Mixed fraction calculator, every step shown.

A mixed fraction calculator adds, subtracts, multiplies and divides mixed numbers, such as 2 1/3 and 1 3/4, and gives the answer as a mixed number, an improper fraction, a decimal and a percent. Every step is written out with your numbers, so you can follow the method or check your homework. It also takes plain fractions, whole numbers, decimals and negative values.

How to use the mixed fraction calculator

1. Type the first mixed number in First number, with a space between the whole part and the fraction, such as 2 1/3.
2. Choose an Operation: add, subtract, multiply or divide.
3. Type the Second number. Swap the two numbers turns A − B into B − A in one click.
4. Read the big answer, which is drawn as a whole number beside a stacked fraction. Below it are the improper fraction, the decimal and the percent.
5. Open The steps to see each stage. Use Copy result to take the answer as text, or Copy link to share the sum.

The method, in four steps

Every sum with mixed numbers follows the same path, and the calculator shows it each time.

1. Turn each mixed number into an improper fraction. Multiply the whole part by the bottom number and add the top. 2 1/3 becomes (2 × 3 + 1)/3 = 7/3, and 1 3/4 becomes 7/4.
2. Do the operation. For adding and subtracting, the bottom numbers must match. For multiplying, multiply across. For dividing, flip the second fraction and multiply.
3. Simplify. Divide the top and bottom by their greatest common factor.
4. Turn the result back into a mixed number. Divide the top by the bottom. The quotient is the whole part and the remainder is the new top.

Worked examples

Adding: 2 1/3 + 1 3/4. The improper forms are 7/3 and 7/4. The lowest common bottom number of 3 and 4 is 12, so 7/3 = 28/12 and 7/4 = 21/12. Add the tops: 28 + 21 = 49, giving 49/12. Divide: 49 ÷ 12 = 4 remainder 1, so the answer is 4 1/12.

Subtracting: 3 1/2 − 1 3/4. 7/2 − 7/4 = 14/4 − 7/4 = 7/4, which is 1 3/4. There is no need to borrow, because the improper form handles it. 5 1/6 − 2 5/6 is 31/6 − 17/6 = 14/6 = 7/3 = 2 1/3.

Multiplying: 2 2/3 × 1 1/2. 8/3 × 3/2 = 24/6 = 4. The threes cancel, and the answer is the whole number 4.

Dividing: 3 1/3 ÷ 1 1/4. 10/3 ÷ 5/4 = 10/3 × 4/5 = 40/15 = 8/3 = 2 2/3.

With a negative: −1 1/2 + 3/4. The first number is −3/2, which is −6/4. Adding 3/4 gives −3/4. The answer is a proper fraction with no whole part.

Real sums with mixed numbers

• Cutting a board. A board 5 1/2 feet long is cut into pieces 1 3/4 feet long. 5 1/2 ÷ 1 3/4 = 11/2 × 4/7 = 22/7 = 3 1/7. You get 3 whole pieces and a bit left over.
• Scaling a recipe. A recipe needs 2 2/3 cups and you make 1 1/2 times as much: 2 2/3 × 1 1/2 = 4 cups.
• A longer take-away. 7 1/4 − 2 3/8 = 29/4 − 19/8 = 58/8 − 19/8 = 39/8 = 4 7/8.

Whole numbers and decimals in the same sum

A whole number is a fraction with 1 on the bottom, so 3 + 1 3/4 is 3/1 + 7/4 = 12/4 + 7/4 = 19/4 = 4 3/4. A decimal is turned into a fraction first, so 2.5 becomes 5/2. This means you can mix the forms freely in the two boxes.

Common mistakes this avoids

• Adding the whole parts and the fractions separately works for addition, but fails when the fractions add to more than 1 and when you subtract a larger fraction from a smaller one. The improper route has no such trap.
• Multiplying the whole parts and the fractions separately is wrong for multiplication. 2 2/3 × 1 1/2 is not 2 × 1 plus 2/3 × 1/2.
• Forgetting to flip the second fraction when dividing.
• Leaving the answer unsimplified. 14/6 and 7/3 are the same number, but 7/3 or 2 1/3 is the finished form.

Which form to use

Use the mixed number for everyday measuring and recipes, the improper fraction for the next step of a longer calculation, and the decimal or percent when you need to compare with a price or a meter reading. A decimal that repeats, such as 2 1/3 = 2.333..., has its repeating digits marked.

For longer sums with several fractions, use the fraction calculator. To turn a mixed number into a decimal on its own, try mixed number to decimal.