We will follow the rules for simplifying an expression using PEMDAS rules - involving integers for solving order of operations.
Follow the order of operation as:
1. Parenthesis → Find the things inside the Parenthesis part before Exponent, Multiply, Divide, Add or Subtract.
For example:
6 × (11 + 3)
= 6 × 14
= 84
2. Exponent → Then do the Exponent part (Powers, Roots, etc.,)
before Multiply, Divide, Add or Subtract.
For example:
7 × 8^{2} + 27 × 8 × 8 + 2
= 7 × 64 + 2
= 448 + 2
= 450
3. Multiplication/ Division → Then do Multiply or Divide part before Add or Subtract start from left to right.
For example:
5 × 3 + 6 ÷ 3
= 15 + 6 ÷ 3
= 15 + 2
= 17
4. Addition/Subtraction → At last do Add or Subtract start from left to right.
For example:
16 + (4 - 1) × 6
= 16 + 3 × 6
= 16 + 18
= 34
Worked-out
problems for solving PEMDAS rules - involving integers:
Simplify using PEMDAS rule:
(a) 18 - 24 ÷ 6 + 3 × 5
Solution:
18 - 24 ÷ 6 + 3 × 5
= 18 - 4 + 3 × 5, (Simplifying ‘division’ 24 ÷ 6 = 4)
= 18 - 4 + 15, (Simplifying ‘multiplication’ 3 × 5 = 15)
= 14 + 15, (Simplifying ‘subtraction’ 18 - 4 = 14)
= 29, (Simplifying ‘addition’ 14 + 15 = 29)
Answer: 29
(b) 11 - [3 + 5 of (13 - 2 × 6)]
Solution:
11 - [3 + 5 of (13 - 2 × 6)]
= 11 - [3 + 5 of (13 - 12)], (Simplifying ‘multiplication’ 2 × 6 = 12)
= 11 - [3 + 5 of 1], (Simplifying inside the ‘parenthesis’ 13 - 2 = 1)
= 11 - [3 + 5 × 1], (Simplifying ‘of’)
= 11 - [3 + 5], (Simplifying ‘multiplication’ 5 × 1 = 5)
= 11 - 8, (Simplifying ‘add’ inside the ‘square brackets’ 3 + 5 = 8)
= 3, (Simplifying ‘subtraction’ 11 - 8 = 3)
Answer: 3
(c) 22 - 4 of (7 - 2) + 4 × 5
Solution:
22 - 4 of (7 - 2) + 4 × 5
= 22 - 4 of 5 + 4 × 5, (Simplifying inside the ‘parenthesis’ 7 - 2 = 5)
= 22 - 4 × 5 + 4 × 5
= 22 - 20 + 4 × 5, (Simplifying ‘of’ 4 × 5 = 20)
= 22 - 20 + 20, (Simplifying ‘multiplication’ 4 × 5 = 20)
= 2 + 20, (Simplifying ‘subtraction’ 22 - 20 = 2)
= 22, (Simplifying ‘addition’ 2 + 20 = 22)
Answer: 22
● 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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