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
Fraction Formulas With Worked Examples
Each operation on this calculator follows one general rule. The letters a and c are numerators; b and d are denominators. Read the formula first, then follow the numbers underneath it.
- Add: a/b + c/d = (ad + bc) / bd — 2/3 + 1/4 = (2×4 + 3×1) / (3×4) = (8 + 3)/12 = 11/12.
- Subtract: a/b - c/d = (ad - bc) / bd — 3/4 - 1/6 = (3×6 - 4×1) / 24 = (18 - 4)/24 = 14/24 = 7/12.
- Multiply: a/b × c/d = ac / bd — 2/3 × 3/5 = (2×3) / (3×5) = 6/15 = 2/5.
- Divide: a/b ÷ c/d = ad / bc — 3/4 ÷ 2/5 = (3×5) / (4×2) = 15/8 = 1 7/8.
Fraction to Decimal to Percent Table
To turn any fraction into a decimal, divide the top by the bottom. To turn that decimal into a percent, multiply by 100. These are the values that show up most often in homework and everyday math.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.3333… | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 3/4 | 0.75 | 75% |
| 1/16 | 0.0625 | 6.25% |
Inch Fraction Reference for Construction and Woodworking
Tape measures in the US are marked in sixteenths of an inch. When you need the metric equivalent, one inch equals exactly 25.4 mm, so any inch fraction converts by multiplying its decimal value by 25.4.
| Inch fraction | Decimal inch | Millimeters |
|---|---|---|
| 1/16 | 0.0625 | 1.59 mm |
| 1/8 | 0.125 | 3.18 mm |
| 3/16 | 0.1875 | 4.76 mm |
| 1/4 | 0.25 | 6.35 mm |
| 3/8 | 0.375 | 9.53 mm |
| 1/2 | 0.5 | 12.70 mm |
| 5/8 | 0.625 | 15.88 mm |
| 3/4 | 0.75 | 19.05 mm |
| 1 | 1.0 | 25.40 mm |
Adding Mixed Numbers
This calculator takes simple fractions, so convert mixed numbers to improper fractions first. To add 2 1/2 and 1 3/4, rewrite them as 5/2 and 7/4. Give both the same denominator: 5/2 becomes 10/4. Now 10/4 + 7/4 = 17/4, and dividing 17 by 4 gives 4 remainder 1, so the answer is 4 1/4.
LCD Versus GCD
These two numbers get mixed up because both come from the same pair of denominators. Take 12 and 18. The greatest common divisor is 6, which is what you divide by to simplify a fraction like 12/18 down to 2/3. The least common multiple is 36, the smallest number both 12 and 18 divide into, which is the common denominator you need before adding or subtracting. Use the GCD to shrink a fraction and the LCM to line two fractions up.
Common Mistakes to Avoid
- Adding the tops and bottoms straight across. 1/2 + 1/3 is not 2/5; you must find a common denominator first, giving 3/6 + 2/6 = 5/6.
- Losing track of a negative sign. -3/4 equals 3/-4; the minus can sit on the numerator, the denominator, or in front of the whole fraction, but not in two places at once.
- Expecting division to make the result smaller. Dividing by a fraction below 1 multiplies by its reciprocal, so 6 ÷ 1/2 = 12, not 3.
- Leaving a zero in the denominator. A fraction like 5/0 is undefined, so the calculator cannot return a value for it.