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
From PEMDAS Rules - Involving Decimals to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Aug 14, 24 09:52 AM
Aug 14, 24 02:39 AM
Aug 13, 24 01:27 AM
Aug 12, 24 03:20 PM
Aug 12, 24 02:23 AM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.