# Simplification in Decimals

Simplification in decimals can be done with the help of PEMDAS Rule.

PEMDAS Rule Table

From the above chart we can observe that first we have to work on "P or Parentheses" and then on "E or Exponents", then from left to right doing either "Multiplication" or "Division" as we find them in the question.

Then from left to right doing either "Addition" or "Subtraction" as we find them we need to solve them accordingly.

Let us consider some of the examples on simplification in decimals:

1. Solve 5.8 – 2.7 + 1.4 – 1.6

Solution:

We first group the numbers having same signs and then add them. Subtract the sum of the numbers with – sign from the sum of the numbers with + sign.

First step: Add 5.8, 1.4 and 2.7 and 1.6

Second step: Now subtract 4.3 from 7.2

Hence, 5.8 – 2.7 + 1.4 – 1.6 = 2.9

2. 4.5 + 3.7 – 3.6 ÷ 1.2

Solution:

4.5 + 3.7 – 3.6 ÷ 1.2

= 4.5 + 3.7 – 3.0

= 8.2 – 3.0

= 5.2

3. 3 ÷ 16 + 1.2 × $$\frac{1}{4}$$ - {$$\frac{1}{5}$$ + (1 - 0.8) }

Solution:

3 ÷ 16 + 1.2 × $$\frac{1}{4}$$ - {$$\frac{1}{5}$$ + (1 - 0.8) }

3 ÷ 16 + 1.2 × $$\frac{1}{4}$$ - {$$\frac{1}{5}$$ + 1 - 0.8}

= 3 ÷ 16 + 1.2 × $$\frac{1}{4}$$ - {$$\frac{1 + 5 - 4.0}{5}$$}

= 3 ÷ 16 + 1.2 × $$\frac{1}{4}$$ - {$$\frac{6 - 4}{5}$$}

= 3 ÷ 16 + 1.2 × $$\frac{1}{4}$$ - {$$\frac{2}{5}$$}

= 3 ÷ 16 + 1.2 × $$\frac{1}{4}$$ - $$\frac{2}{5}$$

= $$\frac{3}{16}$$ + $$\frac{1.2}{4}$$ – $$\frac{2}{5}$$

= $$\frac{15 + 24 - 32}{80}$$

= $$\frac{7}{80}$$

= 0.0875

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Expanded form of Decimal Fractions

Like Decimal Fractions

Unlike Decimal Fraction

Equivalent Decimal Fractions

Changing Unlike to Like Decimal Fractions

Comparison of Decimal Fractions

Conversion of a Decimal Fraction into a Fractional Number

Conversion of Fractions to Decimals Numbers

Subtraction of Decimal Fractions

Multiplication of a Decimal Numbers

Multiplication of a Decimal by a Decimal

Properties of Multiplication of Decimal Numbers

Division of a Decimal by a Whole Number

Division of Decimal Fractions

Division of Decimal Fractions by Multiples

Division of a Decimal by a Decimal

Division of a whole number by a Decimal

Conversion of fraction to Decimal Fraction

Simplification in Decimals

Word Problems on Decimal