Order of operations of the BODMAS rule

Order of operations of the BODMAS rule

The BODMAS rule explains the order of operations to be followed when evaluating or simplifying a mathematical expression. The first letters of words Brackets Of Division, Multiplication, Addition, and Subtraction are used to form the BODMAS rule as shown in the following table:

B	O	D	M	A	S
Brackets	Of	Division	Multiplication	Addition	Subtraction

Evaluation of an expression depends on the operations used in the given expression. An expression is evaluated or simplified by following the order of precedence of operations in the BODMAS rule. If an expression has two or more similar operations, the order of that operation will be from left to right.

The order of operations in accordance to priority given in the BODMAS rule when evaluating or simplifying an expression is as follows:

• B represents Brackets
• O represents Of
• D represents Division
• M represents Multiplication
• A represents Addition
• S represents Subtraction

Mathematical expressions involving two operations

When an expression involves only two operations, each operation is performed by following the order of operations given in the BODMAS rule.

Example 1

Find the value of $72 - 48 \div 3$.

Solution

Using BODMAS rule, follow the steps: Start by dividing, that is divide 48 by 3: $72 - 48 \div 3 = 72 - 16$

Finish by subtracting: $72 - 16 = 56$

Therefore, $72 - 48 \div 3 = 56$.

Example 2

Find the value of $\frac{1}{6} + \frac{1}{2} \times \frac{1}{4}$.

Solution

Using BODMAS rule, follow the steps: Start by multiplying, that is multiply $\frac{1}{2}$ by $\frac{1}{4}$: $\frac{1}{6} + \frac{1}{2} \times \frac{1}{4} = \frac{1}{6} + \frac{1}{8}$

Then add: $\frac{1}{6} + \frac{1}{8} = \frac{4}{24} + \frac{3}{24} = \frac{7}{24}$

Therefore, $\frac{1}{6} + \frac{1}{2} \times \frac{1}{4} = \frac{7}{24}$.

Example 3

Find the value of $2.65 + 0.33 - 1.14$.

Solution

Using the BODMAS rule, follow the steps: Start by adding, that is add 2.65 and 0.33: $2.65 + 0.33 - 1.14 = 2.98 - 1.14$

Finish by subtracting: $2.98 - 1.14 = 1.84$

Therefore, $2.65 + 0.33 - 1.14 = 1.84$.