Adding and Subtracting Mixed Fractions

To add or subtract mixed numbers simply add or subtract the whole numbers and fraction portion separately and then recombine to form the new mixed number.

Example:

You say “two and one-fifth plus one and one-half”.

The word “and” means addition, so we can write this as:

We can add the whole numbers, then get a common denominator and add:

Answer:

Another way is to add or subtract mixed numbers is to convert the mixed numbers into improper fractions, perform the operation and then change the answer back (if necessary) to a mixed number.

 

Example:

(same as above)

Using this method, we first convert mixed fractions to improper fractions.

Next we change them to a common denominator and add.

Finally change back to a mixed fraction. 10 goes into 37 just three times, with a remainder of 7:

Answer:

(same as above!)

 

Hardest Addition in the World

Here is a math problem that might be the hardest fractions to add. Something about the pattern just make syou want to add numbers going straight across. But don't! Follow the same procedure we always use.

 

Example:

Do the 2's cancel each other? No, they may cancel in multiplication but not addition!

Find a common denominator and then add.