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]


Question 2

$9\frac{1}{4}\,-\,3\frac{5}{6}\,=$

 

 

 

 

[show answer]


Question 3

$7\frac{1}{2}\,-\,4\frac{7}{8}\,=$

 

 

 

 

[show answer]


 

 

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