Calculators / Fractions
Fraction math calculator with exact steps
Enter a fraction, mixed number, decimal or whole number, such as -1 1/2 or 0.125, and this fraction math calculator adds, subtracts, multiplies, divides or simplifies it in your browser, showing the exact simplified result, the mixed number, a decimal and every calculation step.
Result
Enter your numbers, choose an operation, then select Calculate.
How to use the fraction calculator
Type a number in First number: a whole number such as 7, a fraction such as -3/4, a mixed number such as -1 1/2, or a decimal such as 0.125. Use a space between the whole and fractional parts of a mixed number, and leave out commas.
Under Operation, choose Add (+), Subtract (−), Multiply (×), Divide (÷) or Simplify. Simplify uses only First number; the other four also need Second number in the same accepted formats. Decimal places sets how many digits the Decimal line rounds to, from 0 for a whole number to as many digits as you need; the exact fraction result never changes.
Select Calculate to see the simplified result, the mixed number, the decimal and the numbered Calculation steps. Reset returns every field to the starting example, -1 1/2 + 2/3, so you can compare a new calculation against it.
How each operation works
Every calculation starts by turning each entry into a fraction. -1 1/2 becomes -3/2, working out to -(1 × 2 + 1)/2. Add and Subtract find a common denominator: for -3/2 and 2/3, the least common denominator is 6, giving -9/6 and 4/6. Adding gives -5/6; subtracting gives -13/6, shown as the mixed number -2 1/6.
Multiply multiplies numerators and denominators directly: -3/2 × 2/3 becomes -6/6, which reduces to -1. Divide multiplies by the reciprocal of the second number instead: -3/2 ÷ 2/3 becomes -3/2 × 3/2, which is -9/4, or -2 1/4 as a mixed number.
Simplify applies the same reduction to one fraction, decimal or mixed number with no second value, so 4/6 simplifies to 2/3. Every result is reduced by its greatest common divisor before it is shown, and each step of the working appears in the Calculation steps list, from parsing the inputs to the final reduction.
Limits
There is no expression parser, so it cannot evaluate something like 1/2 + 1/3 × 2 in one field; enter the two numbers and pick the one operation you need. Leaving Second number blank for Add, Subtract, Multiply or Divide reports an empty-field error rather than treating it as zero.
A fraction's denominator cannot be zero, and Divide needs a nonzero second number; both show an error beside the affected field instead of a wrong result. Repeating-decimal notation, thousands separators, scientific notation and expressions are not accepted.
Decimal places must be a nonnegative whole number; it only changes the rounded decimal display, and the exact fraction and mixed number are unaffected. Because the arithmetic uses whole-number math rather than floating point, there is no size cap on an entered value beyond what your browser's memory and processing time allow. If a calculation takes too long, Cancel stops it.
Questions
Is there a calculator that simplifies fractions?
Yes. Choose Simplify under Operation and enter one value in First number; Second number is not used. Selecting Calculate reduces the fraction by its greatest common divisor, so 4/6 becomes 2/3 and 0.125 becomes 1/8. The result panel also shows the mixed number and a decimal.
Can I use whole numbers in this fraction calculator?
Yes. Type a plain whole number such as 7 in either field, alongside a fraction, mixed number or decimal in the other. The calculator reads 7 as 7/1 and applies the chosen operation the same way, so 7 divided by 2/3 gives 21/2, or 10 1/2.
How do I enter a negative mixed number?
Write -1 1/2 for negative one and one half, which the calculator reads as -3/2. The whole number and the fraction combine before any arithmetic runs, so -1 1/2 and -3/2 give the same result in every operation. To enter an improper fraction instead, type 7/3 directly.
Can the denominator be negative?
Yes, in a plain fraction: 1/-2 simplifies to -1/2, and -1/-2 simplifies to 1/2, because the calculator moves the sign to the numerator. A mixed number always uses a positive denominator and one leading sign, such as -1 1/2, not a negative denominator.
Why is the decimal rounded when the fraction is exact?
Some fractions, such as 1/3, have a decimal that never ends. The exact result stays 1/3 while the Decimal line rounds to the Decimal places you set, with ties away from zero. At zero places, 1/2 rounds to 1 and -1/2 rounds to -1.
What does the text download include?
The downloaded fraction-calculation.txt lists the operation, the entered numbers, the exact simplified result, the mixed number, the decimal with its precision label, and every calculation step. Copy result copies only the exact simplified fraction, not the mixed number or the decimal.