When all the four operations namely addition, subtraction, multiplication and division are involved in a problem, we perform the operations in the following sequence from left to right i.e. division, multiplication, addition and subtraction, remember the order as DMAS.

Easy
and simple way to remember **PEMDAS **rule**!!**

P** ****→** **P**arentheses first

E **→**** ****E**xponent** **(Powers,
Square Roots, Cube Roots, etc.)

MD **→** **M**ultiplication** **and **D**ivision (start from left to right)

AS **→**** ****A**ddition and **S**ubtraction (start from left to right)

**Note:**

(i) Start Multiply/Divide from left side to right side since they perform equally.

(ii) Start Add/Subtract from left side to right side since they perform equally.

Steps
to simplify the order of operation using PEMDAS rule:

First part of an equation is start solving inside the 'Parentheses'.

**For
Example;** (7 + 8) × 3

First solve inside ‘parentheses’ 7 + 8
= 15, then 15 × 3 = 45.

Next solve the mathematical 'Exponent'.

First solve ‘exponent’ part 3

Next,
the part of the equation is to calculate 'Multiplication' and 'Division'.

We know that, when division and multiplication follow one another, then their
order in that part of the equation is solved from left side to right side.

**For
Example;** 21 ÷ 7 × 12 ÷ 2

‘**Multiplication**’ and ‘**Division**’ perform equally, so calculate from left to right side. First solve 21 ÷ 7 = 3, then 3 × 12 = 36, then 36 ÷ 2 = 18.

In the last part of the equation is to calculate 'Addition' and 'Subtraction'. We know that, when addition and subtraction follow one another, then their order in that part of the equation is solved from left side to right side.

**For
Example;** 9 + 11 - 13 + 15

‘**Addition**’ and ‘**Subtraction**’ perform equally, so calculate from left to right side. First solve 9 + 11 = 20, then 20 - 13 = 7 and then 7 + 15 = 22.

*These
are simple rules need to be followed for** ***simplifying or calculating ***using PEMDAS
rule.*

In brief, after we perform "P" and "E", start from left side to right side by solving any "M" or "D" as we find them. Then start from left side to right side solving any "A" or "S" as we find them.

Solved Examples using PEMDAS Rule:

**1.** 225 ÷ 15 + 14 × 5 – 128 ÷ 16 + 25

**Solution:**

First we carry out the divisions (colored in **red**)

**225 ÷ 15** + 14 × 5 – **128 ÷ 16** + 25

15 + 14 × 5 – 8 + 25

Next, we multiply (colored in green)

15 + **14 × 5** – 8 + 25

15 + 70 – 8 + 25

Now, we will workout addition (colored in **blue**)

**15 + 70** – 8 **+ 25**

**15 + 70 + 25** – 8

110 – 8

And then finally subtraction (colored in **yellow**)

**110 – 8 **=** **102

Thus, 225 ÷ 15 + 14 × 5 – 128 ÷ 16 + 25 = 102

Simplify and find the answers using PEMDAS Rule:

**1.** (i) 14 + 8 ÷ 2 - 10

(ii) 13 × 3 – 42 ÷ 6

(iii) 40 ÷ 1 × 15 – 15

(iv) 667248 – 245631 + 1192311

(v) 7742859 + 65500 × 2000

(vi) 7188421 × 20 – 11199999

(vii) 1000 – 6 × 50 + 18 ÷ 6

(viii) 800 + 299 ÷ 299

(ix) 6020 × 5 – 8000 + 2999

(x) 7999 – 2463 ÷ 1 + 3001

**Answers:**

(i) 8

(ii) 32

(iii) 585

(iv) 1613928

(v) 138742859

(vi) 132568421

(vii) 703

(viii) 801

(ix) 25099

(x) 8537

● **Related Concept **

**● ****Decimals**

**● ****Conversion of
Unlike Decimals to Like Decimals**

**● ****Decimal and
Fractional Expansion**

**● ****Converting Decimals
to Fractions**

**● ****Converting
Fractions to Decimals**

**● ****H.C.F. and L.C.M.
of Decimals**

**● ****Repeating or
Recurring Decimal**

**● ****BODMAS/PEMDAS Rules
- Involving Decimals**

**● ****PEMDAS Rules -
Involving Integers**

**● ****PEMDAS Rules -
Involving Decimals**

**● ****BODMAS Rules -
Involving Integers**

**● ****Conversion of Pure
Recurring Decimal into Vulgar Fraction**

**● ****Conversion of Mixed
Recurring Decimals into Vulgar Fractions**

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