GCSE Maths Practice: order-of-operations-bidmas

Understanding Mixed Operations Without Brackets

When an expression includes both multiplication and addition but no brackets, the BIDMAS rule still applies. This means the multiplication must be completed before any addition or subtraction. Following this order avoids confusion and ensures the same result every time the calculation is performed.

How BIDMAS Works Step by Step

1. Identify the operations. Check whether multiplication or division appears anywhere in the expression.
2. Handle those first. Multiply or divide in the order they appear from left to right.
3. Then perform additions or subtractions. Only after the higher-priority operations are finished should you move to the remaining steps.

This process guarantees accuracy even in more complex calculations. Skipping directly from left to right might seem quicker, but it usually produces the wrong result.

Common Mistakes to Watch For

• Adding numbers before completing multiplication.
• Not noticing the multiplication sign when it appears next to a number.
• Entering operations into a calculator in the wrong order.

Always check which operation has priority before pressing any buttons or writing the next line of working.

Why Multiplication Comes First

Multiplication and division change values more dramatically than addition or subtraction. They are used to scale numbers up or down, so they must happen before combining totals. Addition and subtraction merely adjust those totals once the scaling is complete. This logic keeps maths consistent across all problems, from basic arithmetic to algebraic expressions.

Everyday Applications

The same rule applies when solving real-world problems. For example, if something costs a certain amount and you buy several of them, you multiply first to find the total cost before adding taxes or extra charges. Reversing the order would make the cost appear larger or smaller than it really is.

Developing Good Habits

To build accuracy, underline multiplication and division signs in each question before starting. This helps focus attention on higher-priority operations first. Writing every intermediate step on a new line can also prevent missing a sign or skipping an operation. Over time, these small habits turn BIDMAS from a rule you must remember into an instinct you automatically follow.

FAQs

Q1: Do multiplication and division have the same priority?
A: Yes. They are equal in rank and should be completed in the order they appear from left to right before moving to addition or subtraction.

Q2: What if there are brackets?
A: Anything inside brackets always takes priority over everything outside, even before multiplication.

Q3: What happens if there is no multiplication sign, like 3(4)?
A: This still means 3 × 4, and it must be calculated before any addition or subtraction.

Study Tip

When reviewing problems, re-read each line to ensure every multiplication and division was completed before the additions or subtractions. If the order looks wrong, rewrite the steps neatly. Practising this discipline now will make more advanced maths, such as algebra and equations, much easier later on.