We will follow the rules for simplifying an expression using PEMDAS rules - involving decimals 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:
7.04 × (4.07 + 6.72)
= 7.04 × 10.79
= 75.9616
2. Exponent → Then do the Exponent part (Powers, Roots, etc.,) before Multiply,
Divide, Add or Subtract.
For example:
3.05 × (0.2)^{2} + 2
3.05 × 0.2 × 0.2 + 2
= 3.05 × 0.04 + 2
= 0.122 + 2
= 2.122
3. Multiplication/ Division → Then do Multiply or Divide part before Add or Subtract start from left to right.
For example:
5.75 × 3.5 + 6.4 ÷ 1.6
= 20.125 + 6.4 ÷ 1.6
= 20.125 + 4
= 24.125
4. Addition/Subtraction → At last do Add or Subtract start from left to right.
For example:
15.05 + (6.25 – 3.75) × 2.05
= 15.05 + 2.5 × 2.05
= 15.05 + 5.125
= 20.175
Worked-out
problems for solving PEMDAS rules - involving decimals:
Simplify using PEMDAS rule:
(a) 16.5 – 16.5 ÷ 2.2 + 3 × 5
Solution:
16.5 – 16.5 ÷ 2.2 + 3.2 × 5.4
= 16.5 – 7.5 + 3.2 × 5.4, (Simplifying ‘division’ 16.5 ÷ 2.2 = 7.5)
= 16.5 – 7.5 + 17.28, (Simplifying ‘multiplication’ 3.2 × 5.4 = 17.28)
= 9 + 17.28, (Simplifying ‘subtraction’ 16.5 – 7.5 = 9)
= 26.28, (Simplifying ‘addition’ 9 + 17.28 = 26.28)
Answer: 26.28
(b) 10.75 - [3.25 + 3 of (19.45 – 2.65 × 6.75)]
Solution:
10.75 - [3.25 + 3 of (19.45 – 2.6 × 6.7)]
= 10.75 - [3.25 + 3 of (19.45 – 17.42)], (Simplifying 2.6 × 6.7 = 17.42)
= 10.75 - [3.25 + 3 of 2.03], (Simplifying 19.45 – 17.42 = 2.03)
= 1.75 - [3.25 + 3 × 2.03], (Simplifying ‘of’)
= 10.75 - [3.25 + 6.09], (Simplifying ‘multiplication’ 3 × 2.03 = 6.09)
= 10.75 – 9.34, (Simplifying ‘square brackets’ 3.25 + 6.09 = 9.34)
= 1.41, (Simplifying ‘subtraction’ 10.75 – 9.34 = 1.41)
Answer: 1.41
(c) 20.76 - 4 of (6.82 – 4.42) + 8.5 × 3.4
Solution:
20.76 - 4 of (6.82 – 4.42) + 8.5 × 3.4
= 20.76 - 4 of 2.4 + 8.5 × 3.4, (Simplifying ‘parenthesis’ 7 - 2 = 5)
= 20.76 - 4 × 2.4 + 8.5 × 3.4, (Simplifying ‘of)
= 20.76 – 9.6 + 8.5 × 3.4, (Simplifying ‘multiplication’ 4 × 2.4 = 9.6)
= 20.76 – 9.6 + 28.9, (Simplifying ‘multiplication’ 8.5 × 3.4 = 28.9)
= 11.16 + 28.9, (Simplifying ‘subtraction’ 20.76 – 9.6 = 2)
= 22, (Simplifying ‘addition’ 11.16 + 28.9 = 40.06)
Answer: 40.06
● 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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