GCSE Maths Practice: order-of-operations-bidmas

Applying BIDMAS with Division and Addition

Many calculations in mathematics involve more than one operation. The BIDMAS rule tells us the correct order to follow so that everyone obtains the same answer. When both division and addition appear in the same expression, division must be completed first. This principle ensures that the basic quantities are simplified before anything is added or removed.

Understanding the Logic

Division represents sharing or splitting a number into equal parts. Addition represents combining or increasing a total. Because dividing changes the size of the numbers involved more significantly, it needs to happen before adding. Doing the addition first would mean you are combining values that have not yet been correctly simplified.

Using BIDMAS Step by Step

1. Look for any divisions or multiplications in the expression.
2. Complete those calculations first, moving from left to right if more than one appears.
3. After finishing all divisions and multiplications, carry out additions and subtractions in order.

This systematic approach makes even longer questions manageable and prevents simple order mistakes.

Typical Errors

• Adding before dividing, which gives an incorrect total.
• Skipping the division entirely when the number divides neatly and looks easy to overlook.
• Reading the question quickly and not spotting the division sign.

A quick habit that helps is to underline any division or multiplication sign before starting the calculation. This reminder ensures you focus on those parts first.

Practical Uses

Division before addition appears in many everyday situations. When calculating averages, you divide the total by the number of items before adding or subtracting adjustments. In finance, you might divide a cost between people before adding tax or tips. Following BIDMAS keeps those results accurate and fair.

Building Confidence

Practising these small two-step problems is an excellent way to strengthen number sense. Once you are confident dividing before adding, it becomes easier to handle expressions that also include brackets, powers, or mixed signs later on. The process never changes: complete higher-priority operations first, then move to the simpler ones.

FAQs

Q1: Which comes first, division or multiplication?
A: They share the same level of priority and should be completed in the order they appear from left to right.

Q2: Does the rule change when subtraction appears instead of addition?
A: No. After divisions and multiplications are complete, handle additions and subtractions in the order written.

Q3: How do calculators know the order?
A: Calculators are programmed to follow BIDMAS automatically, ensuring consistent results.

Study Tip

When revising, rewrite practice questions on separate lines and label each operation with its type (D for division, A for addition). Cross out each label as you complete it. This visual method reinforces the correct order of operations and helps build strong habits for exam settings.