Smartick Try it for free! Abrir el Menú Móvil Try it for free!
Smartick is an advanced online program that teaches kids math and coding in only 15 min. a day
Try it for free!


Solve Fraction Problems with Halves, Thirds and Quarters

Very often we find, both in mathematical problems and in real life, fraction phrases like: a half, a third or a quarter.

They are the most famous fractions! I’m sure you’ve seen them before.

If you want to see what they are and how to calculate them, you can check out this link:

And if you want more practice with fractions, continue reading and solve some fraction problems with us. Are you ready? Let’s go!fraction problems

Fraction Problems nº 1:

At the farmer’s market a pound of lemons costs $4, how much does half a pound cost?

It’s a good idea to start by remembering that a single unit is the same as two halves or three thirds or four fourths.

fraction problems


In this case, we have to find the price of a half-pound. We can see that a single unit is equivalent to two halves. So, in order to find out how much half of a pound costs, we have to divide by two and take one of these parts.

fraction problems


The price of a one whole pound is $4, so we divide: 4 / 2 = 2. Half of a pound costs $2

It can also be expressed as follows:



And…How much would two quarters of a pound cost?

Here, we divide the single unit into four parts and take two parts.

fraction problems

If we think about it, we can see that two quarters is equivalent to a half.

fraction problems

So, two quarters of a pound would cost $2 as well.

It can also be expressed as such:


Fraction Problems nº 2:

Mark bought three quarters of a pound of lemons. How much did he pay?

He bought three quarters of a pound, so we divide the unit into four parts and take three of them.

fraction problems

Each pound is $4, so we divide 4 / 4 = 1 and multiply by 3. 1 x 3 = 3. He paid $3.

When he got home, Mark squeezed the lemons and got a quarter-gallon of lemon juice. After, he added a half-gallon of water to make lemonade. How much lemonade did he make?

Let’s draw it out:

– He squeezed out a quarter-gallon of lemon juice


– He added a half-gallon of water


In order to add a quarter to a half, we have to find the common denominator.

We should already know that two quarters are equal to one half!

fraction problems

So, we add one quarter to two quarters..


And we get three quarters.

fraction problems

That means that Mark made three quarters of a gallon of lemonade.fraction

Fraction Problems nº 3:

Peter served 7 glasses of lemonade and 14 glasses of water because some of his friends didn’t like lemonade. What fraction of the glasses that he served had lemonade?

fraction problems

How many glasses did he serve in total? 21!  This will be the denominator of the fraction.

How many glasses of lemonade did he serve?  7!  This will be the numerator.


But, it can be simplified!

Let’s look at it this way:


How many groups of glasses are there in total? 3

How many of these groups have lemonade? 1

fraction problems

Therefore, the reduced fraction that represents the amount of glasses of lemonade served is one third.

The next time you make lemonade or any other kind of recipe at home, take a look at the quantities! Try to find the fraction and if you discover any tell us by leaving us a comment!

Also, remember that you can log onto Smartick and try it for free if you want to learn more math!

Learn More:

Share on FacebookTweet about this on TwitterShare on LinkedIn
Content Creation Team.
A multidisciplinary and multicultural team made up of mathematicians, teachers, professors and other education professionals!
They strive to create the best math content possible.

Add a new public comment to the blog:

The comments that you write here are moderated and can be seen by other users.
For private inquiries please write to [email protected]

Your personal details will not be shown publicly.

Privacy Policy

1 Comment;

  • ChidinmaSep 09 2017, 9:55 PM

    Greatly simplified!