# What is Order of Operations?

A branch of mathematics that deals usually with the nonnegative real numbers including sometimes the transfinite cardinals and with the application of the operations of addition, subtraction, multiplication, and division to them. The basic operations under arithmetic are addition, subtraction, division, and multiplication. A certain order is required to solve the various operations, if multiple operations are required to be done, there is an order that is to be followed, known as BODMAS.

### What is the Order of Operations?

Order of operations means if an arithmetic expression is given that contains many operators such as multiplication, addition division, the calculation is done in a certain order which is given by BODMAS. To calculate the value of the expression, follow a BODMAS rule.

The BODMAS rule is followed to order any operation involving +, −, ×, and ÷. The order of operation is:

**B: Brackets**

**O: Order**

**D: Division**

**M: Multiplication**

**A: Addition**

**S: Subtraction **

So according to this rule, if an arithmetic expression is given, follow this rule to calculate the result which means the brackets are to be solved first, then after in four types of operators it is needed to first check if there is a division operator then, divide and then followed by multiplication and similarly for addition and subtraction.

One more order of operation is PEMDAS. It is similar to the BODMAS rule, let’s look at the full form, P is for Parenthesis, E is for exponent, M is for multiplication, D is for division (whichever comes first between M and D), A is for Addition, S is for subtraction. Solving the calculations in proper order helps in obtaining the correct solution.

### Sample Problems

**Question 1: Solve 2+7×8-5**

**Solution:**

By applying BODMAS

=2 + (7 × 8) – 5

=2 + 56 -5

=(2 + 56) – 5

=58 – 5

=53

**Question 2: Can addition be done before doing division in any arithmetic expression?**

**Answer:**

No, BODMAS rule is always followed. According to the BODMAS rule, addition comes after division, therefore, addition shall be done after division.

**Question 3: Find the value of the expression : (8 × 6 – 7) + 65**

**Solution:**

As brackets are provided here, solve them first

(8 × 6 – 7) in this, multiplication operator has the highest priority therefore it will be

(48 – 7) = 41

So, the final result will be 41 + 65 = 106

**Question 4: Find value of 6× 6+ 6× 6+ 6× 6**

**Solution:**

Here, only have two operators that is addition and multiplication.

Therefore, solve multiplication first

36 + 36 + 36

=108

**Question 5: Evaluate 8/4 × 6/3 × 7 + 8 – (70/5 – 6)**

**Solution:**

Example 5 :

Evaluate 8/ 4 × 6/3 × 7 + 8 – (70/5 – 6 )

We can rewrite the expression as

(8/4 × 6/3 × 7 + 8) – (70/5 – 6)

Now we will solve the respective brackets ,

(2 × 2 × 7 + 8) – (14 – 6)

(4 × 7 + 8) – (8)

(28 + 8) – (8)

(36) – (8)

28