# Fraction Calculator

Add, subtract, multiply and divide fractions exactly and see the working. Enter fractions like 3/4, mixed numbers like 1 1/2, decimals like 0.75 or repeating decimals like 0.(3), and the calculator returns the result in lowest terms, as a mixed number and as a decimal rounded to your chosen places. It uses exact arbitrary precision fractions from mathjs, so large numerators never overflow. Ideal for homework, recipes and woodworking measurements.

## Frequently asked questions

### Which formats can I type?

Simple fractions such as 3/4 or -5/8, mixed numbers such as 1 1/2 or -2 3/4, whole numbers, decimals such as 0.75 and scientific notation such as 2.5e-3. Repeating decimals use parentheses, so 0.(3) means 0.333 and so on, which equals 1/3. Each value can be up to 100 characters.

### How are fractions added?

The calculator rewrites both fractions over their least common denominator and adds the numerators. For 3/4 + 5/6 the steps row shows 9/12 + 10/12 = 19/12, and the result is reduced to lowest terms. Subtraction works the same way.

### How are fractions multiplied and divided?

Multiplication multiplies the numerators and the denominators, as in (3 × 5) / (4 × 6) = 15/24, which reduces to 5/8. Division multiplies by the reciprocal of the second fraction, so 3/4 ÷ 5/6 becomes 3/4 × 6/5. The steps row shows the intermediate fraction before reduction.

### Is the result always simplified?

Yes, the result is always given in lowest terms, with the greatest common divisor removed from numerator and denominator. Whole results are shown without a denominator, so 6/3 appears as 2. The sign is always placed in front of the numerator.

### When is a mixed number shown?

Whenever the result is an improper fraction that is not a whole number, such as 19/12, the tool also shows it as a mixed number, 1 7/12. Proper fractions and whole numbers do not need a mixed form. Negative results keep the sign in front, as in -1 1/2.

### How do I enter a negative mixed number?

Put the minus sign in front of the whole part, as in -1 1/2, which means negative one and a half, or -3/2. The sign applies to the whole mixed number. Writing 1 -1/2 is not accepted.

### Why is the decimal sometimes rounded?

Fractions such as 1/3 have decimals that never end, so the decimal row is rounded to the places you choose, 6 by default and up to 15. The fraction result itself is always exact. Use more decimal places when you need a closer decimal value.

### What happens when I divide by zero?

Dividing by a fraction equal to zero is undefined, and the tool shows an error instead of a result. A denominator of zero inside a fraction such as 3/0 is also rejected as an invalid fraction. Zero itself is fine as the first value.

### Can I convert a decimal to a fraction?

Yes, enter the decimal as the first value, choose multiply and enter 1 as the second value. The result row shows the exact fraction, so 0.375 becomes 3/8 and 0.(6) becomes 2/3. Decimals are converted exactly from their digits, not approximated.

### Are there limits on the size of the numbers?

Each input is limited to 100 characters, but the arithmetic itself uses arbitrary precision integers. A result such as 123456789012345678901234567890/7 is kept exactly instead of being rounded. Exponents in scientific notation are limited to 300.

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