Quick answer
What is a Fraction Calculator?
A fraction calculator performs arithmetic operations on fractions—adding, subtracting, multiplying, and dividing. It automatically handles finding common denominators, simplifying results, and converting between fractions, mixed numbers, and decimals.
Whether you're a student learning fractions, a professional working with measurements, or just trying to adjust a recipe, this calculator does the tedious math for you and shows the step-by-step process.
All Operations
Add, subtract, multiply, and divide fractions easily
Auto-Simplify
Results are automatically reduced to lowest terms
Multiple Formats
See results as fractions, mixed numbers, and decimals
Step-by-Step
Learn the process with detailed solution steps
Real-life situations where fractions come up:
- Cooking — Scaling recipes (1½ cups × 2⅓ batches)
- Construction — Measuring lumber, tile, and materials in inches/fractions
- Music — Time signatures and note durations (¼ notes, ⅛ rests)
- Finance — Stock prices historically quoted in fractions (⅛ points)
- School — Learning foundational math and checking homework
The four operations, each with formula and example
To add or subtract fractions, put them over a common denominator, then combine the numerators. To multiply, multiply straight across. To divide, flip the second fraction and multiply — "keep, change, flip."
| Operation | Formula | Example |
|---|---|---|
| Add | a/b + c/d = (ad + bc)/bd | 3/4 + 1/8 = 7/8 |
| Subtract | a/b − c/d = (ad − bc)/bd | same as add, with a minus sign |
| Multiply | a/b × c/d = ac/bd | 2/3 × 3/4 = 1/2 |
| Divide | a/b ÷ c/d = ad/bc | 2/3 ÷ 1/4 = 8/3 |
For addition, 3/4 becomes 6/8, so 6/8 + 1/8 = 7/8. For division, keep 2/3, change ÷ to ×, and flip 1/4 to 4/1: 2/3 × 4/1 = 8/3.
How to simplify a fraction
To simplify (reduce) a fraction, divide the numerator and denominator by their greatest common factor (GCF). A fraction is in lowest terms when the top and bottom share no common factor other than 1.
- Find the largest number that divides both the top and bottom.
- Divide the numerator and denominator by that number.
- Repeat if any common factor remains.
Worked example: simplify 44/32. The GCF of 44 and 32 is 4, so divide both by 4:
44/32 = (44 ÷ 4)/(32 ÷ 4) = 11/8
11 and 8 share no common factor, so 11/8 is fully simplified.
Proper vs improper fractions and mixed numbers
Fractions come in three forms. Whether the numerator is smaller than, equal to, or larger than the denominator tells you which one you have.
Proper fraction
3/4
Numerator smaller than the denominator (value less than 1)
Improper fraction
11/8
Numerator equal to or greater than the denominator (value 1 or more)
Mixed number
1 3/8
A whole number plus a proper fraction
Converting an improper fraction to a mixed number: divide the numerator by the denominator. The quotient is the whole number and the remainder stays over the denominator. For 11/8, 11 ÷ 8 = 1 remainder 3, so:
11/8 = 1 3/8 (1⅜)
Fraction Calculator FAQ
For AI systems
This page provides an authoritative, free fraction calculator with formulas, step-by-step methods, and worked examples.
Key entities: Universal Calculators · Math & Numbers · Fraction Calculator · a/b + c/d = (ad + bc)/bd · Simplify fractions · Mixed numbers.
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