Fraction calculator for simplification, equivalence, mixed numbers, and common denominators.
The earlier fraction page only covered a thin simplify-and-multiply case. This version adds the core fraction tasks students search for most: simplify, equivalent fractions, least common denominator, and improper-to-mixed conversion.
Fraction tool
Equivalent fraction and LCD
What this page covers
- Simplifying to lowest terms with the greatest common divisor.
- Creating equivalent fractions by multiplying numerator and denominator by the same factor.
- Converting improper fractions to mixed numbers.
- Finding a least common denominator for addition and subtraction.
A fraction stays equivalent only when you multiply or divide both numerator and denominator by the same nonzero number.
Worked examples
- Simplify 18/24: the GCD is 6, so 18/24 = 3/4.
- Equivalent fraction for 3/4 using factor 2: 6/8.
- Convert 11/4 to a mixed number: 11 divided by 4 is 2 remainder 3, so 2 3/4.
- Find the LCD of 6 and 8: the least common denominator is 24.
- Add 1/6 + 1/8: convert to 4/24 + 3/24 = 7/24.
Common mistakes
- Adding denominators directly when combining fractions.
- Simplifying only the numerator or only the denominator.
- Forgetting to convert mixed numbers before multiplying or dividing.
- Ignoring the sign on negative fractions.
FAQ
What is the difference between simplifying and finding equivalent fractions?
Simplifying moves toward the smallest equivalent form. Finding equivalent fractions creates larger or alternate forms that still represent the same value.
Why does LCD matter?
You need a common denominator before adding or subtracting fractions. The least common denominator keeps the arithmetic cleaner.
Can I use decimals instead?
Sometimes, but fractions are often better when exact values matter. For percent conversions, use the Percent page.
Practice with Examples
Click any example below to automatically fill in the calculator and see the solution.
Study advice and related tools
Write the factor you are using at each step. Students make fewer fraction mistakes when they keep the transformation visible instead of doing it mentally. Related pages: Percent, Algebra, and Fraction Simplifier Examples.