GCSE Maths Practice: order-of-operations-bidmas

Question 8 of 10

This question focuses on using BIDMAS with powers, division, multiplication, and addition — a typical GCSE Higher skill.

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\( \begin{array}{l}\text{Work out }4^2 + (12 \div 3) \times 2\text{ using BIDMAS.}\end{array} \)

Choose one option:

Follow the correct order: powers, division/multiplication, then addition or subtraction.

Understanding BIDMAS

The BIDMAS rule—Brackets, Indices, Division, Multiplication, Addition, and Subtraction—defines the correct order of operations used in mathematics. It prevents errors that occur when calculations are done out of order. In GCSE Maths, understanding BIDMAS is essential for solving both algebraic and numerical expressions accurately.

Key Concept

When solving expressions that combine several operations, always begin with brackets. After that, handle indices (powers or roots). Division and multiplication come next, followed by addition and subtraction. Operations on the same level—like multiplication and division—are completed from left to right.

Step-by-Step Method

  1. Step 1: Compute powers (e.g., squares or cubes).
  2. Step 2: Simplify brackets by performing their inner operations.
  3. Step 3: Carry out division and multiplication from left to right.
  4. Step 4: Finish with addition or subtraction to combine results.

Worked Examples

Example 1: \(3^2 + (6 \div 2) \times 4\)
Powers: \(3^2 = 9\).
Brackets: \(6 \div 2 = 3\).
Multiply: \(3 \times 4 = 12\).
Add: \(9 + 12 = 21\).

Example 2: \(5^2 + (10 \div 5) \times 6\)
Powers: \(5^2 = 25\).
Division: \(10 \div 5 = 2\).
Multiplication: \(2 \times 6 = 12\).
Add: \(25 + 12 = 37\).

Example 3: \(2^3 + (9 \div 3) \times 5\)
Powers: \(2^3 = 8\).
Division: \(9 \div 3 = 3\).
Multiplication: \(3 \times 5 = 15\).
Final result: \(8 + 15 = 23\).

Common Mistakes

  • Adding before completing multiplication or division.
  • Forgetting to evaluate powers before other operations.
  • Working right-to-left instead of left-to-right for same-level operations.
  • Skipping brackets or expanding incorrectly.

Why BIDMAS Matters

BIDMAS ensures fairness and consistency in all mathematical calculations. Without it, everyone could interpret the same problem differently. It’s used in coding, physics, finance, and daily problem-solving. For instance, financial analysts rely on BIDMAS when calculating compound interest or tax deductions, where performing multiplication before addition changes the outcome significantly.

FAQ

Q1: What’s the difference between BIDMAS and PEMDAS?
A: They are the same rule. PEMDAS (used in the US) means Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

Q2: Do brackets always come first?
A: Yes, brackets have the highest priority. Solve everything inside them before moving on.

Q3: If there are no brackets or powers, what do I do?
A: Begin with division and multiplication from left to right, then perform addition and subtraction.

Real-Life Application

Order of operations applies in everyday scenarios like recipes, construction, and computer programming. For example, when doubling a recipe, multiplying ingredients before adding them ensures accurate measurements. In computer code, the program also follows BIDMAS to calculate expressions correctly.

Study Tip

When faced with long expressions, write each step on a new line. Highlight which operation you perform next, and check the order before moving forward. Consistent practice with varied examples helps reinforce automatic recall of BIDMAS under exam pressure.