In mathematics, an expression of symbols intended to represent a numerical value must follow commonly accepted and unambiguous rules. We have to do certain operations before doing other operations, like multiplication should be done before addition.

**For example**, the rule for evaluate 2 + 3 × 4 in mathematics and in most computer languages is to firslty do the multiplication, so the correct answer is 14. Which have their own rules, may be used to avoid confusion, the convention needed to clarify which operator should be applied first is known as an order of operations.

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Here is math order of operations elaborated for your better understanding. In long math problems with **+, - , x , % , (),** and **exponents **in them, you have to know what and which to do first. Without follow the same rules, you may get different answers. You can easily remember the silly sentence, **P**lease **E**xcuse **M**y **D**ear **A**unt **S**ally, you can memorize the order of operations, and you must follow.

**"P"** denotes **Parentheses**.

**"E" **represents **Exponents**

**"M"** stands for **Multiply**

**"D"** represents **Division.**

**"A"** means **Addition**.

**"S" **refers to **Subtract**.

When an expression with more than one operator comes then we have to follow the above order to obtain the correct answer. It is to be noted that the division and multiplication operations have same order, which means that any of them can be done first. Similarly, the order of subtraction and addition are the same, i.e. any one of them can be performed first. The answer will be the same.

The important thing is that first parentheses (if any) has to be simplified, then exponents, afterwards multiplication or division and lastly addition or subtraction.

Now we will see the examples of how to solve different expressions using the concept of order of operators.

Basically, Order of operation for an arithmetic expression provides is very basic knowledge for the order of calculating different arithmetic operations. The order of operation actually defines few rules explaining in which order to solve an arithmetic expression. These rules are denoted in short by PEMDAS. Here, each letter represents an arithmetic operation. PEMDAS denotes the order of performing operations. Arithmetic operations involve parenthesis, exponents, addition(+), subtraction(-), multiplication(*) and division(÷).

Below you could see the steps for how to do order of operations

Below are order of operations examples:

Eliminate parentheses. 7- 6 =1

$\frac{14}{7}$x1+ 2 -2

Eliminate exponents. We do not have any exponents.

$\frac{14}{7}$x1+ 2 -2

Eliminate Multiply and divide after that in order from left to right

$\frac{14}{7}$=2 then 2x1+ 2 -2

2 x 1 = 2 then 2+2-2

Last, we add and subtract in order from left to right.

2 + 2 =4 then 4 - 2

4 - 2 = 2

Answer is 2

Eliminate parentheses. Here we don't have parentheses

$\frac{12}{4}$ + 4

Eliminate exponents. 42 = 16

$\frac{12}{4}$ + 16 x 3 - 1

Eliminate Multiply and divide after that in order from left to right

$\frac{12}{4}$=3 then 3 + 16 x 3 -1

16 x 3 = 48 then 3 + 48 -1

Last, we add and subtract in order from left to right.

3 + 48 = 51 then 51-1

51-1 = 50

Answer is 50

Eliminate parentheses. 6 + 5 = 11

$\frac{11}{11}$ + 7- 23 × 3 +1

Eliminate exponents. 23 = 8

$\frac{11}{11}$ +7- 8 × 3 +1

Eliminate Multiply and divide after that in order from left to right

$\frac{11}{11}$=1 then 1 + 7- 8 × 3 +1

8 x 3 = 24 then 1+7-24+1

Last, we add and subtract in order from left to right.

1+7=8 then 8-24+1

8-24= -16 then -16+1

-16+1 = -15

Answer is -15

The order of operation with exponents can be done in the following way.

When there is exponentiation in the arithmetic operation, one is required to solve it after opening the parenthesis, as the rule of PEMDAS says. For example :

When there is exponentiation in the arithmetic operation, one is required to solve it after opening the parenthesis, as the rule of PEMDAS says. For example :

13 - 3$^{3}$ + 2 (5 + 1)

We shall first solve parenthesis.

= 13 - 3$^{3}$ + 2 (6)

= 13 - 3$^{3}$ + 12

Now, solve exponent

= 13 - 27 + 12

= 25 - 27 = -2

In case, when exponent is inside the parenthesis, we follow PEMDAS inside it too. For example :

5 + 3 - 4(2$^{2}$ + 3 - 7)

Here, inside parenthesis, first we solve exponent

= 5 + 3 - 4(4 + 3 - 7)

= 5 + 3 - 4(0)

= 5 + 3 = 8

There is no parenthesis so we go to next operation.

Exponents are here. So we have to calculate each exponent operation.

3^{2} = 3 x 3 = 9

4^{3} = 4 x 4 x 4 = 64

So the expression is reduced to 9 x 64 .

Then we go to next operation.

Multiplication of these two numbers are 9 x 64 = 576.

The answer is 576 .

There is no parenthesis so we go to next operation.

Exponent is going to calculate.

4^{3} = 4 x 4 x 4 = 64

So the expression is reduced to 27 - 256 ÷ 64

Now we are going to solve division operation.

256 ÷ 64 = 4

So the expression is reduced to 27 - 4.

We are going to solve subtraction operation.

27 - 4 = 23

The answer is 23.

If one side of hallway is 9 feet then area of the hallway is (9 feet)^{2} .

The arithmetic expression is

$20 x 9^{2} - $30

using order of operations,

We are going to solve exponent operation.

9^{2} = 9 x 9 = 81

So the expression is reduced to Dollar 20 x 81 - Dollar 30

We are going to solve multiplication operation.

20 x 81 = 1620

So the expression is reduced to Dollar 1620 - $30

We are going to solve subtraction operation.

1620 - 30 = $ 1590

The cost of floor is $ 1590 .

Step 1: Let x be Sam’s age now. Look at the problem and put the significant expressions above it.

Five years ago x-5,

Sam’s age was half of the age $(\frac{1}{2})$ he will be in 10 years.

Step 2: copy out the equation in above word problem.

Note: we need to apply order of operations.

x - 5 = $\frac{1}{2}$ (x + 10)

x - 5 = $\frac{1}{2}$ x + 5

Isolate variable x

x - $\frac{1}{2}$ x = 5 + 5

$\frac{1}{2}$ x = 10

x = 20

Answer: Sam is now 20 years old.

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