## Subtracting fractions with regrouping

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

1. Rename with common denominators
2. Regroup the first fraction
3. Subtract the whole numbers and numerators
4. 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

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 Step 3: Regroup the first number Step 4: Subtract

In summary, subtracting fractions that require regrouping is a 4-step process:

1. Re-write the problem using common denominators
2. Model the first number
3. Regroup the first number by cutting one whole into fractional parts
4. Subtract the fractions

For more practice with fractions, please try this Fraction Calculator.

# Self-Check

 Question 1 $5\frac{2}{3}\,-\,1\frac{4}{5}\,=$ [show answer] $5\frac{2}{3}\,-\,1\frac{4}{5}\,=$ $5\frac{10}{15}\,-\,1\frac{12}{15}\,=$ $4\frac{25}{15}\,-\,1\frac{12}{15}\,=$ $3\frac{13}{15}$

 Question 2 $9\frac{1}{4}\,-\,3\frac{5}{6}\,=$ [show answer] $9\frac{1}{4}\,-\,3\frac{5}{6}\,=$ $9\frac{3}{12}\,-\,3\frac{10}{12}\,=$ $8\frac{15}{12}\,-\,3\frac{10}{12}\,=$ $5\frac{5}{12}$

 Question 3 $7\frac{1}{2}\,-\,4\frac{7}{8}\,=$ [show answer] $7\frac{1}{2}\,-\,4\frac{7}{8}\,=$ $7\frac{4}{8}\,-\,4\frac{7}{8}\,=$ $6\frac{12}{8}\,-\,4\frac{7}{8}\,=$ $2\frac{5}{8}$