Mixed Fraction — Definition, Formula & Examples

A mixed fraction is a number that has both a whole number part and a proper fraction part written together, such as

2\tfrac{3}{4}

. It represents a value greater than 1.

A mixed fraction (also called a mixed number) is expressed in the form $a\tfrac{b}{c}$ , where $a$ is a nonzero integer, $\tfrac{b}{c}$ is a proper fraction with $0 < b < c$ , and the value equals $a + \tfrac{b}{c}$ .

Key Formula

a\tfrac{b}{c} = \frac{a \times c + b}{c}

Where:

$a$ = The whole number part
$b$ = The numerator of the fraction part
$c$ = The denominator of the fraction part

How It Works

When you have more parts than make one whole, you can write the amount as a mixed fraction. For example, if you eat 7 quarter-slices of pizza and each pizza has 4 slices, you ate

1\tfrac{3}{4}

pizzas — one whole pizza plus 3 extra quarters. To convert a mixed fraction to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. To go the other way, divide the numerator of an improper fraction by the denominator — the quotient is the whole number and the remainder is the new numerator.

Worked Example

Problem: Convert the mixed fraction

3\tfrac{2}{5}

to an improper fraction.

Multiply whole number by denominator: Multiply 3 by 5.

3 \times 5 = 15

Add the numerator: Add the fraction's numerator, 2, to the result.

15 + 2 = 17

Write over the original denominator: Place 17 over 5.

3\tfrac{2}{5} = \frac{17}{5}

Answer:

3\tfrac{2}{5} = \dfrac{17}{5}

Why It Matters

Mixed fractions appear in everyday measurements — recipes call for

1\tfrac{1}{2}

cups of flour, and rulers mark lengths like

5\tfrac{3}{8}

inches. Comfort with mixed fractions also prepares you for fraction arithmetic in pre-algebra, where converting between mixed and improper forms is a routine step.

Common Mistakes

Mistake: Forgetting to add the numerator when converting to an improper fraction (writing

3\tfrac{2}{5}

\tfrac{15}{5}

instead of

\tfrac{17}{5}

Correction: After multiplying the whole number by the denominator, you must add the original numerator before placing everything over the denominator.