When a mathematical expression contains more than one operation, we have to follow an order for the operations. The BODMAS sum gives the order of precedence for operations**. **This rule is used to find the correct order in which different operations are performed in a given math expression.

- Brackets are calculated first.
- Orders or exponents (xn) come next.
- Then comes division.
- Next is multiplication.
- Addition and subtraction are the last steps in the BODMAS rule.

The order of operations is important because it ensures that we calculate sums correctly. Without an agreed order of operations, there would be many different ways of working out the same sum because different people would do things in different orders.

**Solved BODMAS Examples**

The BODMAS rule is also known as the PEMDAS rule.

We often encounter brackets, exponents, multiplication, division, addition, and subtraction expressions. The expressions can be solved in a particular order of precedence. This order of precedence is known as the BODMAS rule.

Let’s understand it with an example:

Find out the value of the expression: 4 + 5 ÷ 2 − 3 × 8

According to the BODMAS sum, we must perform division and multiplication before addition and subtraction. Since there are two operations of the same priority (÷ and ×), we must perform them in left-to-right order.

Therefore, the correct answer is 7.

- (4 + 5) × 6 ÷ 3 = 54

Explanation: BODMAS rule is applied in the above example. The expression inside the bracket is calculated first, i.e., 4 + 5 = 9. Further, the result obtained from the brackets is multiplied by six and finally divided by 3, i.e., 9 × 6 ÷ 3 = 54.

- 4 + 5 × 6 ÷ 3 = 26

Explanation: We have ignored the BODMAS sum as there are no brackets in the above BODMAS example. Hence, we have performed the arithmetic operations in their natural sequential order (as per the PEMDAS rule). So, firstly multiplication operation is performed i.e., 5 × 6 = 30 and then division operation is performed, i.e., 30 ÷ 3 = 10 and then addition operation is performed i.e., 10 + 4 = 14.

**BODMAS Rule**

Let’s take another BODMAS example: Suppose we have an equation (x + y). z, to remove the bracket and expand the terms, we will use the Distributive Property, which states that a (b + c) = ab + ac. Therefore the given equation will become : (x + y). z = xz + yz.

**Rules for BODMAS**

Always remember to follow the priority of operations. The first step is to simplify brackets, then it is followed by powers and roots, then multiplication and division, and finally addition and subtraction.

You can also divide an expression into two parts; for example, if you have an equation 4x/2y-2z/2x+5y-3z, you can divide it into 4x/2y – 2z/2x and 5y – 3z.

While solving such questions, do not forget to check whether you have got the same answer twice or not!

- Do all the operations within brackets or braces in the order they come.
- Do all multiplications and divisions in the order they come.
- Do all additions and subtractions in the order they come.
- Do all powers in the order they come.

Example 1: Solve the problem:

24 ÷ (6 + 4 ÷ 2) = ?

Solution: First, we must simplify 4 ÷ 2 and 6 + 4 ÷ 2. Before that, let us see what is inside the bracket? Here, there are two operations: addition and division. As per the BODMAS rule, we must first simplify the division operation. So, 6 + 4 ÷ 2 = 6 + 2 = 8

Now, we have to solve 24 ÷ 8 = 3. So, the answer is 3.

**Practice Questions**

Use BODMAS rule to solve these questions:

- Find the value of a in 40 ៖ 2 – a x 3 – 22 = 8
- 100- [40 +{ 60- ( 40- 10)}]
- 24- 1/24 {8+ 7 – (3+ 2- 1 + 3)}
- (8*6)/(1.5+2.5)
- (16+11)-(5*6)
- 9-3*3+1
- 89+{6-(-3)[5+6]+25}
- (28/4)+3+(10-8)*5

**Conclusion**

When solving an arithmetic expression with brackets, the best rule of thumb is first to try and break down the expression into separable terms at whatever level you can. Once you have a separable expression, it can be broken into two segments using the BODMAS sum. We have here that most of us overlook this operation when we think of simplifying brackets. Thus, we fail to bring out the operation between brackets and operate them. Whether you’re a student or a professional, the BODMAS sum can be used to help you do something important for you down the road.