 # PEMDAS

In Mathematics, we do operations like addition, subtraction, multiplication and division. These operations are performed by a certain rule or say there is an order of operation. PEMDAS rule is one of the rules which is exactly equal to BODMAS rule. The full form of PEMDAS is given below:

P – Parentheses  [{()}]

E – Exponents (Powers and Roots)

MD- Multiplication and Division (left to right) (× and ÷)

AS – Addition  and Subtraction (left to right) (+ and -)

whereas the full form of BODMAS is – Brackets Order Division Multiplication Addition and Subtraction.

PEMDAS term is used mainly in the US but in India and the UK, we call it as BODMAS. But there is no difference between them. The order of operations for brackets, orders, addition, subtraction, multiplication and division is the same for both the rule. The PEMDAS rule can be remembered using the acronym “Please Excuse My Dear Aunt Sally”.

PEMDAS formula is nothing but the order of calculations by means of which we calculate difficult equations step by step. Let us discuss it with some examples.

## PEMDAS Rule

PEMDAS rule states that the order of operation starts with the parentheses first or the calculation which is enclosed in brackets. Then the operation is performed on exponents(degree or square roots) and later we do operations on multiplication & division and at last addition and subtraction. Let us discuss in brief.

### PEMDAS: Order of Operations

• P: Solve the calculation or equation which are present in the parentheses or brackets like small brackets( ), curly brackets{ } or big brackets[ ]. Priority is given to brackets first.
• E: Exponential expressions should be calculated first before the operations of multiplication, division, addition and subtraction. Usually, they are expressed in power or roots, like 22 or √4.
• MD: Then perform multiplication or division from left to right, whichever comes first in the equation.
• AS: At last, perform addition or subtraction whichever comes first while moving from left to right.

## PEMDAS Vs BODMAS

There is only an abbreviation difference between them.

 P – Parentheses First B – Brackets First E – Exponents O – Orders M – Multiplication D – Division D – Division M – Multiplication A – Addition A – Addition S – Subtraction S – Subtraction

In Canada, this order of operation is also mentioned as BEDMAS(Brackets, exponents, division, multiplication, addition and subtraction). Though the order of operation has given different names in different countries, the meaning for all is the same.

Let us see how to solve different problems using PEMDAS rule in maths.

Example 1: Solve 58÷ (4 x 5) + 32

Solution:

58 ÷ (4 x 5) + 32

As per the PEMDAS rule, first, we have to perform the operation which is in the parentheses.

= 58 ÷ 20 + 32

Now perform the exponent/power operation

= 58 ÷ 20 + 9

The division should be performed.

= 2.9 + 9

= 11.9
Therefore, 58 ÷ (4 x 5) + 32 = 11.9

Example 2:

$$\begin{array}{l}Simplify\ the\ expression:\ \sqrt{1+8}+12\end{array}$$

Solution:

As per the PEMDAS rule, first we need to perform the operation of exponent, i.e. square root

For this first we need to add the numbers under the square root.

$$\begin{array}{l}=\sqrt{1+8}+12\\ =\sqrt{9}+12\\ =3+12\\=15\end{array}$$

Example 3:

$$\begin{array}{l}Simplify:\frac{5+4}{1+2}-3\end{array}$$

Solution:

A horizontal fractional line also acts as a symbol of grouping:

$$\begin{array}{l}=\frac{5+4}{1+2}-3\\=\frac{9}{3}-3\\=3-3\\=0\end{array}$$

Example 4: Calculate: [25 + {14 – (3 x 6)}]

Solution:

Given,

[25 + {14 – (3 x 6)}]

As per PEMDAS, here we have perform the operations within the parentheses, first (), second {} and finally []

=[25 + {14 – 18}]

= [25 +{-4}]

Here, we have to perform multiplication for the signs

= 25 – 4

= 21