Order of Operations (PEMDAS)

PEMDAS (Parenthesis, exponents, multiplication, division, addition and subtraction) is an acronym that defines the order of operations in arithmetic. In other words, in a mathematical expression, if you have more than one operation involved, then you need to follow this order of operations to get your answer right.

If you don’t follow this order, you will obviously get an answer, but it will wrong. PEMDAS tells you which operation is to be done first, followed by which operation and so on.

The reason this acronym was invented is because it would be very difficult to remember the order of operations if someone just told you to complete everything in parenthesis first, then complete the exponents followed by multiplication, division, addition and subtraction.

Yes, it seems quite difficult to remember this order. And that is the reason the acronym PEMDAS came into existence and if you want to make it even easier, you can remember it in the form of a sentence like Please Excuse My Dear Aunt Sally (PEMDAS). If you remember this phrase, you can then easily remember the order of operations and complete your math problems quickly.

Why Is PEMDAS Important?

The order of operations or PEMDAS is extremely important as it defines the guidelines to work out any math problem correctly. Take for example, the following expression:

3 * 2 + 5

Here I can either multiple 3 * 2 first and add the result with 5 and will get an answer.

3 * 2 + 5 = 11

Or, I can add 2 + 5 and finally multiply the result with 3 and I will also get an answer here. But the main thing is which is the correct answer?

3 * 2 + 5 = 21

If you apply PEMDAS here, it says:

Parenthesis, exponents, multiplication, division, addition and subtraction

So, you need to complete the multiplication first before you add or subtract.

By applying this order, the correct answer is 11, where you multiply first and then add.

Detailed Explanation of PEMDAS

Let’s look at the detailed explanation of PEMDAS:

P denotes parenthesis and it means you need to work out anything inside the parenthesis.

For example:

3 * (4 + 2) is the expression you need to work out
3 * (4 + 2) = 3 * 6 = 18 (CORRECT ORDER)
3 * (4 + 2) = 12 + 2 = 24 (WRONG ORDER)

Next is the exponents, which means you need to calculate the powers and roots before you multiple, divide, add and subtract.

4 * 22 is the expression
4 * 22 = 4 * 4 = 8 (CORRECT ORDER)
4 * 22 = 82 = 64 (WRONG ORDER)

MD stands for Multiply and divide before addition and subtraction

8 + 5 * 2 is the expression you need to work out
8 + 5 * 2 = 8 + 10 = 18 (CORRECT ORDER)
8 + 5 * 2 = 13 * 2 = 26 (WRONG ORDER)

Last comes AS which means you need to do addition and subtraction, only at the last, after you complete the other operations in order.

Example 1 – Calculate 7 – 24 / 8 *4 +6

Here, there are no parentheses or exponents, so either multiplication or division must be performed. In this case, since division is before multiplication, division will be completed first.

7 – (24/8) * 4 + 6
7 – 3 * 4 + 6

Multiplication will be performed next:

7 – 3 * 4 + 6
7 – 12 + 6

Next, since the minus sign occurs before the addition sign, subtraction will be performed next:

7 – 12 + 6 = – 5 + 6

Adding is the last step:

-5 + 6 = 1

Example 2 – (17 – 6 /2) + 4*3

According to PEMDAS, parenthesis comes first, so the expression in parentheses will be considered first.

(17 – 6 /2) + 4*3

In the parenthesis, we do not see any exponents. However, we see a division symbol, so division will be performed.

(17 – 6/2) + 4*3
(17 – 3) + 4*3

Still in the parenthesis, we will perform subtraction:

(17-3) + 4* 3 = 14 + 4*3

Multiplication will be performed next:

14 + 4*3 = 14 + 12

Addition is the last step.

14 + 12 = 26

Example 3 – (3 * 5^2 / 15) – (5-2^2)

According to PEMDAS, expressions in parenthesis will be computed first. We have 2 expressions in parenthesis, so we will consider each expression by itself.

(3 * 5^2 / 15) – (5-2^2)

For the first expression, exponents are next.

(3 * 5^2 / 15) = (3 * 25 / 15)

Since multiplication occurs first before division, multiplication will be performed next.

(3 * 25 / 15) = (75 / 15)

Division is then performed:

75 / 15 = 5

For the second expression inside the parentheses, exponents are considered.

(5 – 2^2)
(5 – 4)

Subtraction is performed:

(5 – 4) = 1

Putting the two simplified expressions together:

5 – 1 = 4

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