PEMDAS Rule

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 Parentheses first

E Exponent (Powers, Square Roots, Cube Roots, etc.)

MD Multiplication and Division (start from left to right)

AS Addition and Subtraction (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'.

For Example; 32+ 5
First solve ‘exponent’ part 32= 3 × 3 = 9, then 9 + 5 = 14.

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

Decimal Numbers

Decimal Fractions

Like and Unlike Decimals

Comparing Decimals

Decimal Places

Conversion of Unlike Decimals to Like Decimals

Decimal and Fractional Expansion

Terminating Decimal

Non-Terminating Decimal

Converting Decimals to Fractions

Converting Fractions to Decimals

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

Repeating or Recurring Decimal

Pure Recurring Decimal

Mixed Recurring Decimal

BODMAS Rule

BODMAS/PEMDAS Rules - Involving Decimals

PEMDAS Rules - Involving Integers

PEMDAS Rules - Involving Decimals

PEMDAS Rule

BODMAS Rules - Involving Integers

Conversion of Pure Recurring Decimal into Vulgar Fraction

Conversion of Mixed Recurring Decimals into Vulgar Fractions





7th Grade Math Problems

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