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)

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

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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