Fraction Calculator
Simplify a fraction or add, subtract, multiply and divide two fractions, with decimal output, the GCF method and worked examples such as 1/2 + 1/3 = 5/6.
Results
Simplified
- Decimal
- 0.50
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Educational estimates · not financial advice · free, no signup
Formula / how it works
Simplify: divide numerator and denominator by their GCF. Add/subtract: a/b ± c/d = (ad ± cb) ÷ bd. Multiply: ac ÷ bd. Divide: multiply by the reciprocal, (a/b) ÷ (c/d) = ad ÷ bc.
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
A fraction describes a part of a whole, written as a numerator over a denominator. Working with fractions involves a few rules: reduce to lowest terms, use a common denominator to add or subtract, multiply across, and divide by multiplying by the reciprocal. This calculator performs those operations and returns the simplified result along with its decimal value. Choose an operation, enter one or two fractions and read the answer in lowest terms. The first fraction can also be simplified on its own. The denominator can never be zero, and dividing by a fraction with a zero numerator is undefined. Fractions are exact, whereas decimals can be rounded, so they are often better for step-by-step algebra.
When to use / who it helps
- You are checking homework on fractions.
- You need to scale a recipe.
- You are adding measurements in carpentry or sewing.
- You want to reduce a fraction to lowest terms.
- You want the decimal value of a fraction.
How to use
Steps
- Enter the numerator and denominator of the first fraction.
- Choose simplify, add, subtract, multiply or divide.
- For two-fraction operations, enter the second fraction.
- Read the simplified fraction.
- Read the decimal value.
- Check the result by hand with a common denominator.
How to interpret results
- A simplified fraction has a GCF of 1 between numerator and denominator.
- Improper fractions have a numerator larger than the denominator.
- The decimal is a rounded form of the exact fraction.
- Division flips the second fraction.
- A zero denominator is invalid.
Common mistakes & gotchas
- Adding numerators and denominators separately.
- Forgetting to flip the second fraction when dividing.
- Leaving the answer unsimplified.
- Using a zero denominator.
- Confusing the decimal approximation with the exact value.
Worked example
Worked example — 2/4 and 1/2 + 1/3
- Simplify 2/4: the GCF of 2 and 4 is 2, so 2/4 = 1/2, which is 0.50.
- Add 1/2 + 1/3: the common denominator is 6, so 3/6 + 2/6 = 5/6.
- Subtract 3/4 − 1/6: 9/12 − 2/12 = 7/12.
- Divide 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2.
Result: 2/4 simplifies to 1/2 (0.50), and 1/2 + 1/3 equals 5/6.
To load the form's own demo values, tap Try example above the Calculate button.
How to calculate / formula
Simplify: divide numerator and denominator by their GCF. Add/subtract: a/b ± c/d = (ad ± cb) ÷ bd. Multiply: ac ÷ bd. Divide: multiply by the reciprocal, (a/b) ÷ (c/d) = ad ÷ bc.
Frequently asked questions
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common factor.
How do I add fractions with different denominators?
Convert them to a common denominator, then add the numerators.
How do I divide fractions?
Multiply by the reciprocal of the second fraction.
What is an improper fraction?
One whose numerator is greater than or equal to its denominator.
Why can't the denominator be zero?
Division by zero is undefined.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator.