Mixed Fraction Calculator

How to use the mixed fraction calculator

1. Enter the first number in three parts: the whole number, the numerator and the denominator. For 2¾, enter 2, 3 and 4.
2. Pick the operation: add, subtract, multiply or divide.
3. Enter the second number the same way. For a plain fraction such as 5/8, leave the whole number at 0. For a whole number such as 5, enter 5 with a numerator of 0.
4. Use the Negative switch for negative mixed numbers. The sign applies to the whole mixed number, so −1 7/8 means −(1 + 7/8).

The answer updates as you type. It is exact: the calculator works with whole-number numerators and denominators the entire time and only turns the result into a decimal at the end.

The method: convert, operate, simplify

Every operation follows the same three steps that the open textbook Prealgebra 2e from OpenStax teaches:

Converting. 3 7/8 becomes (3 × 8 + 7)/8 = 31/8. Going back, divide the numerator by the denominator: 11/6 is 11 ÷ 6 = 1 remainder 5, so 1 5/6. That is the textbook’s own example in section 4.1.

Adding. The textbook’s Example 4.85 adds 3 7/8 + 4 3/8 by converting both: 31/8 + 35/8 = 66/8 = 8 2/8, which simplifies to 8 1/4.

Adding and subtracting mixed numbers

There are two ways to add mixed numbers, and they give the same answer. You can add the whole numbers and the fractions separately, or convert both to improper fractions first. OpenStax’s Example 4.84 does it the first way: 9 5/9 + 5 7/9 = 14 12/9. Because 12/9 is more than one, rewrite it as 1 3/9, giving 15 3/9, which simplifies to 15 1/3.

When the denominators differ, rewrite both fractions over a common denominator, ideally the least common multiple. For 2¾ + 1⅚, the least common denominator of 4 and 6 is 12: 2 9/12 + 1 10/12 = 3 19/12 = 4 7/12. The calculator multiplies the denominators and then reduces, which reaches the same simplest form.

Subtraction sometimes needs borrowing. In Example 4.90, 5 3/5 − 2 4/5: since 3/5 is less than 4/5, take 1 from the 5 and write it as 5/5, so 5 3/5 becomes 4 8/5. Then 4 8/5 − 2 4/5 = 2 4/5. Converting to improper fractions avoids borrowing entirely: 28/5 − 14/5 = 14/5 = 2 4/5.

Multiplying and dividing mixed numbers

For multiplication and division, convert to improper fractions first. Multiplying the whole parts and the fraction parts separately gives the wrong answer: 2½ × 2½ is not 4¼ but 6¼.

Multiplying. In OpenStax Example 4.37, 3 1/3 × 5/8 becomes 10/3 × 5/8 = 50/24, which reduces to 25/12, or 2 1/12. Cancelling common factors before multiplying, as the textbook does, keeps the numbers small; the result is the same.

Dividing. Multiply by the reciprocal of the second number. Example 4.40 divides 2 1/2 by 1 1/4: 5/2 ÷ 5/4 = 5/2 × 4/5 = 20/10 = 2. Example 4.39 divides by a whole number, 3 4/7 ÷ 5 = 25/7 × 1/5 = 5/7.

Signs. A negative times a positive is negative. Example 4.38 multiplies 2 4/5 by −1 7/8: 14/5 × (−15/8) = −210/40 = −21/4 = −5 1/4.

Where mixed numbers come up

Outside math class, mixed numbers appear wherever measurements are in fractions: recipes (scaling 1⅓ cups by 1½ gives 2 cups), woodworking and sewing in inches (a 36-inch board minus two 10⅝-inch cuts leaves 14¾ inches before saw kerf), and time (2¾ hours plus 1⅚ hours is 4 7/12 hours, or 4 hours 35 minutes).

For measurements, the decimal result is handy for a calculator or spreadsheet, and the mixed number is what you can read off a ruler or measuring cup. Both are shown so you can use whichever matches the tool in your hand.

Checking an answer by hand

Two quick checks catch most mistakes. First, estimate with whole numbers: 2¾ × 1⅚ should be a bit under 3 × 2 = 6; the exact answer, 5 1/24, fits. Second, convert the result to a decimal and compare with the decimals of the inputs: 2.75 × 1.8333 = 5.0417, which matches 5 1/24.

If your hand answer differs only in form, such as 10/4 instead of 2 1/2, it is not wrong, just not simplified. Divide the numerator and denominator by their greatest common divisor (2 here) and convert back to a mixed number.

Simplifying: greatest common divisor and least common denominator

Two whole-number tools do most of the work in fraction arithmetic. The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator; dividing both by it puts a fraction in lowest terms. For 66/8, the GCD is 2, so 66/8 = 33/4 = 8 1/4. For 50/24 it is also 2, giving 25/12.

The least common denominator is the least common multiple of the denominators. It keeps numbers small when you add or subtract by hand. For sixths and fourths it is 12, not 24. You can find it by listing multiples of the larger denominator until one is divisible by the other: 6, 12. Done.

The calculator uses Euclid’s algorithm for the GCD: divide the larger number by the smaller, replace the larger with the remainder, and repeat until the remainder is zero. For 48 and 36, 48 ÷ 36 leaves 12, and 36 ÷ 12 leaves 0, so the GCD is 12. The method is fast even for large numbers, which is why the results stay exact.

Simplifying at the end gives the same answer as simplifying along the way. Cancelling first, as textbooks often show, just keeps the intermediate numbers smaller and easier to check by hand.

Sources & assumptions

How this calculator gets its numbers. Full method: our methodology.

• Each mixed number is converted to an improper fraction: (whole × denominator + numerator) ÷ denominator, with the sign applying to the whole number.
• Sums and differences use a common denominator; products multiply straight across; quotients multiply by the reciprocal.
• Results are reduced by the greatest common divisor and converted back to a mixed number.
• Arithmetic is exact with whole numbers up to about 9 quadrillion; the decimal is rounded to six places.

Sources

1. OpenStax (Rice University), Prealgebra 2e, 4.1 Visualize Fractions. Converting between improper fractions and mixed numbers (11/6 = 1 5/6) by division with a remainder.
2. OpenStax (Rice University), Prealgebra 2e, 4.3 Multiply and Divide Mixed Numbers and Complex Fractions. Examples 4.37–4.40: 3 1/3 × 5/8 = 25/12, 2 4/5 × (−1 7/8) = −5 1/4, 3 4/7 ÷ 5 = 5/7 and 2 1/2 ÷ 1 1/4 = 2.
3. OpenStax (Rice University), Prealgebra 2e, 4.6 Add and Subtract Mixed Numbers. Examples 4.84, 4.85 and 4.90: 9 5/9 + 5 7/9 = 15 1/3, 3 7/8 + 4 3/8 = 8 1/4, and 5 3/5 − 2 4/5 = 2 4/5 with borrowing.

Last reviewed November 2, 2026. The steps follow the open Prealgebra 2e textbook; your teacher may ask for the work in a particular form.