GCSE Maths Practice: order-of-operations-bidmas

Question 1 of 10

This logic puzzle tests your understanding of BIDMAS through a robot’s step-by-step instructions combining powers, brackets, multiplication, and division.

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\( \begin{array}{l}\text{A robot follows instructions: it squares 4,}\\\text{multiplies by the sum of 3 and 2, then subtracts}\\\text{the result of 6 divided by 3. What number does}\\\text{the robot output?}\end{array} \)

Choose one option:

Read carefully. Translate each worded instruction into its mathematical operation before applying BIDMAS.

Understanding BIDMAS Through Logic Puzzles

In this question, a robot follows a sequence of programmed instructions. Each command represents a mathematical operation such as squaring, multiplying, or dividing. The puzzle tests how well you can translate worded logic into the correct numerical order using the BIDMAS rule. BIDMAS stands for Brackets, Indices, Division, Multiplication, Addition, and Subtraction.

The Story

Imagine a robot programmed to carry out the following routine. It starts with a number, squares it, multiplies by the sum of two smaller numbers, and then performs a division before subtracting the result from its total energy reading. The challenge is to find the robot’s final output.

Applying BIDMAS

To decode the robot’s instructions correctly, we must respect the BIDMAS order of operations:

  1. Brackets: Solve anything inside brackets first.
  2. Indices (powers): Evaluate powers or roots next.
  3. Division and Multiplication: Work from left to right across these operations.
  4. Addition and Subtraction: Complete these last, also left to right.

Worked Examples

Example 1: A robot computes \(3^2 \times (2 + 3) - 5 \div 1\).
Powers: \(3^2 = 9\). Brackets: \(2 + 3 = 5\). Multiply: \(9 \times 5 = 45\). Divide: \(5 \div 1 = 5\). Subtract: \(45 - 5 = 40\).

Example 2: \(2^3 \times (4 + 1) - 8 \div 2\).
Power: \(2^3 = 8\). Brackets: \(4 + 1 = 5\). Multiply: \(8 \times 5 = 40\). Divide: \(8 \div 2 = 4\). Subtract: \(40 - 4 = 36\).

Example 3: The one solved here: \(4^2 \times (3 + 2) - 6 \div 3\).
Powers: \(4^2 = 16\). Brackets: \(3 + 2 = 5\). Multiply: \(16 \times 5 = 80\). Divide: \(6 \div 3 = 2\). Subtract: \(80 - 2 = 78\).

Common Mistakes

  • Doing addition before multiplication.
  • Forgetting to square the number first.
  • Misinterpreting the robot’s sequence and solving from left to right without using BIDMAS.
  • Mixing division and subtraction order.

Why This Matters

Word problems like this develop logical thinking and help you connect arithmetic to algorithms. Robots, calculators, and computer programs all follow a strict order of operations, which mirrors BIDMAS exactly. Misplacing one step could change the entire result, just like a coding error changes how a program behaves.

Real-Life Connections

In robotics and programming, BIDMAS ensures mathematical commands execute correctly. For example, a robot calculating distances or energy usage must process powers before multiplications to produce an accurate reading. Understanding this sequence helps students move smoothly into computer science, engineering, and AI programming, where such order of execution is vital.

FAQ

Q1: Why are puzzles like this used in GCSE exams?
A: They test both reasoning and calculation skills, showing that you can translate words into operations correctly.

Q2: Can BIDMAS be broken down further?
A: Yes—think of it as groups: (1) brackets, (2) powers, (3) division/multiplication, (4) addition/subtraction.

Q3: Do computers use BIDMAS too?
A: Yes. Programming languages like Python or C++ follow the same precedence rules, so learning BIDMAS prepares you for coding.

Study Tip

When faced with a word problem, rewrite it in symbols before solving. Identify brackets and powers, underline them, and check each stage before moving on. Always write each operation clearly, line by line. This builds precision and confidence under exam pressure.

Summary

This robot puzzle combines creativity with logic to reinforce BIDMAS. Solving such problems strengthens both mathematical accuracy and computational thinking—skills that go beyond exams into the real world.