CAT 2025 Lesson : Number Theory - Arithmetic Operations

2.4 Arithmetic operations

While performing mathematical calculations, we must operate in order.

Eg., $3 + \dfrac{4}{2} = 3 + 2$ and not $\dfrac{3 + 4}{2}$

Eg., $3 \times 5 - 2 = 15 - 2 = 13$ and not $3 \times 3 = 9$.

The rules of which mathematical operator comes first are denoted by BODMAS

2.4.1 BODMAS

BODMAS is an acronym, where each letter (as stated below) represents an arithmetic operation.

B = Brackets
O = Orders (i.e. Powers and Square Roots, Cube Roots, etc.)
D = Division
M = Multiplication
A = Addition
S = Subtraction

BODMAS represents the order in which arithmetic operations are to be performed in an expression, from left to right.

In other words, operations involving Brackets are completed first, followed by those involving Orders (Powers), Division, Multiplication, Addition and finally Subtraction.

We should always follow this BODMAS order while solving questions. If not our answers might go wrong.

The order in which the operations within different types of brackets are to be done is as follows

1) $\overline{\color{white} 123}$ called line bracket. Eg, $4 \times \overline{5 + 3} = 4 \times 8 = 32$
2) () called parenthesis or common bracket
3) {} called curly bracket
4) [] called rectangular bracket

2.4.2 Basics of Remainders

When a number say $n$ (also called dividend) is divided by divisor ($d$), it leaves a quotient ($q$) and remainder ($r$).



So, $n$ can be expressed as $n = dq + r$

For example, when $37$ is divided by $9$, we get a quotient of $4$ and remainder of $1$.

$37 = 9 \times 4 + 1$