GCSE Maths Practice: order-of-operations-bidmas

Question 6 of 10

This exercise checks your understanding of BIDMAS with powers, brackets, and decimals—core for GCSE Higher-tier algebra and arithmetic reasoning.

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\( \begin{array}{l}\text{Work out }2 + 3 \times (4^2 - 3) \div 5\text{ using BIDMAS.}\end{array} \)

Choose one option:

Use the BIDMAS hierarchy and check each step before moving on.

Understanding BIDMAS

The BIDMAS rule (Brackets, Indices, Division, Multiplication, Addition, Subtraction) tells us the correct order of operations in any numerical expression. Using this order ensures everyone obtains the same result. If you mix the order or skip steps, the answer can change dramatically.

Step-by-Step Method

  1. Brackets: Solve everything inside brackets first. Simplify any expression contained within them.
  2. Indices (powers): Compute powers or roots after brackets are resolved.
  3. Division and Multiplication: Work from left to right for these operations.
  4. Addition and Subtraction: Handle these last, again from left to right.

Worked Examples

Example 1: \(1 + 2 \times (3^2 - 1) \div 4\).
Inside brackets: \(3^2 - 1 = 8\).
Then multiplication/division: \(2 \times 8 \div 4 = 4\).
Finally add 1 → 5.

Example 2: \(5 + 2 \times (3^2 - 2) \div 3\).
Compute power: \(3^2 = 9\). Inside brackets: \(9 - 2 = 7\).
Then \(2 \times 7 \div 3 ≈ 4.67\).
Add 5 → ≈ 9.67.

Example 3: \(6 - 4 \times (2^2 + 1) \div 2\).
Brackets: \(2^2 + 1 = 5\).
Then \(4 \times 5 \div 2 = 10\).
Subtract: \(6 - 10 = -4\).

Common Mistakes

  • Adding or subtracting before finishing multiplication or division.
  • Forgetting to apply powers before multiplying.
  • Solving brackets in the wrong order when nested.
  • Dropping decimals or rounding too early—always finish calculation before rounding.

Real-Life Applications

BIDMAS appears in daily contexts such as tax and discount calculations, science formulas, or coding. For instance, in programming languages, similar order rules ensure mathematical statements give consistent outputs. Financial analysts use it when applying percentage changes sequentially to investments.

FAQ

Q1: Why does order matter?
A: Because arithmetic is not associative across all operations. Without an order, results differ between people.

Q2: Is BIDMAS the same as PEMDAS?
A: Yes—PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) is the U.S. version.

Q3: What if operations appear at the same level?
A: Work left to right for division and multiplication, then left to right for addition and subtraction.

Study Tip

Whenever you face a long expression, rewrite it step-by-step on separate lines, clearly marking which part you are solving. This habit prevents careless mistakes and builds accuracy under exam pressure.