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Mixed Number Calculator
A mixed number calculator adds, subtracts, multiplies, and divides mixed numbers — the whole-number-plus-fraction amounts you meet in recipes, woodworking, and homework. Enter two mixed numbers, pick an operation, and it shows the answer as a mixed number, as an improper fraction, and as a decimal. It also converts between improper fractions and mixed numbers, and whole numbers work too — just leave the fraction part as 0.
| As an improper fraction | |
| As a decimal | |
| First number as improper fraction | |
| Second number as improper fraction |
| As an improper fraction | |
| As a mixed number | |
| As a decimal |
How it works
A mixed number is a whole number joined to a fraction, like 2 3/4, which means two wholes plus three quarters. You see them everywhere measurements are written in fractions: a recipe calling for 1 1/2 cups of sugar, a board cut to 3 1/4 inches, a runner finishing a race in 2 1/2 hours. They are easy to read, but awkward to calculate with — and that is where this calculator helps.
The trick is to convert each mixed number into an improper fraction first. Multiply the whole number by the denominator, add the numerator, and keep the same denominator. So 2 3/4 becomes (2 × 4 + 3) ÷ 4 = 11/4. Improper fractions are easy to work with: to add or subtract, find a common denominator and combine the numerators; to multiply, multiply straight across; to divide, flip the second fraction and multiply.
Add/subtract: a/b ± c/d = (a×d ± c×b) ÷ (b×d), then simplify
Multiply: (a/b) × (c/d) = (a×c) ÷ (b×d) • Divide: (a/b) ÷ (c/d) = (a/b) × (d/c)
Back to mixed: divide numerator by denominator; the quotient is the whole part, the remainder is the new numerator
Once the arithmetic is done, the calculator converts the answer back. It divides the numerator by the denominator: the quotient becomes the whole part and the remainder becomes the numerator over the same denominator. It also simplifies the fraction by dividing the numerator and denominator by their greatest common divisor, so 18/4 becomes 9/2 and then 4 1/2, never a clumsy unsimplified answer — unless you switch off the "simplify to lowest terms" option, which shows the answer exactly as the arithmetic produced it, useful when a teacher wants to see the unsimplified step. If the result is negative — for example when you subtract a larger mixed number from a smaller one — the minus sign goes in front of the whole mixed number.
Whole numbers fit the same system: a whole number is a mixed number with a zero fraction part, so enter 3 as whole part 3 with numerator 0. The convert mode works the other way too — an improper fraction like 11/4 becomes the mixed number 2 3/4, and a mixed number like 2 3/4 becomes 11/4 — using the same rule in reverse: multiply the whole part by the denominator and add the numerator.
Subtraction deserves a warning that trips up many students: you cannot simply subtract the whole parts and the fractions separately when the first fraction is smaller than the second. The safe method is always to convert to improper fractions first and let the common denominator handle it. The same advice applies to division, where the most common mistake is forgetting to flip the second fraction before multiplying. This calculator does every step for you, but knowing the method means you can check its work by hand.
Worked example
Sam is baking two batches of cookies in Denver. The first batch uses 1 1/2 cups of flour and the second uses 2 3/4 cups. How much flour does he need in total?
Step 1 — convert to improper fractions: 1 1/2 = (1 × 2 + 1) ÷ 2 = 3/2, and 2 3/4 = (2 × 4 + 3) ÷ 4 = 11/4. Step 2 — find a common denominator: 3/2 = 6/4, so the sum is 6/4 + 11/4 = 17/4. Step 3 — convert back to a mixed number: 17 ÷ 4 = 4 with a remainder of 1, so the answer is 4 1/4 cups. As a decimal that is 4.25 cups.
Enter the same numbers in the calculator above — 1 1/2 plus 2 3/4 — and you get the same result: 4 1/4, or 17/4, or 4.25.
FAQ
Can I use whole numbers in the mixed number calculator?
Yes. A whole number is just a mixed number with a zero fraction part: enter the whole number and put 0 in the numerator box. For example, 3 plus 1 1/2 is entered as 3 0/1 plus 1 1/2, and the answer is 4 1/2. The same works for subtraction, multiplication, and division.
What is a mixed number?
A mixed number combines a whole number with a fraction, such as 2 3/4. It means 2 whole units plus three quarters of another unit. Mixed numbers are common in cooking, woodworking, and everyday measurements, where amounts like 1 1/2 cups or 3 1/4 inches come up all the time.
How do you convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and put the result over the same denominator. For example, 2 3/4 becomes (2 x 4 + 3) / 4 = 11/4. An improper fraction has a numerator larger than its denominator, which makes it easy to add, subtract, multiply, and divide.
How do you add mixed numbers?
Convert both mixed numbers to improper fractions, find a common denominator, add the numerators, simplify, and convert the answer back to a mixed number. For example, 1 1/2 + 2 3/4 becomes 3/2 + 11/4 = 6/4 + 11/4 = 17/4 = 4 1/4.
How do you divide mixed numbers?
Convert both mixed numbers to improper fractions, then flip the second fraction (swap its numerator and denominator) and multiply. For example, 1 1/2 divided by 2 1/4 becomes 3/2 x 4/9 = 12/18 = 2/3. Flipping and multiplying is the standard rule for dividing any fractions.