Using the calculator
Type two fractions with + − × or ÷ between them, like 1/4 + 1/6. Mixed numbers go in with a space, as in 2 3/4, and a whole number on its own is fine too. The answer is always simplified. On a keyboard without × or ÷, x and the words divided by work instead; a / always means a fraction.
Show the steps explains the working line by line, with fraction bars underneath: one bar for each fraction and one for the answer, all the same length, so you can see how they compare. Answer as switches between a mixed number such as 1 3/4, an improper fraction such as 7/4, and a decimal.
Type a single fraction, like 18/24, to simplify it. Put one sum on each line to do several at once.
Adding and subtracting fractions
Fractions can only be added when they're cut into the same size of piece. A quarter and a sixth are different sizes, so first find a number both bottoms go into. For 4 and 6, the smallest is 12.
Rewrite each fraction in twelfths. 1/4 becomes 3/12, because 4 × 3 is 12 and the top gets multiplied by 3 as well. 1/6 becomes 2/12. Now the pieces match, so add the tops and keep the bottom: 3/12 + 2/12 = 5/12. Subtraction works the same way, taking the tops away instead.
Multiplying and dividing fractions
Multiplying is the easy one. Multiply the tops together and the bottoms together: 2/3 × 3/4 = 6/12, which simplifies to 1/2. There's no need to match the bottoms first.
To divide, turn the second fraction upside down and multiply instead. 1/2 ÷ 1/4 becomes 1/2 × 4/1, which is 4/2, or 2. It makes sense when you ask the question the division is asking: how many quarters fit into a half? Two.
Simplifying and mixed numbers
A fraction is in its simplest form when no number bigger than 1 divides both the top and the bottom. To get there, divide both by the biggest number that goes into each. 18/24 divides by 6 on both, giving 3/4.
When the top is bigger than the bottom, the fraction is more than a whole. 7/4 is seven quarters, and four of them make a whole, so it's 1 whole and 3 quarters left over: 1 3/4. To go back, multiply the whole number by the bottom and add the top: 1 × 4 + 3 = 7, over 4.
Why top and bottom have the names they do
The bottom number is the denominator, from the Latin for a namer. It names the size of the piece: quarters, sixths, twelfths. The top is the numerator, the counter, which counts how many of those pieces there are. So 3/4 reads as three of the pieces called quarters, which is why only fractions with the same name can be added straight away.
Questions
How do I type a mixed number?
Leave a space between the whole number and the fraction: 2 3/4 is two and three quarters.
How do I divide fractions here?
Use ÷, or type divided by, as in 3/4 divided by 1/2. A / is always read as the line in a fraction.
Can I use negative fractions?
Yes. Put a minus sign in front, as in -1/2. A bar for a negative answer is marked below 0.
What's the lowest common denominator?
The smallest number that all the bottoms go into. It keeps the numbers small when adding, though any shared bottom gives the same answer once it's simplified.