Subtract fractions with unlike denominators

Subtraction of fractions with unlike denominators represents finding a difference between quantities measured in different fractional units. The learner generates equivalent fractions with a common denominator, subtracts the numerators while preserving the common unit, and interprets or simplifies the result, including positive mixed numbers when regrouping is needed; the denominators are not subtracted. The understanding applies to numerical fractions and mixed numbers, not algebraic fractions or more advanced symbolic rational expressions.

Detailed Explanation: Subtract fractions with unlike denominators

To subtract fractions with unlike denominators, first rewrite them with a common denominator. Then subtract the numerators and keep the common denominator. The denominators show the size of the pieces, so they are not subtracted.

Example

Subtract:

4\frac14-1\frac23

1. Find a common denominator

The denominators are $4$ and $3$ . Their least common denominator is $12$ .

Rewrite each fraction:

\frac14=\frac{3}{12} \qquad\text{and}\qquad \frac23=\frac{8}{12}

So the problem becomes:

4\frac{3}{12}-1\frac{8}{12}

2. Regroup because $\frac{3}{12}$ is smaller than $\frac{8}{12}$

Borrow $1$ whole from $4$ :

4\frac{3}{12}=3\frac{15}{12}

This works because $1=\frac{12}{12}$ , so:

3\frac{3}{12}+\frac{12}{12}=3\frac{15}{12}

Now subtract:

3\frac{15}{12}-1\frac{8}{12}

3. Subtract the whole numbers and fractions

3-1=2

and

\frac{15}{12}-\frac{8}{12}=\frac{7}{12}

Therefore,

\boxed{4\frac14-1\frac23=2\frac7{12}}

Remember: Make equivalent fractions with a common denominator, subtract only the numerators, and keep the denominator.

Learn by doing: Subtract fractions with unlike denominators

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Fraction Subtraction - Basic (Simplifying Answers) - One Changed Denominator

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