Finding the Total Number when the Fractional Part is Known

Finding the total number of something when you are given the fractional part can be tough for students. Most students are taught how to solve this by working backwards, but using a bar model might actually be easier for kids who have not worked through these problems before.

The bar model shows them visually how we work backwards to get to the total.

Here’s an example:

Samantha bought a pair of shoes for $36, which was 2/3 of her money. How much money did she have initially?

In this problem we know the part is $36, but we don’t know the total. Divide the total into three parts and mark the two parts that are $36.

If two parts are $36, then one part is $18.

And three parts of the total is:

So the answer to the money she had initially is: $54

By representing the fractional parts in a bar model, students can more clearly see the relationship between the fractional parts and the total.

If you are looking for more fractions word problems, we offer them in our math worksheet center. Here are the adding and subtracting fractions word problem worksheets for grade 4 and grade 5.