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Problems with Fractions and How to Solve Them

In this post, we are going to give you some guidelines and advice for confronting problems with fractions.

Problems with fractions, in no time!

Fortywinklesburg is an imaginary kingdom where all of its inhabitants have a peculiar habit: they sleep for days without waking up. The Winklean’s, as they are called, sleep for so long that they do not know the amount of time that they have been asleep. The fearless prince of Fortywinklesburg, Dozian, has devised a plan to calculate the duration of his next slumber. Before going to bed he will shave his beard, and since it grows 3/100 of an inch a day, when he wakes up he will be able to deduce how many days have passed while he was dreaming. If Dozian discovers that his beard is 9/50 of an inch when he wakes up, how many days has he been asleep?


When we are faced with these types of problems with fractions the first thing that we should do is find the data. Do you have it? The data is:

3/100 in

1 day

9/50 in

Once we have the necessary data the next step is to carefully read the question, this way we know exactly what we should be calculating in order to solve the problem. Look at the question and read it again. Done? Perfect. In this case, we need to calculate the number of days that Dozian has slept.

Next, we have to design a strategy to solve the problem. This part is a bit more complicated, and because of that, we need to be careful.

For this problem we have the following strategy: If it takes 1 day for Dozian’s beard to grow 3/100 in, growing 9/100 in took the number of days that Dozian has slept.

You can outline all of the information like this:

problems with fractions

Now we have all the information at a glance and can move on to the calculations. In this problem, the operation we need is division: 9/50 by 3/100. And in case you forgot how to do division with fractions look at this post, and don’t forget to simplify!

problems with fractions

Finally, we always recommend that, whenever you have a problem with fractions, to check to see if the solution makes sense within the context of the original problem

Additionally, you should write the result indicating the corresponding unit. In this case, the solution is:

Dozian has slept for 6 days.

I hope that this post has helped you develop a useful strategy for solving problems with fractions. Do you think you can do it by yourself? Login here and keep learning with Smartick.

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