# BODMAS/PEMDAS Rules - Involving Decimals

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)

(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)

(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)

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