We will obey the rules for simplifying an expression using BODMAS/PEMDAS rules - involving decimals for solving order of operations.
Follow the order of operation as:
1. Bracket → Solve inside the Brackets/parenthesis before Of, Multiply, Divide, Add or Subtract.
For example:
1.6 × (0.5 + 0.3)
= 1.6 × 0.8
= 1.28
2. Of → Then, solve Of part (Exponent, Powers, Roots, etc.,) before Multiply, Divide, Add or Subtract.
For example:
3.2 + 0.5 of 1.6 - 0.1
= 3.2 + 0.5 × 1.6 - 0.1
= 3.2 + 0.8 - 0.1
= 4 - 0.1
= 3.9
3. Division/Multiplication → Then, calculate Multiply or Divide before Add or Subtract start from left to right.
For example:
1.2 + 1.5 ÷ 0.3 × 0.3
= 1.2 + 5 × 0.3
= 1.2 + 1.5
= 2.7
4. Addition/Subtraction → At last Add or Subtract start from left to right.
For example:
1.7 + (4.2 - 0.5) × 0.1
= 1.7 + 3.7 × 0.1
= 1.7 + 0.37
= 2.07
Worked-out
problems for solving BODMAS/PEMDAS rules - involving decimals:
Simplify using BODMAS/PEMDAS rule:
(a) 8 - 4.2 ÷ 6 + 0.3 × 0.4
Solution:
8 - 4.2 ÷ 6 + 0.3 × 0.4
= 8 - 0.7 + 0.3 × 0.4, (Simplifying ‘division’ 4.2 ÷ 6 = 0.7)
= 8 - 0.7 + 0.12, (Simplifying ‘multiplication’ 0.3 × 0.4 = 0.12)
= 7.3 + 0.12, (Simplifying ‘subtraction’ 8 - 0.7 = 7.3)
= 7.42, (Simplifying ‘addition’ 7.3 + 0.12 = 7.42)
Answer: 7.42
(b) 7.6 - [3 + 0.5 of (3.1 - 2.3 × 1.02)]
Solution:
7.6 - [3 + 0.5 of (3.1 - 2.3 × 1.02)]
= 7.6 - [3 + 0.5 of (3.1 - 2.346)], (Simplifying 2.3 × 1.02 = 2.346)
= 7.6 - [3 + 0.5 of 0.754], (Simplifying ‘subtraction’ 3.1 - 2.346 = 0.754)
= 7.6 - [3 + 0.5 × 0.754], (Simplifying ‘of’)
= 7.6 - [3 + 0.377], (Simplifying ‘multiplication’ 0.5 × 0.754 = 0.377)
= 7.6 - 3.377, (Simplifying ‘addition’ 3 + 0.377 = 3.377)
= 4.223, (Simplifying ‘subtraction’ 7.6 - 3.377 = 4.223)
Answer: 4.223
(c) 12.8 - 0.4 of (7.2 - 3.7) + 2.4 × 3.02
Solution:
12.8 - 0.4 of (7.2 - 3.7) + 2.4 × 3.02
= 12.8 - 0.4 of 3.5 + 2.4 × 3.02, (Simplifying 7.2 - 3.7 = 3.5)
= 12.8 - 0.4 × 3.5 + 2.4 × 3.02, (Simplifying ‘of’)
= 12.8 - 1.4 + 2.4 × 3.02, (Simplifying ‘multiplication’ 0.4 × 3.5 = 1.4)
= 12.8 - 1.4 + 7.248, (Simplifying ‘multiplication’ 2.4 × 3.02 = 7.248)
= 11.4 + 7.248, (Simplifying ‘subtraction’ 12.8 - 1.4 = 11.4)
= 18.648, (Simplifying ‘addition’ 11.4 + 7.248 = 18.648)
Answer: 18.648
● 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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