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Fraction Calculator

Fraction and mixed-number arithmetic, simplifying and decimal conversion, with steps.

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Formats: 3/4, 1 1/2 (mixed), 0.75, 0.(3) (repeating)
Result
2 1/6
1 1/2 + 2/3 = 13/6 = 2.1(6)
Simplest form
13/6
Mixed number
2 1/6
Decimal
2.1(6)
Percent
216.666667%
Steps
Convert to improper fractions 1 1/2 = 3/2 Common denominator (LCD 6) 3/2 + 2/3 = 9/6 + 4/6 Combine the numerators (9 + 4)/6 = 13/6 Write as a mixed number 13/6 = 2 1/6

How to use

  1. In Arithmetic, enter two numbers and pick + − × ÷.
    • Fractions 3/4, mixed numbers 1 1/2 (with a space), whole numbers 5, decimals 0.75 and repeating decimals 0.(3) all work.
  2. The result is shown as a mixed number, with the simplest fraction, decimal, percent and the steps (common denominator → combine → simplify → mixed number).
  3. In Simplify & convert, reduce a single fraction to lowest terms or turn a decimal into a fraction.

Methods

Operation Method Example
Add / subtract Rewrite over the least common denominator, then combine numerators 1/2 + 1/3 = 3/6 + 2/6 = 5/6
Multiply Multiply numerators and denominators 2/3 × 3/4 = 6/12 = 1/2
Divide Multiply by the reciprocal of the divisor 1/2 ÷ 1/4 = 1/2 × 4/1 = 2
Simplify Divide top and bottom by the greatest common divisor 6/8 → (6÷2)/(8÷2) = 3/4
Mixed → improper Whole × denominator + numerator 1 1/2 = (1×2+1)/2 = 3/2

Decimal to fraction: put the digits over a power of ten and simplify (0.375 = 375/1000 = 3/8). For repeating decimals, wrap the repeating part in parentheses: 0.(3) = 3/9 = 1/3 and 0.1(6) = 15/90 = 1/6.

Example

1 1/2 + 2/3:

  1. Convert to an improper fraction: 1 1/2 = 3/2
  2. Common denominator (LCD 6): 3/2 + 2/3 = 9/6 + 4/6
  3. Combine the numerators: (9 + 4)/6 = 13/6
  4. As a mixed number: 13/6 = 2 1/6 (2.1666…, written 2.1(6))

Things to watch

  • Separate the whole number and the fraction with a space. 11/2 is read as eleven halves (5 1/2).
  • A negative mixed number -1 1/2 means −(1 + 1/2) = −3/2, not −1 + 1/2.
  • Fractions are computed with exact integer arithmetic, so there is no rounding error. Decimal expansions longer than 1,000 digits are cut off with “…”.

FAQ

Why does 1/3 never end as a decimal?

If the simplified denominator has any prime factor other than 2 and 5 (such as 3 or 7), the decimal repeats forever: 1/3 = 0.(3), 1/7 = 0.(142857).

How do I turn a fraction into a ratio or percentage?

The percent appears under the result. For ratios between several numbers use the ratio calculator, and for percentages the percentage calculator.

Ratio CalculatorSolve proportions, simplify ratios and split a total by ratio. Percentage CalculatorX% of Y, X as a percent of Y, and percentage increase or decrease. Average CalculatorMean, median, mode and standard deviation — plus weighted averages.

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