tigtools

Fraction Calculator

Enter two fractions, mixed numbers or decimals and pick an operation to get the simplified answer and every step. Below, convert between decimals and fractions.

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Calculate with fractions

Operation

Accepted: 3/4, -5/8, 1 1/2 (mixed number), 7, 0.25 and repeating decimals such as 0.(3).

= 13/6

Mixed number
2 1/6
Decimal
2.1(6)

Steps

  1. Rewrite both fractions with the least common denominator 6: 3/2 = 9/6, 2/3 = 4/6
  2. Add or subtract the numerators: (9 + 4)/6 = 13/6
  3. Already in lowest terms: 13/6

Decimal ⇄ fraction

Put repeating digits in parentheses: 0.(3) = 0.333…, 0.1(6) = 0.1666…

Fraction
1/6
Mixed number
1/6
Decimal
0.1(6)

The digits in parentheses repeat forever.

How to use it

  1. Type the first number: a fraction (3/4), a mixed number (1 1/2), a whole number or a decimal.
  2. Choose +, −, × or ÷ and type the second number.
  3. Read the simplified result, the mixed number, the exact decimal and the steps.
  4. To convert a decimal to a fraction, type it in the lower field; mark repeating digits with parentheses.

How it works

To add or subtract, both fractions are rewritten with the least common denominator (the least common multiple of the denominators), then the numerators are combined. To multiply, numerators and denominators are multiplied. To divide, the second fraction is flipped (its reciprocal) and multiplied. Finally the result is reduced by the greatest common divisor (GCD) of numerator and denominator, found with Euclid's algorithm.

A terminating decimal becomes a fraction over a power of ten: 0.75 = 75/100 = 3/4. A repeating decimal x = I.A(B), where B repeats, equals (IAB − IA) ÷ (10^|A| × (10^|B| − 1)); for example 0.1(6) = (16 − 1) ÷ 90 = 1/6. Going the other way, long division is carried out until a remainder repeats, which marks the start of the repeating digits.

All arithmetic uses exact big integers, so very long numerators and denominators give exact answers without rounding.

Examples

Adding mixed numbers

1 1/2 + 2/3: 3/2 = 9/6 and 2/3 = 4/6, so 9/6 + 4/6 = 13/6 = 2 1/6 = 2.1(6).

Dividing

3/4 ÷ 3/8 = 3/4 × 8/3 = 24/12 = 2 after dividing by the GCD 12.

Repeating decimal

0.(142857) = 142857/999999 = 1/7, and 1/7 in decimal is 0.(142857).

Frequently asked questions

How do I enter a mixed number?

Type the whole part, a space and the fraction: 2 3/4. For a negative mixed number put the minus sign first: -2 3/4 means −(2 + 3/4).

How do I type a repeating decimal?

Put the repeating digits in parentheses after the decimal point: 0.(3) for 0.333…, 2.1(45) for 2.14545…

Is 0.(9) really equal to 1?

Yes. By the formula, 0.(9) = 9/9 = 1. The tool shows this as the whole number 1.

Are results rounded?

Fractions are always exact. A decimal expansion is cut off only if it has more than 200 digits before repeating, and the tool says so.

Privacy

All calculations happen in your browser. Nothing you type is sent or stored.