# Simplifying Fractions Calculator

## Calculator Use

Convert improper fractions to mixed numbers in simplest form. This calculator also simplifies proper fractions by reducing to lowest terms and showing the work involved.

## What is an Improper Fraction?

An improper fraction is any fraction where the numerator is greater than the denominator. Examples of improper fractions are 16/3, 81/9, 525/71.

## How to Convert an Improper Fraction to a Mixed Number

- Divide the numerator by the denominator
- Write down the whole number result
- Use the remainder as the new numerator over the denominator. This is the fraction part of the mixed number.

Example: Convert the improper fraction 16/3 to a mixed number.

- Divide 16 by 3: 16 ÷ 3 = 5 with remainder of 1
- The whole number result is 5
- The remainder is 1. With 1 as the numerator and 3 as the denominator, the fraction part of the mixed number is 1/3.
- The mixed number is 5 1/3. So 16/3 = 5 1/3.

When possible this calculator first reduces an improper fraction to lowest terms before finding the mixed number form.

Example: Convert the improper fraction 45/10 to a mixed number.

- This calculator reduces the improper fraction to lowest terms by dividing numerator and denominator by the greatest common factor (GCF). The GCF of 45 and 10 is 5.
- \( \dfrac{45\div5}{10\div5} = \dfrac{9}{2}\)
- Use this reduced improper fraction and divide 9 by 2: 9 ÷ 2 = 4 with remainder of 2
- The whole number result is 4
- The remainder is 1. With 1 as the numerator and 2 as the reduced denominator, the fraction part of the mixed number is 1/2.
- The mixed number 4 1/2. So 45/10 = 4 1/2.

### Related Calculators

For additional explanation of factoring numbers to find the greatest common factor (GCF) see the Greatest Common Factor Calculator.

If your improper fraction numbers are large you can use the Long Division with Remainders Calculator to find whole number and remainder values when simplifying fractions by hand.

To perform math operations on fractions before you simplify them try our Fractions Calculator. This calculator will also simplify improper fractions into mixed numbers.

### Notes

This calculator performs the reducing calculation faster than other calculators you might find. The primary reason is that it utilizes Euclid's Algorithm for reducing fractions, as shown on The Math Forum.

**Cite this content, page or calculator as:**

Furey, Edward "Simplifying Fractions Calculator"; from *http://www.calculatorsoup.com* - Online Calculator Resource.