Mixed Number to Fraction Converter

What is a Mixed Number?

A mixed number (or mixed fraction) is a combination of a whole number and a proper fraction. For example, $3 \frac{2}{5}$ is a mixed number where $3$ is the whole number and $\frac{2}{5}$ is the proper fraction. It represents a value that is greater than 3 but less than 4.

What is an Improper Fraction?

An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). For example, $\frac{17}{5}$ is an improper fraction because 17 is larger than 5.

How to Convert a Mixed Number to an Improper Fraction

To convert any mixed number to an improper fraction, follow these three simple steps:

1. Multiply: Multiply the whole number by the denominator of the fraction part.
2. Add: Add the numerator of the fraction to the product from step 1. This sum becomes the new numerator of the improper fraction.
3. Write: Write the sum over the original denominator.

Mathematically, the formula is expressed as: $$a \frac{b}{c} = \frac{(a \cdot c) + b}{c}$$

Example Conversion

Let's convert $3 \frac{2}{5}$ to an improper fraction:

1. Multiply the whole number $3$ by the denominator $5$: $3 \cdot 5 = 15$.
2. Add the numerator $2$: $15 + 2 = 17$.
3. Write the result over the original denominator: $\frac{17}{5}$.

If you need to perform the reverse conversion, you can use our Fraction to Mixed Number Converter.