To buy footwear, you will check your foot size first. Then you will look for the occasion for which you are wearing it. Next, you check for comfort, budget, and color. At last, you buy it. If you skip any of these steps you may end up in trouble, because you can’t wear smaller-sized footwear or funky footwear to a formal occasion. So all these steps are mandatory to follow while buying footwear. Similarly, in math, we have to follow a set of rules while solving an expression. The PEMDAS rule is one such rule that is globally accepted to solve an expression consisting of multiple mathematical operations and braces.

## Order of Operations

When you have an expression with addition, subtraction, exponential operations, etc. you often get confused with what to solve first. To avoid such confusion, we make use of a rule called the PEMDAS/BODMAS rule. Here the name PEMDAS or BODMAS is an acronym used to remember the order of operations. PEMDAS is abbreviated as Parentheses, Exponents, Multiplication or Division, and Addition or subtraction. Similarly, BODMAS is expanded as Braces, Order, Division or multiplication, and addition or subtraction. Thus, the order remains the same in both cases but the terms used are different.

You can also remember PEMDAS as “Please Excuse My Dear Aunt Sally”. Hence as per the PEMDAS rule the correct way to solve an expression is solving the braces first, then exponents followed by multiplication or division, and lastly addition or subtraction.

## PEMDAS Rule:

Let us learn to use this PEMDAS rule with an example:

**Example:** [29 { 3 + (225 15)} – 9]

**Solution:** P in PEMDAS stands for parentheses, when we have different types of parentheses involved then we have to start solving from common parentheses. Hence let us solve the operations within the common braces first.

∴ (225 15) = 15

Next solve the flower parentheses

{3 + (225 15)} = 3 + 15 = 18

Now solve the square bracket.

That is, [29 {3 + (225 15)} – 9] = [29 {18} – 9].

Within the square bracket we have many operations to solve. So we have to look for the next letter of PEMDAS, that is E stands for exponents. Hence solve the exponents

∴ 29 = 2 3 = 6

Next we have MD, which stands for multiplication or division.

[29 { 3 + (225 15)} – 9] = [29 { 18 } – 9]

= 618 – 9 (Multiplication)

= 48 – 9 = 39 (Subtraction)

Thus we got [29 { 3 + (225 15)} – 9] = 39.

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## Key Takeaways

- Operations within common brackets are solved first followed by flower bracket operations and then the square brackets operations.
- If present, solve the exponents.
- Solving from left to right multiplication or division, the operation that comes first is solved.
- Solving from left to right addition or subtraction, the operation that comes first is solved.

### Examples

**Example 1:** Solve: 5 + 48 ÷ (4 x 4) – 23

**Solution:** In accordance with PEMDAS rules, we have to perform the operation in parentheses first.

(4 x 4) = 16.

Now perform exponents

23 = 8

Next is division

48 ÷ (4 x 4) = 48 16 = 3

Since addition comes first from left to right, we do addition.

5 + 48 ÷ (4 x 4) = 5 + 3 = 8

Lastly subtraction

5 + 48 ÷ (4 x 4) – 23 = 8 – 8 = 0

**Example 2:** Solve: 33 – 240+9

**Solution:** Solve parentheses first

40+9 = 49 = 7

Next multiplication

240+9 = 2 7 = 14

Now, subtraction

33 – 240+9 = 33 -14 = 19

This is all about PEMDAS. For more information log onto the Cuemath website.