Calculator Fraction Button

Fraction Simplifier and Mixed Number Converter

Use this calculator to simplify any fraction to its lowest terms and convert improper fractions into mixed numbers. Understanding fractions in their simplest form and as mixed numbers is crucial for various mathematical operations and real-world applications.

What is a Fraction?

A fraction represents a part of a whole. It consists of two numbers: a numerator (the top number) and a denominator (the bottom number). The numerator tells you how many parts you have, and the denominator tells you how many equal parts make up the whole.

For example, in the fraction 3⁄4, the numerator is 3, and the denominator is 4. This means you have 3 parts out of a total of 4 equal parts.

Why Simplify Fractions?

Simplifying a fraction means reducing it to its lowest terms. A fraction is in its simplest form when its numerator and denominator have no common factors other than 1. Simplifying fractions makes them easier to understand, compare, and work with in calculations.

To simplify a fraction, you find the greatest common divisor (GCD) of the numerator and the denominator, and then divide both by the GCD. For instance, if you have the fraction 12⁄18:

  • The factors of 12 are 1, 2, 3, 4, 6, 12.
  • The factors of 18 are 1, 2, 3, 6, 9, 18.
  • The greatest common divisor (GCD) of 12 and 18 is 6.
  • Divide both the numerator and denominator by 6: 12 ÷ 6⁄18 ÷ 6 = 2⁄3.

So, 12⁄18 simplified is 2⁄3.

Converting Improper Fractions to Mixed Numbers

An improper fraction is a fraction where the numerator is greater than or equal to the denominator (e.g., 7⁄3). A mixed number combines a whole number and a proper fraction (e.g., 2 1⁄3).

Converting an improper fraction to a mixed number can make it easier to visualize and understand the quantity it represents. Here's how to do it:

  1. Divide the numerator by the denominator. The whole number part of the result becomes the whole number of the mixed number.
  2. The remainder of the division becomes the new numerator of the fractional part.
  3. The denominator stays the same.

Let's take the improper fraction 7⁄3:

  • Divide 7 by 3: 7 ÷ 3 = 2 with a remainder of 1.
  • The whole number is 2.
  • The remainder is 1, so the new numerator is 1.
  • The denominator remains 3.

Thus, 7⁄3 as a mixed number is 2 1⁄3.

How to Use This Calculator

Simply enter the numerator and denominator of your fraction into the respective fields. Click the "Calculate Fraction" button, and the calculator will instantly provide the simplified form of your fraction and, if applicable, its mixed number equivalent.

Example 1: Simplifying a Proper Fraction
Input: Numerator = 15, Denominator = 25
Output: Simplified Fraction: 3⁄5

Example 2: Converting an Improper Fraction
Input: Numerator = 10, Denominator = 4
Output: Simplified Fraction: 5⁄2, Mixed Number: 2 1⁄2

Example 3: A Whole Number Result
Input: Numerator = 9, Denominator = 3
Output: Simplified Fraction: 3⁄1, Whole Number: 3

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