Let’s review types of fractions before discussing subtracting fractions with regrouping.
Fractions are in the form of numerator/denominator.
Mixed numbers consist of a whole number with a fraction such as 4 ½.
Fractions are considered proper fractions when the numerator is smaller than the denominator such as 3/5.
Improper fractions have a numerator larger than the denominator such as 12/5.

Memory Tip:
Here’s a way to remember the difference between proper and improper fractions. The everyday definition of proper means the correct way of doing something. For example, it is proper to eat milk and cereal with a spoon. However it is not proper table manners to slurp your spaghetti. In other words, it is considered improper, or not the correct way. So, it is with fractions. If the numerator is larger than the denominator, I would say with disdain and my nose in the air, “That is an improper fraction and action must be taken immediately! Convert to a mixed number!”

How to Convert an Improper Fraction to a Mixed Number:

Example: 33/7
The line between the 33 and 7 is called the fraction bar. The fraction bar denotes division. So read this number as 33 divided by 7. When you do the division, you get 4 with a remainder of 5.
Thus, 33/7 = 4 5/7. Notice that the denominator stays the same.

What does this really mean? Recall that a fraction is part/whole. 33/7 indicates there are 33 individual parts of equal size and 7 of those parts put together would make a whole or make the picture complete, or make a whole pizza. How many wholes? 4

Practice:
1) 104/33
2) 59/4
3) 87/8

Answers:
1) 3 5/33
2) 14 ¾
3) 10 7/8

How to Convert a Mixed Number to an Improper Fraction:

Example: 4 3/8 = 4 x 8 + 3 / 8 = 35/8
Multiply the whole number and the denominator. Then, add the numerator. The denominator stays the same.

Example: 12 5/6 = 12 x 6 + 5 = 77/6

Application:

If you can change a mixed number into an improper fraction and vice versa, you can subtract fractions that normally require borrowing without doing so.

Example: 7 3/8 – 4 6/8 =

1. It is not possible to subtract 6 from 3. Instead of borrowing one from the whole number, 7, let’s
2. change both fractions into improper fractions --- 59/8 – 38/8
3. subtract ----- 59/8 – 38/8 = 21/8
4. The answer is an improper fraction. Change it into a mixed number.
5. 21/8 = 2 5/8
6. in summary, 7 3/8 – 4 6/8 = 2 5/8

Please remember you can only use this method when the denominators are the same.

In order to master any math skill, practice, practice, practice. Mastering Essential Math Skills: Fractions provides short review fraction exercises for converting fractions and all the other fraction skills. You can read a review of the award winning author, Richard Fisher’s math books for upper elementary and middle school at the link below.