Enter fractions, mixed numbers or decimals
Select Add, Subtract, Multiply, Divide, Compare or Convert fraction. Enter a fraction such as 1/2, a mixed number such as 2 1/3, an integer or a finite decimal. Convert fraction uses only the first input. The result is reduced to lowest terms and, for arithmetic or conversion, includes a mixed-number display, decimal approximation and percentage approximation.
Worked example: adding different denominators
Choose Add with 1/2 and 1/3. A common denominator is 6: 1/2 becomes 3/6 and 1/3 becomes 2/6. Add the numerators to get 5/6. The calculator’s general rule is (a × d + b × c) ÷ (b × d), followed by reduction. Adding denominators to give 2/5 would change the sizes of the pieces and is incorrect.
Division, comparison and mixed-number examples
Choose Divide with 2 1/3 and 1/2. Convert the first input to 7/3 and multiply by the reciprocal of the second: (7/3) × (2/1) = 14/3, or 4 2/3. Compare with 2/3 and 3/4 gives <, because the cross-products 2 × 4 = 8 and 3 × 3 = 9 show that 2/3 is smaller.
Convert -2 1/3 to get -7/3. The negative sign applies to the entire mixed number. Convert 0.125 to get 1/8, with decimal 0.125 and percent 12.5%. Finite decimal input is treated as an exact fraction; a recurring decimal is not supported as recurring notation.
Exact results and display limits
Arithmetic uses arbitrary-size integers and reduces by the greatest common divisor, so the fraction result is exact for the entered values. Decimal and percentage outputs use floating-point approximations: 5/6 is exact even though its decimal display cannot show infinitely many sixes. A denominator cannot be zero, and division by a zero fraction is rejected. Mixed-number fractional parts must be proper, such as 1/3 rather than 4/3. Inputs are limited to 80 characters, and decimal input to 18 places. Use the percentage calculator for increases, decreases or relative percent change.
Method reference
OpenStax: Rational Numbers explains rational-number arithmetic and fraction forms.
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