Fraction Calculator
Enter two fractions and choose an operation to get the simplified result, decimal value and mixed number.
Reviewed by the ToolNestr Editorial Team — July 2026
How fraction arithmetic works
To add or subtract fractions, you first find a common denominator — a shared multiple of both bottom numbers. The least common denominator is the LCM of the two denominators. Once both fractions have the same denominator, you add or subtract only the numerators and keep the denominator unchanged.
For multiplication, multiply the numerators together and the denominators together, then simplify using the greatest common divisor (GCD). For division, flip the second fraction (take its reciprocal) and multiply. The result is always reduced to its simplest form by dividing numerator and denominator by their GCD.
Worked example
Add 2/3 and 3/4 using the common denominator method.
Common fraction values you will encounter
These fractions appear most often in everyday situations — from recipes and measurements to schoolwork.
Baker
Scale recipes up or down by adding and multiplying fractions like ⅔ cup of sugar or ¼ teaspoon of salt.
Student
Check fraction homework, practice addition and multiplication, and verify answers before submitting assignments.
Carpenter
Add and subtract fractional measurements like ⅛ inch and ¹⁵⁄₁₆ inch accurately for precise cuts and joins.
Chef
Adjust portion sizes by multiplying or dividing ingredient fractions when changing recipe serving sizes.
| Fraction Type | Definition | Example |
|---|---|---|
| Proper | Numerator is smaller than denominator | ¾ |
| Improper | Numerator is larger than denominator | ⁷⁄₄ |
| Mixed Number | Whole number plus a proper fraction | 1 ¾ |
| Unit Fraction | Numerator is exactly 1 | ⅕ |
| Equivalent | Different fractions that equal the same value | ½ = ²⁄₄ = ⁴⁄₈ |
| Like Fractions | Fractions sharing the same denominator | ⅕, ⅗ |
| Decimal | Fraction expressed as a decimal number | 0.75 |
How to use the fraction calculator
Enter the fractions
Type the numerator and denominator for each of the two fractions you want to work with.
Pick an operation
Choose add (+), subtract (−), multiply (×) or divide (÷) from the dropdown menu between the fractions.
Read the full result
See the simplified fraction, exact decimal value and mixed-number form all displayed at once.
Tips for accuracy
Always check the mixed-number result
Improper fractions like 7/4 are easier to visualise as 1 ¾. The calculator shows this automatically, so use it to build intuition.
Verify denominators are not zero
A zero denominator makes the fraction undefined. The calculator warns you, but always double-check your entries.
Use negative numerators for negative fractions
Enter -3 / 4 to represent negative three-quarters. The calculator correctly places the negative sign in the result.
Why fraction calculation accuracy matters
Real-world precision requirements
Decimal approximations can introduce rounding errors that compound over multiple calculations. A fraction like 1/3 is exactly one third, while its decimal equivalent 0.333333 is only an approximation. When you add 1/3 three times, the fraction gives exactly 1, while the decimal approach yields 0.999999. This tool preserves exact fractional values throughout all operations and only rounds for the decimal display, ensuring that chained calculations remain accurate and free from cumulative error.
Cooking and baking applications
Recipes frequently use fractional measurements such as 1/2 cup, 3/4 teaspoon, and 1/3 tablespoon. Scaling a recipe from 4 servings to 6 requires multiplying each fraction by 1.5. This calculator handles such conversions precisely, whether you are halving a recipe, doubling it, or adapting it for a different number of servings. The mixed-number output is especially helpful here because 2 1/4 cups is more intuitive to measure than 9/4 cups.
Construction and woodworking measurements
Carpenters and builders work with fractional inch measurements constantly: 1/8 inch, 3/16 inch, 5/8 inch. Adding and subtracting these fractions is essential for calculating material lengths, spacing, and joinery offsets. A calculator error of 1/16 inch on a single cut can compound across multiple pieces, potentially ruining a project. This tool's exact fraction arithmetic eliminates that risk by preserving precision throughout every operation.
Education and homework verification
Students learning fraction arithmetic benefit from immediate feedback and multiple representations. Entering 2/3 + 3/5 and seeing 19/15 with its mixed-number equivalent 1 4/15 and decimal 1.266667 provides three complementary views of the same result. This multi-format output helps build intuition about the relationship between fractions, decimals, and mixed numbers while allowing students to verify their manual calculations.
Frequently asked questions
Does it simplify the answer?
Yes. The result is always reduced to its simplest form, and we also show the decimal and mixed-number versions.
Can I use negative fractions?
Yes — put a minus sign in the numerator, e.g. -3 / 4.
How do I divide fractions?
Just pick the ÷ operation. Dividing by a fraction multiplies by its reciprocal, which the calculator handles for you.
What if the denominator is zero?
A denominator of zero is undefined in mathematics. The calculator will show an error message if you try it.
Can I enter improper fractions?
Yes, absolutely — any numerator larger than the denominator is fine. The result will show the mixed-number form automatically.
Is the decimal result rounded?
Yes, the decimal is rounded to 6 decimal places for readability. The underlying fraction is exact.
How do I add fractions with different denominators?
The calculator finds the least common denominator automatically. Just enter both fractions and choose add.
What is a mixed number?
A mixed number combines a whole number and a fraction, like 1 ¾. This calculator converts improper fractions to mixed numbers automatically.
Can I multiply more than two fractions?
Not directly. Multiply two at a time by re-entering the result with your next fraction.
Why is simplifying important?
Simplified fractions are easier to read, compare and use in further calculations. The calculator does this using the greatest common divisor.