Fraction calculator
Plain fractions like 3/4, mixed numbers like 1 1/2, whole numbers like 5, and decimals like 0.75, which is converted to 3/4 before the sum. Answers come back fully reduced, so 2/4 + 2/4 is 1 rather than 4/4.
To add or subtract fractions, put them over a common denominator, combine the numerators, then reduce. To multiply, multiply across the top and the bottom. To divide, flip the second fraction and multiply. Every answer here is reduced by dividing both parts by their greatest common divisor.
How to use it
Reducing is the step people skip and teachers mark down. Adding 1/6 and 1/3 gives 3/6 before reduction and 1/2 after it. Both are the same quantity, but only one is the answer as it is normally written. The greatest common divisor is found here with Euclid’s algorithm, the same method as by hand: divide, take the remainder, repeat until the remainder is zero.
Everything is done in exact whole numbers, never in floating point, and the difference shows up the moment a decimal goes in. A decimal is converted to the fraction it literally is, over a power of ten: 0.75 becomes 75/100 and reduces to 3/4, 0.125 becomes 1/8. A repeating decimal has no such form, so typing 0.3333 for a third gives 3333/10000, which is close to but not the same as 1/3, and every later step carries that difference along. Type 1/3 when you mean a third.
The input is more forgiving than it looks. A whole number is read over one, a mixed number needs a space before the fraction part (1 1/2, not 1-1/2), a leading minus applies to the whole mixed number rather than only its fraction, and a comma is accepted as a decimal point, so 0,75 and 0.75 both give 3/4. The one thing it will not do is chain three fractions in a single go: work left to right, taking the answer from one step into the first box of the next.
What people use it for
- Adding up tape-measure readings written in sixteenths and eighths
- Halving or thirding a recipe that is written in cups and quarters
- Handing in homework reduced to lowest terms rather than left as 6/8
- Reading a fraction as a decimal and a percentage at the same time
- Doing arithmetic on mixed numbers without converting them first
- Turning a decimal measurement back into the nearest usable fraction of an inch
Questions
Yes. A whole number is read as itself over one, so 5 − 1/4 gives 19/4, shown as 4 3/4.
With a space: 1 1/2. A hyphen is not recognised, and 1-1/2 is quietly read as plain 1. The working line under the answer shows how each side was understood, so check it there if a result looks wrong.
A minus sign is carried through and always ends up on the numerator of the answer. On a mixed number it applies to the whole thing, so −1 1/2 is −3/2 rather than −1 + 1/2.
Yes, and it is converted to an exact fraction first. 0.75 becomes 3/4 and 0.125 becomes 1/8. A comma works as the decimal point too.
Because 0.3333 is exactly 3333/10000, and 3333/10000 is what goes in. A repeating decimal has no finite fractional form, so type 1/3 when you mean a third.
Because you are asking how many of the second fraction fit into the first. Three-quarters divided by a half is 1.5, since a half fits into three-quarters one and a half times.
The answer fields show a dash. Dividing by zero has no value, so nothing is invented in its place.
Not in one step. Add the first two, put the answer in the first box, and add the third to it. The result is exact either way, since nothing is rounded between steps.
Yes, every time, by dividing both parts by their greatest common divisor. 2/4 + 2/4 comes back as 1 rather than 4/4.
The answer is the improper fraction, 19/4. The mixed form splits off the whole part, 4 3/4. Both are shown because homework and tape measures want different ones.
Adding fractions multiplies the denominators before reducing. 1/99991 plus 1/99989 is a genuine result over roughly ten billion, and it is exact rather than rounded.
Type them as they are. The common denominator is found for you, so 3/16 + 1/8 comes back as 5/16.
Enter it and add zero, or multiply by one. The decimal row shows six places and the percentage row shows the same value scaled.
Indirectly. Subtract one from the other: a positive answer means the first was larger, and a negative one means it was smaller.
Because an improper fraction is greater than one. 19/4 is 475 per cent, which is correct rather than an error.
It is the right quantity written in a form most marking schemes will not accept. Reduced to lowest terms it is 3/4.
Yes. Put it in the first box, choose add, and put 0 in the second. The answer comes back reduced.
For two-part ratios the arithmetic is the same, but the ratio calculator states the result as 3 : 4 and also splits an amount by shares, which this page does not.
No. The arithmetic runs in this page, on integers, with nothing uploaded.