# PEMDAS Rules - Involving Decimals

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)

(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)

(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)

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