Fraction Calculator
Enter two fractions and choose an operation to calculate the simplified result.
How to use this fraction calculator
- Enter the first fraction
Type the top number into Numerator 1 and the bottom number into Denominator 1.
- Choose an operation
Select Add, Subtract, Multiply, or Divide from the Operation selector.
- Enter the second fraction
Type the top number into Numerator 2 and the bottom number into Denominator 2.
- Read the simplified result
The calculator returns the answer reduced to its lowest terms as a Simplified fraction.
- Check the decimal equivalent
Review the Decimal result to see the fraction expressed as a standard number.
How this fraction calculator works
This calculator performs one of the four basic operations on two fractions, then simplifies the result by dividing both numerator and denominator by their greatest common divisor. It also shows a decimal equivalent so you can compare the fraction with a standard number-line value.
Addition and subtraction use a common denominator. Multiplication multiplies numerators and denominators. Division multiplies by the reciprocal of the second fraction. 1/2 + 3/4 = 2/4 + 3/4 = 5/4 = 1.25.
2/3 × 3/5 = 6/15 = 2/5 = 0.4.
7/8 − 1/4 = 7/8 − 2/8 = 5/8 = 0.625.
- ✓ Denominators must be non-zero.
- ✓ The result is simplified when possible.
- ✓ Division is undefined if the second fraction equals zero.
- The unsimplified result is useful for checking the arithmetic before reduction.
- Negative fractions are handled naturally by the sign of the numerator or denominator.
- This is useful for school arithmetic, recipes, and ratio work.
- Elementary arithmetic rules for fractions
What are fractions and why simplify them?
A fraction represents a part of a whole by placing a numerator over a denominator. The numerator tells you how many parts you have, and the denominator tells you how many equal parts make up the whole. Simplifying a fraction means dividing both numerator and denominator by their greatest common divisor so the fraction is expressed in the fewest possible terms. For example, 6/8 simplifies to 3/4 because both 6 and 8 are divisible by 2. Simplified fractions are easier to compare, combine, and interpret. They are also the standard expected form in most academic and professional settings, from math class to engineering specifications.
How fraction arithmetic works
Each operation follows specific rules. For addition and subtraction, the fractions must share a common denominator before the numerators can be combined. The calculator finds the least common denominator automatically. For multiplication, the numerators are multiplied together and the denominators are multiplied together — no common denominator is needed. For division, the second fraction is flipped (its numerator and denominator swap places) and then the two fractions are multiplied. These rules ensure that the relative sizes of the parts are handled correctly in every case. Understanding these mechanics helps when working with recipes, ratios, probability, and algebra, where fractions appear frequently and must be combined or compared accurately.
Fraction calculator FAQs
Why do I need a common denominator for addition and subtraction?
Because the fractions must describe equal-sized parts before their numerators can be combined correctly.
What does simplify mean?
It means reducing the fraction to lowest terms by dividing the numerator and denominator by their greatest common divisor.
Why is division done by flipping the second fraction?
Dividing by a fraction is equivalent to multiplying by its reciprocal.