next operation and fills in its expression tree, so you can see why 2 + 3 × 4 is 14 and not 20. Switch to a common mistake to see the wrong value it gives. Other screens move brackets, test the laws of arithmetic, undo operations in reverse order and quiz you.

How to use

On Step by step, choose an Expression or build your own with the keys, then press Next step; change Reading to compare a mistake. On Move the brackets, tap two numbers or use the ( and ) counters to reach the target value. On Laws of arithmetic, pick a Law and an Operation and drag a, b and c. On Inverse operations, set the machine or press New puzzle and find x. The Quiz checks your answers.

Parameters you can change

  • Screen Step by step, Move the brackets, Laws of arithmetic, Inverse operations, Quiz
  • Expression (Step by step) 3 + 4 × 2 − 6 ÷ 3, 24 ÷ 4 × 2, 10 − 4 + 3, 5 × (8 − 2 × 3), 2 × 3², −3² + 10, (−3)² + 10, 6 ÷ 2(1 + 2), 2³ − 4 × (5 − 3)², −2 × (4 − 7) − 5, 2 × ((3 + 5) ÷ 4 + 1)
  • Reading Correct order, Mistake: strictly left to right, Mistake: × before ÷, + before −, Mistake: −3² read as (−3)², Other convention: implied product first
  • Own expression (+ - * / ^ and brackets)
  • Numbers and operations (Move the brackets) 2 + 3 × 4 − 1, 12 ÷ 2 + 4 × 3, 20 − 8 − 2 × 3, 2 × 3 + 4 × 5, 3 + 2² × 4
  • Law Commutative, Associative, Distributive
  • Operation Addition, Subtraction, Multiplication, Division
  • Number a -9–9
  • Number b -9–9
  • Number c -9–9
  • Quiz level No brackets, Brackets, Powers and negatives
  • Machine step 1 Add, Subtract, Multiply, Divide
  • Number in step 1 1–10
  • Machine step 2 Add, Subtract, Multiply, Divide
  • Number in step 2 1–10
  • Machine step 3 None, Add, Subtract, Multiply, Divide
  • Number in step 3 1–10
  • Machine input x -10–10

Questions to explore

  1. Why is 2 + 3 × 4 equal to 14 and not 20?
  2. Which of the four operations are commutative, and which are not?
  3. How do you undo “multiply by 3, then add 4”?

Related simulations