Solving Order of Operations

Introduction to order of operations:

Solving order  of operations:-

Order of operations includes addition, subtraction, multiplication, division, exponents and paranthesis.

When all these operations  or some of them  are  present in a math problem, we follow a rule.

It is called PEMDAS

P stands for paranthesis, E for exponents, M for multiplication, D for division, A for addition and S for subtractionfrom left to right.

If a student follows this order, then he gets the correct answer.

Order of Paranthesis and Exponents:-

When solving  Order of operations the first operation is paranthesis.

It is denoted by (        )

Within the paranthesis, we may have numbers in addition, subtraction, multiplication , division or exponent form

We must do the paranthesis operation first.

For example let us do this problem

8 + 5(42x 3) - (5+3)2  divided by  8

Let us do paranthesis (42x 3 ) first.  Note within the paranthesis is an exponent. so we must do that operation now.

42= 4 x 4 = 16

next 16x3=48

Now take the second paranthesis(5+3)2

5+3=8

82= 8x8=64

Now write 8 + 5(48) -(64) divided by 8

Here we dealt both paranthesis and exponents

Order of Multiplication and Division

In  solving order of operation , after paranthesis and exponents  comes multiplication and  division.

let us look at the problem now.

It is reduced to 8 + 5x48 - 64 divided by 8

Multiply 5 x48

We get 240

Next divide 64 by 8 to get 8

Now the problem is reduced to 8 +240 - 8

Order of Addition and Subtraction:-

Now we do addition and subtraction in solving the order of operations

The problem is reduced to 8 + 240 - 8

Add 8+240 to get 248

Then subtract   that is 248 - 8 = 240

The final answer is 240.

There is a trick to remember  this formula,while solving order of operations.

Look at this sentence:  Please excuse my dear aunt Sally.

P in please = paranthesis

E in excuse = exponent

M in my = multiplication

D in dear= division

A in aunt = adition

S in Sally= subtraction

Order of Operations:- another Example

Example to solve order of  operations

(v9+v16÷2 x 2)2 + v64 +  4  x 3 ÷ 3  +10 -  72 x  100%

First paranthesis should be done. v9  = 3 and v16 = 4

so we write (3 + 4÷ 2 x 2)2

Next division inside paranthesis must be done  4÷2 = 2  now let us write ( 3 + 2 x2)2

next multiplication within paranthesis should be done.  (3 +4)2   Now add  3+4=7 Si it is 72= 49

The paranthesis has been reduced to 49

Next comes v64  = 8

Now let us write  49  + 8 + 4 x 3÷ 3  + 10 - 72 x 100%

72= 49 and 100%=  1

So the problem reduces to 49  +  8  + 4  x  3÷ 3 + 10 - 49 x 1

Now we  must do division  3÷3 =1

So now we write 49 + 8 + 4 x  1 + 10  - 49 x 1

Now we do multiplication  49 + 8 + 4 + 10-   49 x 1

Now the problem is reduced to 49 + 8 + 4 + 10 - 49

Next we do  addition.  49 +8+4 + 10= 71

Now subtraction  71  - 49 = 22

We can do addition and subtraction simultaneously too.  49 + 8 + 4 + 10 - 49

49  cancels -49  and we have 8 + 4  + 10 =  22

This is a tough problem for  middle school students.  Only by following the PEMDAS formula they can arrive at the right answer.

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