# Help Zone

### Student Question

My teacher keeps talking about PEMDAS, but what exactly is it?

Mathematics ## Explanations (1)

• Explanation from Alloprof  Explanation from Alloprof

This Explanation was submitted by a member of the Alloprof team.

Hi!

PEMDAS is a trick to remember the order of operations.

• P: Parentheses
• E: Exponents
• MD: Multiplication and Division

As you can see, PEMDAS is a mnemonic device for retaining an order we must follow in a chain of operations.

Indeed, the first thing to calculate is what is in the parentheses, followed by the exponents. Then, the multiplications and divisions in the order in which they appear (from left to right). Finally, additions and subtractions in the order in which they appear too (from left to right).

Here is a small example:

(5 ∗ 2−3 + 10) + 32− (10 ÷ 5 ∗ 2) −1 + 22

Let's start by solving what is in the parentheses (respecting PEMDAS):

• (5 * 2- 3 + 10) = (10-3 + 10) = (7 + 10) = (17)

We do the multiplication first. Then we do the subtraction, because it comes before the addition.

• (10 ÷ 5 * 2 ) = (2 * 2) = (4)

We do the division first, because it comes before the multiplication.

So,

(5 ∗ 2−3 + 10) + 32− (10 ÷ 5 ∗ 2) −1 + 22 =

(17) + 32− (4) −1 + 22

Now, let's go to the exponents:

(17) + 32− (4) −1 + 22 =

17 + 9−4−1 + 4

Let's finish with the additions and subtractions in the order in which they appear (from left to right):

17 + 9−4−1 + 4 =

26−4−1 + 4 =

22−1 + 4 =

21 + 4 = 25

Hope this helped you, let us know if you have any other questions! :)