Convert Between Improper Fractions and Mixed Numbers

A mixed number has a fraction and a whole number.
An improper fraction has a numerator that is equal or greater than the denominator. It can be represented via a mixed number.

Step by step to convert an improper fraction to a mixed number:

Step 1: Divide the numerator by its denominator. The result is the whole number, and whatever remains is the new fraction’s numerator.
Step 2: The denominator of the new fraction is the same number as the original denominator.
Step 3: If there is no remainder, there is no fraction, so the resulting number is a whole number.

Convert Between Improper Fractions and Mixed Numbers – Examples 1

Write \(4 \frac{3}{4}\) as an improper fraction.
Solutions:
Step 1: Multiply the whole number in the denominator. \(4×4\)
Step 2: Add the result to the numerator and write it in the numerator. 16+3
Step 3: The denominator is the same as the mixed number. 4
\(4 \frac{3}{4}=\frac{(4×4)+3}{4}=\frac{19}{4}\)

Convert Between Improper Fractions and Mixed Numbers – Examples 2

Write \(\frac{63}{8}\) as a mixed fraction.
Step 1: Divide the numerator by the denominator. \(61÷8\)
Step 2: The whole number is 7.
Step 3: The rest is the new fraction’s numerator, 5.
\(\frac{61}{8}=\frac{(8×7)+5}{8}=7 \frac{5}{8}\)