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'.

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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