Ctrl+k

Subtract mixed numbers with like denominators

A mixed number represents the sum of a whole number and a fractional part, so subtracting mixed numbers with the same denominator involves finding the difference of quantities partitioned into equal-sized fractional units. When the minuend’s fractional part is smaller, one whole is regrouped as an equivalent fraction containing the denominator’s number of units; the denominator remains unchanged, and the result is expressed as a whole number or mixed number. This understanding supports fraction computation in measurement and later algebraic reasoning.

Detailed Explanation: Subtract mixed numbers with like denominators

To subtract mixed numbers with like denominators:

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

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 regroup one whole from 55.

Since 11 whole equals 44\frac{4}{4}:

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

Now subtract:

454−2344\frac{5}{4}-2\frac{3}{4}

Subtract the fractions:

54−34=24\frac{5}{4}-\frac{3}{4}=\frac{2}{4}

Subtract the whole numbers:

4−2=24-2=2

So,

514−234=2245\frac{1}{4}-2\frac{3}{4}=2\frac{2}{4}

The denominator stays 44 because the fractional pieces are fourths.

Learn by doing: Subtract mixed numbers with like denominators

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 (No Simplifying Answers) - No Changed Denominator

      ?