Fraction Calculator
Add, subtract, multiply, and divide fractions with step-by-step work.
Step-by-Step Solution
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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This calculator lets you perform arithmetic with fractions and see every step of the solution. Here is how to use it:
- Enter the first fraction. Type the numerator (top number) and denominator (bottom number) on the left side.
- Choose an operation. Select addition (+), subtraction (-), multiplication, or division from the dropdown.
- Enter the second fraction. Type the numerator and denominator on the right side.
- Read the result. The simplified answer appears instantly along with the decimal equivalent, mixed number (if applicable), and a full step-by-step breakdown of the work.
You can also share your calculation by clicking the Share button. The URL updates with your inputs so anyone with the link sees the same problem and answer.
About Fraction Arithmetic
Fractions represent parts of a whole. Each fraction has a numerator (the top number, which counts the parts) and a denominator (the bottom number, which defines the size of each part). Arithmetic with fractions follows specific rules depending on the operation.
For addition and subtraction, fractions must share a common denominator before you can combine the numerators. The calculator finds the least common denominator (LCD) automatically and converts both fractions before combining them. For multiplication, you simply multiply the numerators together and the denominators together. Division works by flipping the second fraction and then multiplying.
After every operation, the result is simplified to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). This ensures you always get the cleanest possible answer.
Frequently Asked Questions
How do you add fractions with different denominators?
First, find the least common denominator (LCD) of both fractions. Convert each fraction so it uses the LCD as its denominator by multiplying both the numerator and denominator by the necessary factor. Then add the numerators and keep the common denominator. For example, 1/2 + 1/3: the LCD is 6, so you get 3/6 + 2/6 = 5/6.
What does it mean to simplify a fraction?
Simplifying a fraction means reducing it to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). For example, 4/8 simplifies to 1/2 because the GCD of 4 and 8 is 4. The value of the fraction does not change, only the representation.
Can I enter negative fractions?
Yes. You can enter negative numbers for any numerator or denominator. The calculator handles negative values correctly and will normalize the sign in the result so the denominator is always positive. For instance, entering 3/(-4) will display as -3/4.
What is a mixed number?
A mixed number combines a whole number with a proper fraction. For example, 7/4 as a mixed number is 1 3/4 (one and three-quarters). The calculator automatically shows the mixed number form whenever the result is an improper fraction, meaning the numerator is larger than the denominator.