Leave the whole number empty for a simple fraction. For a negative mixed number, put the minus sign on the whole number.
Steps
- Common denominator: LCD(2, 3) = 6, so 3/2 = 9/6 and 2/3 = 4/6.
- Add the numerators: 9 + 4 = 13, giving 13/6.
- 13/6 is already in lowest terms (GCD = 1).
- As a mixed number: 13 ÷ 6 = 2 remainder 1, so 2 1/6.
How to use the Fraction Calculator
- 1Enter the first fraction: an optional whole number for a mixed number, then the numerator (top) and denominator (bottom).
- 2Choose the operation: add, subtract, multiply or divide.
- 3Enter the second fraction the same way. Leave the whole number empty for a simple fraction.
- 4Read the simplified result in the highlighted box, with the mixed number and decimal beside it.
- 5Follow the numbered steps to see how the answer was reached.
How to add and subtract fractions
Fractions can only be added or subtracted when they share a denominator. Find the least common denominator (LCD), which is the smallest number both denominators divide into, rewrite each fraction over it, then add or subtract the numerators and keep the denominator.
For example, 5/6 − 1/4: the LCD of 6 and 4 is 12, so 5/6 becomes 10/12 and 1/4 becomes 3/12. Subtracting gives 7/12, which is already in lowest terms. Mixed numbers are first turned into improper fractions, so 1 1/2 becomes 3/2. Then 1 1/2 + 2/3 = 9/6 + 4/6 = 13/6, or 2 1/6 as a mixed number.
How to multiply and divide fractions
Multiplication needs no common denominator: multiply the numerators together and the denominators together. So 3/4 × 2/5 = 6/20, which simplifies to 3/10.
To divide, flip the second fraction upside down (take its reciprocal) and multiply. So 3/4 ÷ 2/5 becomes 3/4 × 5/2 = 15/8, which is 1 7/8 or 1.875 as a decimal. Dividing by a fraction equal to zero is undefined, and the calculator tells you so instead of returning a misleading number.
Simplifying fractions with the GCD
A fraction is in lowest terms when the numerator and denominator have no common factor other than 1. To simplify, divide both by their greatest common divisor (GCD). For 18/24 the GCD is 6, so the fraction reduces to 3/4. The calculator finds the GCD with Euclid's algorithm, which repeatedly replaces the larger number with the remainder of dividing it by the smaller one.
Negative results are written with the minus sign in front of the whole fraction, such as −5/4 or −1 1/4. For a negative mixed number input, put the minus sign on the whole number: −2 1/3 means −(2 + 1/3), or −7/3.
Fractions, decimals and percentages
Every fraction has a decimal form found by dividing the numerator by the denominator. Some end neatly, like 3/8 = 0.375, while others repeat forever, like 1/3 = 0.333…, so the calculator rounds the decimal to six places. The fraction itself is always exact.
To express a fraction as a percentage, multiply its decimal by 100: 3/8 is 37.5%. The guide on how to calculate percentages covers the next step, such as finding what percent one number is of another.
Learn more
Frequently asked questions
What is a mixed number?
A mixed number combines a whole number and a proper fraction, such as 2 1/6. It means the same as the improper fraction 13/6, because 2 × 6 + 1 = 13. The calculator accepts both forms and shows the result in both.
Why does a zero denominator cause an error?
A denominator says how many equal parts the whole is split into, and splitting into zero parts has no meaning. Mathematically, division by zero is undefined, so any fraction with 0 on the bottom is rejected.
Can I enter decimals in the boxes?
No. Numerators, denominators and whole numbers must be whole numbers so the answer stays exact. Convert a decimal first: 0.25 is 25/100, which simplifies to 1/4. If you need percentages instead, our percentage calculator works with decimals.
How do I enter a whole number on its own?
Type it in the whole number box and leave the numerator and denominator empty. For example, to work out 3 ÷ 3/4, enter 3 as the first value and 3/4 as the second. The answer is 4.
How can I average several fractions?
Convert each fraction to a decimal, then enter the decimals in the average calculator. Alternatively, add them here one pair at a time and divide the total by the count.