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 }

Adding all the numbers;

⟹ 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 }

Now add the numbers;

⟹ 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.