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About this tool
Add, subtract, multiply and divide mixed numbers and fractions exactly, convert mixed ↔ improper ↔ decimal with repeating digits, and see every step.
This Mixed Number Calculator does arithmetic on mixed numbers such as 2 3/4 and 1 2/3, proper and improper fractions, whole numbers and decimals. Each value is turned into an exact fraction using whole-number (BigInt) arithmetic, so there is no rounding, even with very large numbers. The steps follow the textbook method: convert to improper fractions, find the least common denominator for addition and subtraction, multiply straight across, or keep-change-flip for division, then simplify with the greatest common divisor and convert back to a mixed number. Answers are also given as a decimal with any repeating digits marked, a percent and a pie or bar picture. A converter mode turns any value into every form.
Open Mixed Number Calculator on AltFTool — it loads instantly in your browser.
In Calculate (+ − × ÷), fill the whole number, numerator and denominator boxes for the First number and Second number, for example 2 3/4 and 1 2/3.
Choose +, −, × or ÷ (or press those keys) and read the Result as a mixed number, improper fraction, decimal and percent.
Follow the Steps for the LCD, keep-change-flip and GCD simplification, switch the picture between Pie and Bar, and use Save to history.
Switch to Convert mixed ↔ improper ↔ decimal and type a value such as 17/6, -3 5/8 or the repeating decimal 0.(3) to see every form.
Arithmetic uses whole-number fractions, not floating point, so 1/3 + 1/6 is exactly 1/2 and large numerators never round off.
Improper conversion, LCD, keep-change-flip, GCD simplification and the remainder method for mixed numbers are written out with your numbers.
Decimals are found by long division and the repeating cycle is marked, such as 0.1(6); you can also type repeating decimals in that form.
Pie and bar pictures show the result as whole units plus equal parts, alongside percent and reciprocal.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.(3) | 33.3333% |
| 2/3 | 0.(6) | 66.6667% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1(6) | 16.6667% |
| 1/7 | 0.(142857) | 14.2857% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 1/9 | 0.(1) | 11.1111% |
| 1/12 | 0.08(3) | 8.3333% |
| 1/16 | 0.0625 | 6.25% |
Percents are rounded to four decimal places.
Convert each mixed number to an improper fraction, rewrite both over the least common denominator, add the numerators, then simplify and convert back. For 2 3/4 + 1 2/3: 11/4 + 5/3 = 33/12 + 20/12 = 53/12 = 4 5/12. You can also add the whole numbers and fractions separately and carry any extra whole.
Use the same method as addition but subtract the numerators. For 5 1/2 − 3 3/4: 11/2 − 15/4 = 22/4 − 15/4 = 7/4 = 1 3/4. Working with improper fractions avoids having to borrow a whole when the second fraction is larger than the first.
Convert both to improper fractions, multiply the numerators together and the denominators together, then simplify. For 1 1/2 × 2 2/3: 3/2 × 8/3 = 24/6 = 4. Do not multiply the whole parts and fraction parts separately; that gives the wrong answer.
Convert to improper fractions, keep the first fraction, change division to multiplication, and flip the second fraction to its reciprocal. For 3 1/3 ÷ 1 1/4: 10/3 ÷ 5/4 = 10/3 × 4/5 = 40/15 = 8/3 = 2 2/3. Dividing by zero is undefined.
Multiply the whole number by the denominator, add the numerator, and put the result over the original denominator. For 2 3/4: 2 × 4 + 3 = 11, so it is 11/4. For a negative mixed number such as −2 3/4, the whole value is negative: −11/4.
Divide the numerator by the denominator. The quotient is the whole number and the remainder becomes the new numerator over the same denominator. For 17/6: 17 ÷ 6 = 2 remainder 5, so 17/6 = 2 5/6. If the remainder is zero, the answer is a whole number.
Subtract the non-repeating digits from all the digits, and divide by as many 9s as repeating digits followed by as many 0s as non-repeating decimal digits. For 0.1(6): (16 − 1) / 90 = 15/90 = 1/6. For 0.(3): 3/9 = 1/3.
A simplified fraction gives a terminating decimal only when its denominator has no prime factors other than 2 and 5. So 3/8 = 0.375 terminates, while 1/3, 1/6, 1/7 and 5/12 repeat. The repeating cycle of 1/7 is six digits long: 0.142857142857…
The least common denominator (LCD) is the smallest number that both denominators divide into evenly; it is the least common multiple of the denominators. For 3/4 and 2/3 it is 12. Using the LCD keeps numbers small, so the answer needs less simplifying.
Divide the numerator and denominator by their greatest common divisor (GCD). For 40/15 the GCD is 5, giving 8/3. A fraction is in lowest terms when the GCD of its top and bottom is 1. The calculator always shows the GCD it used.
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