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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