GCSE Maths Practice: order-of-operations-bidmas

Division Before Addition

In any expression that mixes division and addition, BIDMAS tells us that division must be completed before addition or subtraction. This rule keeps calculations consistent no matter how many numbers are involved. Ignoring it can easily lead to wrong answers, especially when more than one operation appears on the same line.

Why Division Comes First

Division and multiplication share the same level of priority in mathematics, and both come before addition and subtraction. This order exists because dividing or multiplying changes the size of a number more dramatically than adding or subtracting. Performing these operations first ensures the base quantities are correct before they are increased or decreased later in the process.

How to Approach Mixed Operations

When solving a mixed expression, take a moment to identify which operations appear. If you see division or multiplication alongside addition or subtraction, complete the division or multiplication first. Only when those steps are done should you move to the remaining operations. Writing each stage on a new line is an effective way to keep the working neat and prevent skipped steps.

Common Mistakes

• Adding numbers before completing a division.
• Reading from left to right without applying the order of operations.
• Rounding division results too early, causing inaccuracy later on.
• Forgetting that multiplication and division share the same level of priority and must be handled in the order they appear from left to right.

To avoid these mistakes, underline the division or multiplication part first, carry out that step carefully, and then move on to the next operation.

Real-Life Applications

The same logic applies in real-world settings. When splitting costs, for instance, you divide a total by the number of people before adding any extra amounts such as service fees or taxes. In cooking, you divide ingredients to scale a recipe before adding them together. Following the correct sequence makes sure results stay proportional and reliable.

Worked Ideas (without numbers)

Suppose an expression includes one division and one addition. First, divide the earlier quantity by the divisor to simplify it. Then, take that result and add the next value. This approach mirrors how calculators and computer software handle calculations automatically—they follow BIDMAS behind the scenes to avoid ambiguity.

FAQs

Q1: What if the division appears after the addition sign?
A: Division still comes first; the order depends on operation type, not position.

Q2: What if multiplication also appears?
A: Handle multiplication and division in the order they appear from left to right before addressing addition or subtraction.

Q3: Can I group parts of the problem using brackets?
A: Yes—adding brackets is a useful way to make the intended order clear and reduce confusion.

Study Tip

When reviewing your work, check whether any divisions or multiplications remain incomplete before moving to addition or subtraction. If you get different results after re-ordering the steps, your first calculation probably ignored BIDMAS. Consistent use of this rule will make every multi-step problem far easier to manage.