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; 3^{2}+ 5Next,
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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