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)

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

Decimal Numbers

Decimal Fractions

Like and Unlike Decimals

Comparing Decimals

Decimal Places

Conversion of Unlike Decimals to Like Decimals

Decimal and Fractional Expansion

Terminating Decimal

Non-Terminating Decimal

Converting Decimals to Fractions

Converting Fractions to Decimals

H.C.F. and L.C.M. of Decimals

Repeating or Recurring Decimal

Pure Recurring Decimal

Mixed Recurring Decimal

BODMAS Rule

BODMAS/PEMDAS Rules - Involving Decimals

PEMDAS Rules - Involving Integers

PEMDAS Rules - Involving Decimals

PEMDAS Rule

BODMAS Rules - Involving Integers

Conversion of Pure Recurring Decimal into Vulgar Fraction

Conversion of Mixed Recurring Decimals into Vulgar Fractions

Simplification of Decimal

Rounding Decimals

Rounding Decimals to the Nearest Whole Number

Rounding Decimals to the Nearest Tenths

Rounding Decimals to the Nearest Hundredths

Round a Decimal

Adding Decimals

Subtracting Decimals

Simplify Decimals Involving Addition and Subtraction Decimals

Multiplying Decimal by a Decimal Number

Multiplying Decimal by a Whole Number

Dividing Decimal by a Whole Number

Dividing Decimal by a Decimal Number


7th Grade Math Problems

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