## How to use order of operations

Read,3 minutes

In mathematics, sometimes we are presented with a set of complex equations containing lot of operations. So, to sequentially and **correctly** solve the equation, we apply the order of operations. The order of operations tells the **sequence** in which the multiple operations in the mathematical expressions should be solved.

Now, to keep it simple, there is a short-form to remember the sequence of the order of operations. This is known as **PEMDAS**. Here each letter stands for:

- P = Parentheses
- E = Exponent
- M = Multiplication
- D = Division
- A = Addition
- S = Subtraction

So, the **PEMDAS** rule dictates the sequences in which the multiple operations should be carried out.

**Parentheses-**This is of the primary importance. Each and every group under the parenthesis should be solved first.**Exponents-**Next in sequence is all exponent operations. Work them out.**Multiplication and Division-**Now here, carefully divide or multiply each expression, moving from left to right.**Addition and Subtraction-**Similar to the multiplication and division part, carry out the addition or subtraction, moving from left to right.

#### Why should we follow the PEMDAS Rule?

The fundamental concept behind the discovery of **PEMDAS** rule was to let everyone conclude to the similar answer. Following any other sequence in the order of operations will lead you to a completely different and incorrect solution. Let’s look at what happens when we don’t follow PEMDAS rule.

**Not Following Order of Operations:** Here we just solve from left to right.

\(7 \times 2 + 6 \times (8 \div 4)\)

\(= 14 + 6 \times (8 \div 4)\)

\(= 20 \times (8 \div 4)\)

\(= 160 \div 4\)

\(= 40\)

**Following Order of Operations:** Here we apply PEMDAS rule.

\(7 \times 2 + 6 \times (8 \div 4)\)

\(= 7 \times 2 + 6 \times 2\)

\(= 14 + 6 \times 2\)

\(= 14 + 12\)

\(= 26\)

Now, we hope you understand why it is very important to apply **PEMDAS** rule in multiple operation expressions.

### Related Topics

How to Order Integers and Numbers

How to Do Mixed Integer Computations

How to Arrange, Order, and Compare Integers

### Exercises for order of operations

**1)** \(9 \ \times \ 0 - 4 \) \( \ = \)

**2) **\(6 \ \times \ (-7) + 12 \) \( \ = \)

**3) **\(6 \ \times \ 4 - 12 \) \( \ = \)

**4) **\(3 \ \times \ (-8) + 5 \) \( \ = \)

**5) **\(7 \ \times \ 8 - 19 \) \( \ = \)

**6) **\((-4) \ \times \ (-6) - 8 \) \( \ = \)

**7) **\((-4) \ \times \ 6 + 3 \) \( \ = \)

**8) **\(4 \ \times \ 1 + 6 \) \( \ = \)

**9) **\((-1) \ \times \ 4 - 6 \) \( \ = \)

**10) **\(16 \ \div \ 4 + 1 \) \( \ = \)