Mathematical Operations | CIE IGCSE Maths: Core Revision Notes 2025

Mathematical Symbols

Starting with the basic four operations
- $+$ Addition, plus, sum, total
- $-$ Subtraction, minus, difference, take away
- $\times$ Multiplication, product, times
- $\div$ Division, quotient, divide, share

Equals signs
- Equal to
  - e.g. $3 x + 7 = 19$
- Not equal to
  - e.g. $2 - 5 \neq 5 - 2$
- Approximately equal to
  - e.g. $π \approx 3.14$
- Identical (equivalent) to
  - e.g. $12 x + 6 \equiv 3 (4 x + 2)$

Inequality signs
- Greater than
  - e.g. $5 > - 2$
- Less than
  - e.g. $\frac{1}{2} < \frac{2}{3}$
- $\geq$ Greater than or equal to
- $\leq$ Less than or equal to

If there is more than one operation in a calculation then they should be done in the following order
- Brackets: ( )
  - Perform any calculation(s) inside brackets first
- pOwers or Indices (sometimes Order): ², ³, √ and similar
  - These include powers, roots, reciprocals
- Divisions or Multiplications: × or ÷
  - If there are more than one of these then work them out left to right
  - Division includes fractions
- Additions or Subtractions: + or -
  - If there are more than one of these then work them out left to right
The acronym BODMAS or BIDMAS can help you remember the order of operations

Fractions mean division in calculations (BODMAS/BIDMAS)
There may be "invisible brackets" around the numerator and around the denominator
- - e.g. $\frac{2 + 5}{7 - 2}$ means $(2 + 5) \div (7 - 2)$
- Instead of brackets we extend the fraction line to show exactly what is on the top and what is on the bottom
Roots are pOwers (BODMAS/BIDMAS)
There may be "invisible brackets" under the root
- e.g. $\sqrt{9 + 16}$ means $\sqrt{(9 + 16)}$
- Instead of brackets we extend the top line on the root symbol to show everything that is to be rooted

Ensure that you enter a long or complicated calculation carefully
- For most modern calculators, the calculation can be typed in exactly as it is written on paper
- You may need to use additional brackets on older calculators

Work out $(5 - 3) + 2 \times 7^{2}$ .

Use BODMAS

First calculate anything inside Brackets, $5 - 3 = 2$ , so the question becomes

$2 + 2 \times 7^{2}$

Then any pOwers, $7^{2} = 49$

$2 + 2 \times 49$

followed by any Multiplications and Divisions, $2 \times 49 = 98$

$2 + 98$

and finally any Additions and Subtractions, $2 + 98 = 100$

$(5 - 3) + 2 \times 7^{2} = 100$