Fraction arithmetic
Add, Subtract, Multiply, or Divide Fractions
Accepted formats: 2/7, -3/4, 1 2/3, or 0.25.
37/56
Mixed37/56
Decimal0.660714285714
Fraction arithmetic and conversion
Fraction Calculator
Add, subtract, multiply, divide, simplify, and convert fractions with exact arithmetic, visible steps, mixed number output, and decimal equivalents.
Method preview
Common denominator first
For addition and subtraction, the calculator rewrites fractions with a common denominator, combines numerators, then simplifies.
Available fraction tools
Choose the Fraction Task You Need
Each calculator below is visible on the page, so you can solve the exact task without switching tabs.
Mixed numbers
Mixed Number Calculator
27/28
Mixed27/28
Decimal0.964285714286
Simplify
Simplify Fractions Calculator
3/7
Mixed3/7
Decimal0.428571428571
Conversion
Decimal to Fraction Calculator
11/8
Mixed1 3/8
Decimal1.375
Conversion
Fraction to Decimal Calculator
2/7
Mixed2/7
Decimal0.285714285714
Method
How This Fraction Calculator Works
The calculator converts each entered value into an exact numerator and denominator, performs the requested arithmetic with integer values, and reduces the result using the greatest common divisor.
For addition and subtraction, it uses a common denominator. For multiplication, it multiplies numerators and denominators. For division, it multiplies by the reciprocal of the second fraction.
Input guidance
Supported Fraction Formats
You can enter simple fractions such as 3/4, improper fractions such as 11/8, mixed numbers such as 1 3/8, negative mixed numbers such as -2 1/2, and finite decimals such as 0.125.
Denominators cannot be zero. If an input is invalid, the result panel explains what needs to be fixed instead of returning a misleading number.
Formulas
Common Fraction Formulas
These formulas show the arithmetic used behind the result.
a/b + c/d
(ad + bc) / bd, then simplify.
a/b - c/d
(ad - bc) / bd, then simplify.
a/b × c/d
(ac) / (bd), then simplify.
a/b ÷ c/d
(ad) / (bc), then simplify.
Examples
Practical Fraction Examples
Fraction calculators are most useful when the result needs to stay exact, not rounded.
Cooking and recipe scaling
Add or multiply fractions such as 1/2 cup and 3/4 cup while keeping the answer in a kitchen-friendly format.
Homework and study checks
Review each step after adding, subtracting, multiplying, or dividing fractions so the arithmetic is easier to audit.
Measurements and shop math
Convert fractions to decimals for rulers, materials, and measurement comparisons, then keep the simplified fraction when needed.
Precision
Exact Fractions vs. Rounded Decimals
A simplified fraction is often the most exact answer because it keeps the numerator and denominator. Decimal output is useful for comparison, but repeating decimals must be shortened for display.
For example, 1/3 is exact as a fraction. Its decimal form is shown as a rounded repeating decimal, so it should not replace the exact fraction when precision matters.
Check before relying on a result
- Make sure negative signs are entered correctly.
- Use a space for mixed numbers, such as 2 1/3.
- Confirm the selected operation.
- Use the fraction result when exactness matters.
Related tools
Related Calculators
Use these tools when your math problem moves beyond fractions.
FAQ
Fraction Calculator FAQ
How do I add fractions with different denominators?
Find a common denominator, rewrite each fraction with that denominator, add the numerators, then simplify the result. For two fractions, a/b + c/d = (ad + bc) / bd before simplification.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. For example, 18/24 simplifies to 3/4 because both numbers can be divided by 6.
Can this calculator handle mixed numbers?
Yes. You can enter mixed numbers such as 2 3/4 or -1 1/2. The calculator converts them to improper fractions for the calculation and can show the final answer as a mixed number.
How do I convert a decimal to a fraction?
Count the digits after the decimal point, place the number over the matching power of 10, then simplify. For example, 0.375 becomes 375/1000, which simplifies to 3/8.
Why is the denominator not allowed to be zero?
A fraction represents division by its denominator. Division by zero is undefined, so any fraction with a denominator of zero is invalid.
Does the calculator round fraction results?
Fraction arithmetic is calculated exactly with integer numerator and denominator values. Decimal equivalents are rounded for display, while the simplified fraction remains the main exact result.
Disclaimer
This calculator is for general informational purposes and simple arithmetic checks. Verify important academic, engineering, financial, or professional calculations with an appropriate source or qualified professional.