Think of the order operations as math grammar and punctuation. We use the order of operations to know what to do first, second and last in a math equation so we get the correct answer. By changing the order of words and punctuation in a sentence the meanings change dramatically. Look at the difference of “Will you eat your chicken, Honey?” and “Your honey chicken will eat you.” Not following the rules for the order of operations in math will lead to equally confusing outcomes!

Imagine this scenario. Your child comes looking to you for help and shows you a problem that has lots of numbers and symbols. Maybe the equation looks something like this:

5 x 6 + 5 ^{2} - 3 ^{2} =

You want to help but you haven’t done equations like this for a long time. Maybe you remember that there is an order of operations but aren’t exactly sure what it is or how to apply the rules. Use this explanation to help.

First, you remember that we read math from left to right, just like we do when reading a book or an article.

So, you think 5 x6 = 30.

Then, if you continue following left to right exactly you might think:

30+5= 35 and then square 35 that equals 1,225. Then subtract 3 to get 1,222 and then square that and the answer becomes 1,493, 284. Is that right? No! You went left to right but did not take into account the order of operations.

The order of operations is:

**P**arentheses

**E**xponents

**M**ultiplication

**D**ivision

**A**ddition

**S**ubtraction

Some teachers help kids remember the order with the mnemonic device, Please Excuse My Dear Aunt Sally, to create the acronym PEMDAS which helps them remember the order. Exponents are the little numbers to the right of a larger number. They only get applied to the number it is directly beside, unless parentheses are involved. So using PEMDAS and the order of left to right, we can clearly see the correct order of steps. Let’s go back to the problem.

5 x 6 + 5 ^{2}- 3 ^{2}

Step 1 Square 5 which equals 25

Step 2 Square 3 which equals 9

Step 3 Multiply 5 and 6 which equals 30

Step 4 Add 30 and 25 which equals 55

Step 5 Subtract 9 from 55 which equals 46

But what about the parentheses?

Think of whatever is enclosed in the Parentheses as a single quantity. Do the operations within the Parentheses and then go left to right to solve.

The Parentheses in different places will greatly affect the outcome. Here are some examples so you get a sense of it.

Example 1

5 x 6 + (5 ^{2}- 3 ^{2}) = 5 x 6 + (25-9) = 5x6 + (16) = 30 + 16 = 46

Example 2

5 x (6 + 5) ^{2}- 3 ^{2} = 5 x = 5 x 121- 9= 596

**More questions?**

If you, or your child, continue to need help with the order of operations, or other math problems, come check out Mathnasium of Parker. “We Make Math Make Sense.”

This article was written by and owned by Cuttlefish Copywriting, www.cuttlefishcopywriting.com . It is copyright protected. Mathnasium of Parker has permission to use it. Other Mathnasium locations should contact Heather at [email protected] before using it.