Number OperationsEdexcel GCSE Maths: Revision notes
Section 1
How do we order and compare numbers?
Positive and negative integers, decimals and fractions can all be placed on a number line and compared using the symbols:
- = equal to
- ≠ not equal to
- < less than
- > greater than
- ≤ less than or equal to
- ≥ greater than or equal to
When comparing negative numbers, remember that the number further to the right on the number line (closer to positive) is larger — so −2 > −5.
To compare fractions and decimals, convert to a common format (usually decimals) before ordering.
Students often think −8 is bigger than −3 because 8 > 3 — but on the number line −8 is further left, so −8 < −3.
Section 2
How do we apply the four operations to different number types?
The four operations — addition, subtraction, multiplication and division — apply to integers, decimals, and fractions (proper, improper and mixed), including negative numbers.
Key rules for negative numbers:
| Operation | Same signs | Different signs |
|---|---|---|
| Multiply/Divide | Positive result | Negative result |
| Add | Add and keep the sign | Subtract, take sign of larger magnitude |
Formal written methods (long multiplication, long division, column addition/subtraction) should be used confidently for larger numbers and decimals without a calculator.
−7 × −3 = 21 (same signs, positive); −7 × 3 = −21 (different signs, negative)
Section 3
How does place value matter with very large, very small and decimal numbers?
Place value describes what each digit represents based on its position. This becomes crucial for:
- Very large numbers (e.g. millions, billions) — keeping track of place value avoids errors of a factor of 10
- Very small numbers (e.g. 0.00042) — understanding how many places the first significant digit is from the decimal point
- Decimal calculations — aligning decimal points correctly when adding/subtracting, and adjusting for the number of decimal places when multiplying/dividing
When multiplying decimals, multiply as if they were whole numbers, then count the total decimal places in both numbers to place the decimal point in the answer.
0.4 × 0.03: multiply 4 × 3 = 12, then place the decimal point 3 places from the right (1 + 2 decimal places) = 0.012
Section 4
What is BIDMAS/BODMAS and how do we use inverse operations?
BIDMAS (Brackets, Indices, Division/Multiplication, Addition/Subtraction) gives the order in which operations must be carried out.
- Brackets first
- Indices (powers and roots)
- Division and Multiplication (left to right)
- Addition and Subtraction (left to right)
Inverse operations undo each other and are used to check answers or rearrange calculations: addition ↔ subtraction, multiplication ↔ division, squaring ↔ square rooting.
3 + 4 × 2² = 3 + 4 × 4 = 3 + 16 = 19 (indices before multiplication, then addition)
Show each BIDMAS step on a separate line in working — examiners award method marks for correct order even if the final answer is wrong.
Section 5
What are systematic listing strategies and the product rule for counting?
Systematic listing means organising all possible outcomes in a clear, methodical order (e.g. alphabetically, numerically) so none are missed or repeated.
The product rule for counting states that if there are m ways to do one thing and n ways to do another independent thing, there are m × n ways to do both.
- A café has 4 sandwich fillings and 3 types of bread: 4 × 3 = 12 different sandwiches possible
Must Know
- Use =, ≠, <, >, ≤, ≥ correctly, especially with negative numbers on a number line
- Same signs multiply/divide to give a positive result; different signs give a negative result
- Align decimal points when adding/subtracting; count total decimal places when multiplying
- Follow BIDMAS: Brackets, Indices, Division/Multiplication, Addition/Subtraction
- Use inverse operations to check your answers
- The product rule: multiply the number of options for each independent choice to find the total combinations
That's the notes covered.
Carry on to the next subtopic.