gizmobench

Fraction Calculator

Two boxes and five operations: add, subtract, multiply, divide, or take a fraction of a fraction. Each box accepts a fraction like 3/4, a mixed number like 1 3/4, a whole number like 7 or a decimal like 0.75, and the answer comes back simplified and in every form at once: the improper fraction, the mixed number, the decimal and the percentage. The arithmetic runs on whole number numerators and denominators from start to finish, so 2/3 of 5/8 is 10/24 and then exactly 5/12, never a rounded 0.42, and a decimal that repeats is printed with its period in brackets, so 1/3 is 0.(3) and 1/7 is 0.(142857) instead of a number quietly cut off. The working is printed underneath line by line, the way you would write it on paper. Nothing is uploaded, nothing needs an account, and the only thing kept is your last entry in this browser.

2/3 of 5/85/1210/24 before simplifying · 0.41(6), where the digits in brackets repeat for ever · 41.(6)%
Operation
First
Second
Show

Each box takes a fraction like 3/4, a mixed number like 1 3/4, a whole number like 7 or a decimal like 0.75, and the answer comes back in every form at once. First box: a fraction, like 2/3. Second box: a fraction, like 5/8.

  • Simplifiedreduced from 10/24
    5/12
  • As a mixed numbersmaller than one, so there is no whole part
    5/12
  • As a decimalthe digits in brackets repeat, 1 of them, for ever
    0.41(6)
  • As a percentagethe same value out of a hundred
    41.(6)%

The working

The same steps you would write on paper, and only the ones these two numbers actually needed.

  • 2/3 of 5/8 means 2/3 × 5/8.
  • Multiply across: (2 × 5) over (3 × 8) = 10/24.
  • Divide both by 2: 10/24 = 5/12.

Worked cases

Each one is computed by the same code that answers your own numbers, every time this page loads.

  • Decimal in0.375 as a fraction
    3/8 · 0.375 as a decimal
  • Mixed numbers2 1/4 by 1 1/3
    3 · 36/12 before simplifying, 3 as a decimal
  • Whole number5/8 of 24
    15 · 120/8 before simplifying, 15 as a decimal
Exact rational arithmetic, then the conversions. Exact fraction arithmetic with no rounding: the result is simplified, shown as an improper fraction, a mixed number and a decimal, and a repeating decimal is marked with its period. It cannot know the form your teacher wants the answer in. The numerator and the denominator stay whole numbers from start to finish, the answer is reduced once by the greatest common divisor, and where a decimal is too long for the page it is cut short rather than rounded, so every digit on screen is a real digit of the value at that place.

Common questions

What does a fraction of a fraction mean?
It means multiply. Two thirds of five eighths is 2/3 × 5/8, and the word "of" and the multiplication sign do exactly the same job on this page. Multiply the top numbers together and the bottom numbers together: (2 × 5) over (3 × 8) is 10/24, which reduces by 2 to 5/12, or 0.41(6) as a decimal. The bracketed 6 repeats for ever. The tool prints those three lines as the working, so the answer can be checked rather than trusted.
How do I enter a mixed number?
Write the whole part, a space, then the fraction: 1 3/4. The tool converts it to 7/4 and says so as the first line of the working, because that is the step every mixed number calculation starts with. A minus sign applies to the whole quantity, so -1 3/4 is -7/4 rather than -1 plus three quarters. If you paste a fraction glyph from a document, 1½ is read the same as 1 1/2. Answers come back as an improper fraction and as a mixed number together, so 7/2 and 3 1/2 are both on screen.
Why does the decimal repeat?
Because of what the denominator is made of. Once a fraction is in its lowest terms its decimal stops only if the denominator is built from twos and fives, the two numbers that divide ten. So 1/8 is 0.125 and stops, while 1/3 is 0.(3), 1/6 is 0.1(6) and 1/7 is 0.(142857), each repeating for ever. The digits inside the brackets are the part that repeats, and the tool finds them by long division rather than assuming them: it watches for a remainder it has seen before, which is the moment the pattern starts over.
Does this calculator round?
No. Numerators and denominators are whole numbers throughout, of any size, so nothing is lost on the way to the answer: 0.1 + 0.2 is exactly 3/10 here, where a calculator that works in decimals the way a computer stores them gets 0.30000000000000004 and has to decide what to do with the stray 4 on the end. The decimal is worked out to 240 places and a repeat inside that is shown with its period, which covers every denominator into the low hundreds. In the rare case that a decimal runs past that, it is cut short and marked with an ellipsis, never rounded up, so every digit on screen is a real digit of the value at that place.
How do I convert a decimal to a fraction?
Type the decimal into the first box and leave the second at 0, since adding zero changes nothing and the answer is then the first number itself in every form. 0.375 comes back as 3/8, and 0.2 as 1/5. A repeating decimal can be typed the way this page prints one: 0.(3) is read as 1/3 and 0.41(6) as 5/12, which is the exact value, not the 0.416 approximation a decimal written out by hand would give.
Can it multiply a fraction by a whole number?
Yes. Put the whole number in either box on its own: 5/8 × 24 gives (5 × 24) over (8 × 1), which is 120/8 and reduces to 15. Written as "of" it reads the way the question usually does, five eighths of 24, and gives the same answer. When the result does not land on a whole number you get both forms, so 2/3 × 5 is 10/3 and 3 1/3.

Exact fraction arithmetic with no rounding: the result is simplified, shown as an improper fraction, a mixed number and a decimal, and a repeating decimal is marked with its period. It cannot know the form your teacher wants the answer in.