How to Subtract Mixed Numbers With Regrouping

By Janel Flynn

Mixed numbers consist of a whole number portion and a fraction portion. In the mixed number 4 1/8, 4 is the whole number and 1/8 is the fraction. When subtracting mixed numbers, you will sometimes be required to regroup. This is an easy process; if you just think about the meaning behind the steps it will all make sense.

Look at the denominators in the fractions being subtracted. If the denominators are different, rewrite the fractions so they have like denominators. For example, in 4 1/8 and 3 1/4, the lowest common denominator of 8 and 4 is 8. The mixed number 4 1/8 would not change. The fractional part of 3 1/4 would change.

3 1/4= 3 + 1/4 x ?/?=?/8

Since 8 is the lowest common denominator, you'd ask what do you multiply 4 by to get 8? The answer is 2. Whatever you do to the denominator, you also do to the numerator. Because 1 x 2 = 2, the new mixed number is 3 2/8.

Now your problem looks like this 4 1/8 - 3 2/8=?

Decide if you need to regroup. In this problem 1/8 - 2/8 is not possible because 1/8 is bigger than 2/8. You need to regroup.

4 1/8 = 3 + 8/8 + 1/8 = 3 9/8

To make the 1/8 larger, you are going to borrow 1 from the whole number 4. The 1 you are borrowing from 4 is the same as borrowing 8/8. The 4 becomes a 3 and you add the 8/8 to the 1/8 leaving you with 3 9/8.

Now your problem looks like this: 3 9/8 - 3 2/8 = ?

Subtract the fractions.

9/8 - 2/8 = 7/8

Subtract the whole numbers.

3 - 3 = 0

Write the difference in simplest form.

7/8 is already in simplest form.

About the Author

Janel Flynn is a freelance writer and editor for a company in the United Kingdom. Her articles have appeared on various websites, including eHow.com and Associated Content. She holds a Bachelor of Science in elementary and special education, as well as a master's degree in curriculum design and instruction focusing on literacy.