Ctrl+k

Subtract mixed numbers with regrouping

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.

Detailed Explanation: Subtract mixed numbers with regrouping

To subtract mixed numbers with regrouping:

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

Example:

514−2345\frac{1}{4}-2\frac{3}{4}

The fractional part 14\frac{1}{4} is smaller than 34\frac{3}{4}, so we need to regroup one whole.

Rewrite 5145\frac{1}{4} by taking 11 whole from 55:

514=4+(1+14)5\frac{1}{4}=4+\left(1+\frac{1}{4}\right)

Since 1=441=\frac{4}{4}:

514=4545\frac{1}{4}=4\frac{5}{4}

Now subtract the fractional parts and whole-number parts:

454−234=(4−2)+(54−34)4\frac{5}{4}-2\frac{3}{4} =(4-2)+\left(\frac{5}{4}-\frac{3}{4}\right) =2+24=2+\frac{2}{4}

Simplify 24\frac{2}{4}:

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

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

Learn by doing: Subtract mixed numbers with regrouping

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

    Practice with unlimited practice problems

    Fraction Subtraction - Mixed (Simplifying Answers) - No Changed Denominator

      ?