To change an improper fraction into a mixed number, divide the numerator by the denominator and use the resulting quotient, remainder and divisor as the whole numeral, numerator and denominator, respectively. The mixed number makes clear how many complete wholes and fractional parts are present.
Consider the improper fraction 14/3 as an example. Dividing the numerator by the denominator means dividing 14 by three. Since three divides into 14 entirely a maximum of four times, the whole numeral part of the mixed number is 4.
The remainder left after completing the division is two, so the numerator in the fractional part of the mixed number is two. Since the number by which everything is divided is three, the denominator in the fractional part of the mixed number is three.
When the whole numeral and two fractional parts are combined, the resulting mixed number is 4 2/3. This reveals that the improper fraction 14/3 is comprised of four complete wholes and two-thirds of a whole. Notice that the denominator remained the same throughout the entire process.
To change the mixed number back into an improper fraction, multiply the whole numeral by the denominator, which equals 12 in this example. Add this product to the current numerator. The resulting sum returns a new numerator of 14. The denominator again remains the same, so the improper fraction is 14/3, as expected.