To subtract fractions that require regrouping, there are four steps you must follow:

Rename with common denominators
Regroup the first fraction
Subtract the whole numbers and numerators
Simplify (if necessary)

The problem	$$2\frac{1}{3}\,-\,1\frac{1}{2}\,=$$
Rename with common denominators	$$2\frac{2}{6}\,-\,1\frac{3}{6}\,=$$
Regroup the first fraction	$$1\frac{8}{6}\,-\,1\frac{3}{6}\,=$$
Subtract	$$\frac{5}{6}$$
Simplify (if necessary)	not needed on this problem

Subtracting from a mixed number

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Example 1: $3\frac{2}{5}\,-\,2\frac{4}{5}\,=$

Step 1: Model the first number

Step 2: Regroup the first number

Step 3: Subtract

Example 2: $4\frac{3}{7}\,-\,2\frac{5}{7}\,=$

Step 1: Model the first number

Step 2: Regroup the first number

Step 3: Subtract

So far, the examples shown have not involved fractions with different denominators. Before subtracting fractions with different denominators, you must first rename both fractions with a common denominator.

Example 3: $3\frac{1}{2}\,-\,1\frac{2}{3}\,=$

Step 1: Re-write the problem with common denominators

$3\frac{1}{2}\,-\,1\frac{2}{3}\,=$

$3\frac{3}{6}\,-\,1\frac{4}{6}\,=$

Step 2: Model the first number