 maths > wholenumbers

Precedence of Arithmetic Operations

what you'll learn...

overview

The expression 3×21$3 \times 2 - 1$ can possibly be simplified in two ways (considering a rule for the precedence order of operation is not established yet.)

•  3×21=3×1=3$3 \times 2 - 1 = 3 \times 1 = 3$ (subtracted first) and

•  61=5$6 - 1 = 5$ (multiplied first)

Which one is correct? To resolve this, the precedence order of arithmetic operations in a numerical expression is established as a rule.

Simplify 2+4×3$2 + 4 \times 3$.

•  One person adds first and multiplies next, 2+4×3$2 + 4 \times 3$ =6×3$= 6 \times 3$ $= 18$
•  Another person multiplies first and then adds, $2 + 4 \times 3$ $= 2 + 12$ $= 14$

Which answer is the correct one?

To resolve this, a rule of precedence is accepted by all and agreed on. As per that rule,
•  It is wrong to do $2 + 4 \times 3$ $= 6 \times 3$ $= 18$
Addition $2 + 4$ is not to be performed first.

•  $2 + 4 \times 3$ $= 2 + 12$ $= 14$
Multiplication $4 \times 3$ is performed first and then addition is performed.

Multiplication is higher in precedence to addition. In $2 + 4 \times 3$, the multiplication is to be simplified ahead of addition.

The word "precedence" means: priority over another; order to be observed.

In a numerical expression, the precedence order is:
•  division and multiplication (both in the same level same level of precedence)
•  addition and subtraction (both in the same level of precedence)

This is abbreviated as BODMAS (Division, Multiplication, Addition, Subtraction) or PEMDAS (Multiplication, Division, Addition, Subtraction).

The letters B O or P E are explained later

examples

Simplify $1 + 6 \times 3$.
The answer is "$19$".
Multiplication is higher in precedence over addition. so

$\quad 1 + 6 \times 3$

$\quad = 1 + 18$

$\quad = 19$.

Simplify $9 - 6 \div 3$
The answer is "$7$". Division is higher in precedence over subtraction. So

$\quad 9 - 6 \div 3$

$\quad = 9 - 2$

$\quad = 7$

Simplify $3 + 6 \div 3$.
The answer is "$19$".
Division is higher in precedence over addition. so

$\quad 3 + 6 \div 3$

$\quad = 3 + 2$

$\quad = 5$.

summary

In a numerical expression, the precedence order is:

•  division and multiplication (both in the same level same level of precedence)

•  addition and subtraction (both in the same level of precedence)

This is abbreviated as BODMAS (Division, Multiplication, Addition, Subtraction) or PEMDAS (Multiplication, Division, Addition, Subtraction).

The letters B O or P E are explained later

Outline