GCSE Maths Practice: order-of-operations-bidmas

Combining Brackets and Fractions

At this stage, calculations often include both brackets and fractions together. These expressions test how well you understand BIDMAS and how confident you are at managing more than one type of operation. The most important rule remains the same: always handle the brackets first before working with any divisions or multiplications, even when those divisions appear as fractions.

How to Approach Mixed Expressions

When a fraction appears in a question, it represents a division. The line in the fraction acts as a dividing symbol, separating the numerator (top) from the denominator (bottom). Before performing that division, simplify everything inside the numerator and denominator separately if needed. If either part contains brackets, complete those brackets first. This process keeps your calculation organised and prevents sign or order mistakes.

Step-by-Step Structure

1. Identify the brackets. Anything inside brackets must be finished first.
2. Evaluate the fraction. Simplify the top and bottom parts individually, then divide.
3. Complete any remaining addition or subtraction. Work from left to right to finish the question.

This sequence ensures that every step is handled correctly and prevents you from mixing inside and outside operations too soon.

Common Errors

• Dividing too early before simplifying the bracketed part.
• Adding the result from the numerator and denominator instead of dividing them.
• Forgetting that the fraction line itself represents a division sign.

Writing out each step explicitly is the best way to avoid these errors. Even short questions can hide multiple layers of BIDMAS if a fraction and bracket appear together.

Real-World Applications

Fractions are a part of many practical situations: sharing quantities, working out discounts, and comparing ratios. Brackets appear in spreadsheet formulas, computer code, and scientific equations. Understanding how they interact prepares you for handling multi-step operations where precision matters, such as averaging results or adjusting scales in recipes or experiments.

Building Confidence

Always check that the order of operations inside the fraction is correct before dividing. In more advanced problems, fractions may appear in both numerators and denominators with separate brackets on each side. The same rule applies: complete every bracket first, simplify each part, and then perform the division.

FAQs

Q1: What comes first: the fraction or the bracket?
A: Brackets come first. Simplify them before carrying out the division represented by the fraction line.

Q2: Do I divide the entire fraction by something outside?
A: Only if the structure of the question includes operations outside the fraction — then treat the fraction as one value when continuing.

Q3: How can I avoid confusion?

A: Use clear working lines, write each stage separately, and underline completed sections as you move through them.

Study Tip

Whenever a fraction contains a bracket, imagine the bracket as a mini calculation inside the main one. Work from the deepest part outward. This mindset ensures you follow BIDMAS correctly, keeps your work tidy, and builds strong habits for handling more complex algebraic or decimal-based problems later on.