Skill: Subtract mixed numbers with regrouping

Explanation and Free Practice Resources

Subtracting mixed numbers with regrouping involves interpreting each number as a whole-number part and a fractional part, then decomposing one whole into an equivalent fraction when the minuend’s fractional part is smaller than the subtrahend’s. The quantities may first be rewritten with a common denominator, after which whole parts and fractional parts are subtracted while preserving value; denominators are not subtracted. The scope is positive mixed numbers and standard proper fractions, excluding negative, complex, or algebraically generalized forms.

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Detailed Explanation: Subtract mixed numbers with regrouping

To subtract mixed numbers with regrouping:

Subtract the fractional parts first.
If the first fraction is smaller, regroup one whole as a fraction.
Subtract the whole-number parts.
Simplify the answer if possible.

Example:

5\frac{1}{4}-2\frac{3}{4}

The fractional part $\frac{1}{4}$ is smaller than $\frac{3}{4}$ , so we need to regroup one whole.

Rewrite $5\frac{1}{4}$ by taking $1$ whole from $5$ :

5\frac{1}{4}=4+\left(1+\frac{1}{4}\right)

Since $1=\frac{4}{4}$ :

5\frac{1}{4}=4\frac{5}{4}

Now subtract the fractional parts and whole-number parts:

4\frac{5}{4}-2\frac{3}{4} =(4-2)+\left(\frac{5}{4}-\frac{3}{4}\right)

=2+\frac{2}{4}

Simplify $\frac{2}{4}$ :

\boxed{2\frac{1}{2}}

The denominators stay the same because the fractions already have a common denominator. You do not subtract the denominators.

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Fraction Subtraction - Mixed (Simplifying Answers) - Two Changed Denominators

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