Simplification in Decimals

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

PEMDAS Rule Table

$Simplification in Decimals, PEMDAS Rule Table$ 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

$Decimal Addition$

Second step: Now subtract 4.3 from 7.2

$Decimal Subtraction$

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

Answers: 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 × $\frac{1}{4}$ - $\frac{2}{5}$

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

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

= $\frac{7}{80}$