# BODMAS/PEMDAS rules – Solving decimal expression

In this chapter we will solve some decimal expressions using BODMAS/PEMDAS rules.

## Solving decimal expression using PEMDAS

Before solving the expressions let us review the concept of PEMDAS.

### What is PEMDAS?

PEMDAS provides rules for solving algebraic expression.

It says that while simplifying algebraic expression, follow the below order;

P ⟹ Parenthesis
E ⟹ Exponents
MD ⟹ Multiplication & Division ( from left to right )
AS ⟹ Addition & Subtraction ( from left to right )

We have to strictly follow the above orders otherwise we will get the wrong answer.

Notes:
(i) There are multiple ways to represent parenthesis. Brackets like ( ), [ ], { } are used in expressions.

(ii) Exponents are also known as power in Math

(iii) When both division and multiplication are present then start from left and simplify whichever operation comes first.

(iv) Similarly of both addition or subtraction are present then start from left and simplify whichever comes first.

Given below are examples of solving decimal expressions using PEMDAS rule.

### Solving Decimal Expression using PEMDAS

Example 01
10 – 6.5 ÷ 2 + 4.8 x 5

Solution
Both division and multiplication is present.
In this case start solving from left.

⟹ 10 – 3.25 + 4.8 x 5
{ Simplifying division 6.5 ÷ 2 }

⟹ 10 – 3.25 + 24
{ Simplifying multiplication 4.8 x 5 }

Here both subtraction and addition is present.
Start solving from left.

⟹ 6.75 + 24
{ simplifying subtraction 10 – 3.25}

⟹ 30.75

Hence, 30.75 is the solution of expression.

Example 02
10.2 x ( 3.6 – 0.4 ) – 1.2 x 3

Solution
⟹ 10.2 x 3.2 – 1.2 x 3
{ simplifying parenthesis ( 3.6 – 0.4 ) }

⟹ 32.64 – 1.2 x 3
{simplifying multiplication 10.2 x 3.2}

⟹ 32.64 – 3.6
{simplifying multiplication 1.2 x 3}

⟹ 29.04

Hence, 29.04 is the solution of above expression.

Example 03
\mathtt{2^{3}} + 4.5 x 3 + 7.6 ÷ 2

Solution
⟹ 8 + 4.5 x 3 + 7.6 ÷ 2
{ Simplifying exponent \mathtt{2^{3}} }

Now we have both multiplication and division.
Solve from the left side.

⟹ 8 + 13.5 + 7.6 ÷ 2
{ Simplifying multiplication 4.5 x 3 }

⟹ 8 + 13.5 + 3.8
{ Simplifying division 7.6 ÷ 2 }

⟹ 25.3

Hence, 25.3 is the solution of given expression.

Example 04
16.4 ÷ (9.6 – 7.6) x 4.5 + 7

Solution

⟹ 16.4 ÷ 2 x 4.5 + 7
{Simplifying parenthesis (9.6 – 7.6)}

Both division and multiplication is present.
Start solving from left.

⟹ 8.2 x 4.5 + 7
{ Simplifying division 16.4 ÷ 2 }

⟹ 36.9 + 7
{ Simplifying multiplication 8.2 x 4.5 }

⟹ 43.9

Hence, 43.9 is the solution of expression.

Example 05
36 ÷ 4.5 + \mathtt{( 3.2+0.8)^{2}} x ( 3.5 – 3.4 )

Solution
Solving the expression using PEMDAS rule;

⟹ 36 ÷ 4.5 + \mathtt{(4)^{2}} x ( 3.5 – 3.4 )
{ Simplifying parenthesis (3.2 + 0.8) }

⟹ 36 ÷ 4.5 + \mathtt{(4)^{2}} x (0.1)
{ Simplifying parenthesis ( 3.5 – 3.4 ) }

⟹ 36 ÷ 4.5 + 8 x 0.1
{ Simplifying exponent \mathtt{(4)^{2}} }

Both multiplication and division is present.
Start simplifying from the left.

⟹ 0.8 + 8 x 0.1
{ Simplifying division 36 ÷ 4.5 }

⟹ 0.8 + 0.8
{ Simplifying multiplication 8 x 0.1 }

⟹ 1.6
{ Adding numbers 0.8 & 0.8 }

Hence, 1.6 is the solution of given expression.