Below is a guide to help understand the idea behind Fractions as Division Problems. This doesn’t cover every scenario, but if confused, it should help understand what’s happening in these types of problems.

When you see a number like 3/4, what is really being said is 3 divided by 4.

You can also understand this idea using models, which we will use to help our conceptual understanding of these ideas.

Note, there ARE shortcut strategies that can be used when working with fractions, but these shortcuts eventually become useless as we move into future Units and Grades unless we understand the WHY behind what we are doing.

Below are a couple more examples you can try. If you want to check the answers, scroll to the very bottom of the page.

1. 2/5

2. 3/7

3. 4/5

4. 2/3

THE DON’T KILL PEOPLE RULE: When understanding fractions as division problems, it’s common that you might come across a word problem dealing with people and some object. Because these fractions will mimic real world situations, it’s very important to understand the meaning behind out numbers. When it comes to dividing and people, we never cut people in half, or thirds, or any other kind of sections. We need to think about what is being cut and for who. Look to the example problem below.

EX: 5 students are working together to bake 2 pans of cookies and will split them equally amongst themselves. Write a fraction that represents the action taking place.

There are two potential ways this problem could be written: either as 5/2 or as 2/5, but if we take a moment to understand what the problem is asking and write down what our pieces mean, we will gain some clarity.

Our 5 = students, and our 2 = cookie pans.

Numerator What is being cut or split____________Denominator Who or what it’s being split for

With this in mind, as well as the “Don’t Kill People” rule, we know that we must put the 2 pans of cookies on top because this is what’s being split for the 5 students.

2__5

Answers to the examples above: