Word Problems on Adding and Subtracting Mixed Fractions

In a birthday party, Naina was given 1 piece of cake.

Najma was given 1 piece of cake.

Find the total amount of cake that was given to both of them.

Let us solve the problem together.

To find the total piece of cake Naina and Najma have, we have to add two mixed fractions 1 and 1

So the total cake given to Naina and Najma is as shown.

In addition to the method we have solved we can also add the fractions...

...by converting the mixed fractions to improper fractions.

In Both the cases the answer is the same.

Problem 2

Jaidev takes 2 minutes to walk across the school ground.

Rahul takes 1 minutes to do the same.

Who takes less time and by what fraction?

First to find out, who took less time we need to compare the fractions as above.

So, Rahul takes less time.

To find the answer by what fraction, we have to subtract the two fractions as shown.

So Rahul took less time by a fraction of min

Problem 3:

Asha and Samuel have bookshelves of the same size partly filled with books.

Asha’s shelf is 1\dfrac{1}{6}$$ th full.

Whose bookshelf is more full? By what fraction?

So, Samuel’s shelf is more filled than Asha's

To find by what fraction we have to find the difference between the fractions.

So, Samuel’s shelf is more filled than Asha's by a fraction


We have solved problems based on adding mixed fractions.

And subtracting mixed fractions.

The End