Fraction arithmetic with simplification and working shown.
What it's for
Add, subtract, multiply, divide or compare two fractions and get the answer in lowest terms — or turn a decimal into an exact fraction.
Before you start
Have the fractions you are working with, such as 1/2 and 1/3 from a recipe, a measurement or homework, or the decimal you want to convert.
Choose what to do
Pick Two fractions to work with two fractions, or Decimal to fraction to turn a decimal such as 0.375 into a fraction.
Pick the operation
For two fractions, press Add, Subtract, Multiply, Divide or Compare. Compare tells you which of the two is bigger.
Type the fractions
Put the number above the line in Top and the number below it in Bottom. Use Whole only for a mixed number such as 2 1/3, and put any minus sign there, not on top. For a decimal, type it in Decimal.
Press Calculate
Press Calculate. The answer already updates as you type; the button brings it into view. Each step is listed under Working.
Reading the result
If it goes wrong
Add, subtract, multiply, divide and compare fractions, with mixed numbers going in and coming out. Every answer is simplified, and the working shows how it got there.
Internally everything is an improper fraction with the sign on top and the denominator always positive. That one rule removes most of the sign bugs a fraction calculator can have: 1/−2 and −1/2 are the same number, and cross multiplication for comparison stays valid.
Minus two and a third — that is, −7/3. The sign belongs to the whole quantity, not to the fraction part alone. Reading it as −2 plus a third gives −5/3, which is a different number by two thirds, and it is the commonest bug in a fraction calculator. This tool asks you to put the sign on the whole number so there is nothing to misread.
Because it is not one third. 0.3333 is 3333/10000, and that is what the tool gives you. It does show the simplest fraction close to what you typed — a third, in this case — clearly labelled as an approximation. Offering it is useful; substituting it silently would be a lie about what you entered.
By cross multiplication: 3/4 against 5/7 is 3 × 7 = 21 against 5 × 4 = 20, so the first is larger. That shortcut is only valid while both denominators are positive, which is why every fraction is normalised with its sign on the numerator before anything else happens.
Yes, and the tool treats them as the same number. Both are normalised to −1/2 before any arithmetic, so a negative typed in the denominator cannot produce a different answer from the same negative typed on top.
Because past a certain size the products stop being exact in JavaScript arithmetic, and an inexact fraction answer is worse than no answer. The tool refuses rather than handing back a figure that is quietly wrong in the last digits.
then divide through by the greatest common divisor.
Two thirds apart. The tool asks for the sign on the whole number so there is nothing to misread.
Both are shown. The first is what you typed; the second is what you probably meant. Which of those you want is your call, not the calculator's.
Important
Exact arithmetic within the sizes the tool accepts. Decimal conversion is exact on the digits you type — a close fraction is offered alongside, never substituted. Nothing you type here is sent to our servers — the calculation runs entirely in your browser.
