How to use this fraction calculator
- Type the first two fractions. Each one has a Whole box, a numerator (top) and a denominator (bottom).
- Choose +, −, × or ÷ between them.
- Press Add fraction to include up to five fractions, and the × next to a fraction to remove it.
- The answer updates as you type: a simplified fraction, a mixed number, a decimal and a percentage, with every step of the working.
All the maths is done with exact whole numbers, however large, so answers are never rounded. Nothing you type is saved.
What is a fraction?
A fraction describes part of a whole. The denominator (the bottom number) says how many equal parts the whole is split into, and the numerator (the top number) says how many of those parts you have. In 3/4, the whole is cut into 4 equal parts and you have 3 of them. The denominator can never be 0, because you can’t split something into zero parts: division by zero has no answer.
How to add and subtract fractions
You can only add or subtract fractions when they have the same denominator, so the first job is to find a common denominator. The smallest one, the least common denominator (LCD), is the least common multiple (LCM) of the denominators, and using it keeps the numbers small.
Worked example: 1/2 + 1/3. The LCM of 2 and 3 is 6. Rewrite each fraction over 6: 1/2 = 3/6 and 1/3 = 2/6. Now add the numerators and keep the denominator: 3/6 + 2/6 = 5/6.
Subtraction works the same way: 3/4 − 5/6 = 9/12 − 10/12 = −1/12.
How to multiply fractions
Multiplying is the easiest operation: multiply the numerators together and the denominators together, with no common denominator needed. Then simplify.
a/b × c/d = (a × c) / (b × d)
For 2/3 × 9/4: (2 × 9)/(3 × 4) = 18/12. The GCF of 18 and 12 is 6, so the answer is 3/2, or 1 1/2 as a mixed number.
How to divide fractions
To divide by a fraction, multiply by its reciprocal, the same fraction flipped upside down. A popular way to remember it is “keep, change, flip”: keep the first fraction, change ÷ to ×, and flip the second.
a/b ÷ c/d = a/b × d/c
For 3/4 ÷ 3/8: 3/4 × 8/3 = 24/12 = 2. That makes sense, because 3/8 fits into 3/4 exactly twice. Dividing by a fraction equal to 0 is impossible, because 0 has no reciprocal.
Whole numbers, mixed numbers and negative fractions
Before calculating, every number is written as an improper fraction. A whole number goes over 1 (2 = 2/1). A mixed number becomes (whole × denominator + numerator)/denominator, so 1 1/2 = 3/2 and 2 2/3 = 8/3. Then, for example, 1 1/2 + 2 2/3 = 9/6 + 16/6 = 25/6 = 4 1/6.
Negative fractions follow the usual sign rules: a negative times a positive is negative, so −1/2 × 4/5 = −4/10 = −2/5. A minus sign on the top or the bottom means the same thing, and the answer always shows it in front.
Calculating with 3 or more fractions
With more than two fractions, the calculator uses the standard order of operations: multiplication and division first, working from left to right, then addition and subtraction, also from left to right.
Worked example: 1/2 + 1/3 × 3/4. The multiplication comes first: 1/3 × 3/4 = 3/12 = 1/4. Then add: 1/2 + 1/4 = 2/4 + 1/4 = 3/4. Working strictly from left to right would give a different, wrong answer (5/8).
When the order of operations changes the order of the working, the calculator shows a note, and the steps list each operation in the order it was done.
Common mistakes
- Adding the denominators. 1/2 + 1/3 is not 2/5. Only the numerators are added, once the denominators match.
- Finding a common denominator when multiplying. It isn’t wrong, but it isn’t needed: just multiply across.
- Flipping the wrong fraction. When dividing, flip only the fraction you are dividing by.
- Forgetting to simplify. 18/12 is correct but not finished. Divide the top and bottom by their GCF to get 3/2.
- Converting to decimals too early. 1/3 as 0.33 loses precision. Keep fractions exact until the end.
Frequently asked questions
How do you add fractions with different denominators?
Rewrite both fractions over a common denominator, ideally the least common denominator (the LCM of the denominators), then add the numerators. For 1/2 + 1/3 the LCD is 6, so 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
How do you multiply fractions?
Multiply the numerators together and the denominators together, then simplify. For example, 2/3 × 9/4 = 18/12 = 3/2 = 1 1/2. No common denominator is needed.
How do you divide fractions?
Multiply the first fraction by the reciprocal of the second (flip the second fraction upside down). For example, 3/4 ÷ 3/8 = 3/4 × 8/3 = 24/12 = 2.
Can I calculate with 3 or more fractions?
Yes. Use “Add fraction” for up to 5 fractions. The calculator follows the order of operations: multiplication and division are done first, from left to right, then addition and subtraction. So 1/2 + 1/3 × 3/4 = 1/2 + 1/4 = 3/4.
How do I enter whole numbers, mixed numbers and negative fractions?
Each fraction has an optional Whole box. Type just a whole number for 2, a numerator and denominator for 3/4, or all three for 1 1/2. For a negative number, type a minus sign in the Whole box of a mixed number, or on the numerator of a fraction.
Why is my answer not 0.999… when I add 1/3 three times?
Because the calculator works with exact fractions, not rounded decimals. 1/3 + 1/3 + 1/3 = 3/3, which is exactly 1. Converting to decimals first would give 0.333… three times, which is why rounded decimals can drift.