How to use this mixed number calculator
- Calculate: enter two numbers, each as a whole number, a fraction or both, and choose +, −, × or ÷. The answer appears as you type, as a mixed number, an improper fraction, a decimal and a percentage, with the full working.
- Improper → Mixed: enter a numerator and denominator to turn a fraction such as 14/3 into a mixed number.
- Mixed → Improper: enter a whole number, numerator and denominator to turn a mixed number such as 3 2/5 into an improper fraction.
Negative numbers and decimals work in every tab, and nothing you type is saved.
Mixed numbers vs improper fractions
A mixed number combines a whole number and a proper fraction, like 3 7/12 (“three and seven twelfths”). An improper fraction has a numerator at least as big as its denominator, like 43/12. Both describe the same amount, so you can switch between them freely. Mixed numbers are easier to picture, while improper fractions are much easier to calculate with.
That is why you see mixed numbers in recipes (2 1/2 cups of flour), measurements (5 3/4 inches) and times (1 1/2 hours), while maths work usually switches to improper fractions, does the calculation, and converts back to a mixed number only at the end.
Converting between mixed numbers and improper fractions
Mixed to improper: multiply the whole number by the denominator, add the numerator, and keep the denominator.
a b/c = (a × c + b) / c
For 3 2/5: 3 × 5 + 2 = 17, so 3 2/5 = 17/5.
Improper to mixed: divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator. For 14/3: 14 ÷ 3 = 4 remainder 2, so 14/3 = 4 2/3. If the fraction part can be simplified, do it: 45/10 = 4 5/10 = 4 1/2.
How to add, subtract, multiply and divide mixed numbers
The reliable method is the same for every operation: convert to improper fractions, calculate, simplify, then convert back. These examples all use 1 2/6 = 8/6 and 2 1/4 = 9/4.
Adding
a/b + c/d = (a × d + c × b) / (b × d)
The formula always works, but using the lowest common denominator (LCD) keeps the numbers smaller. The LCD of 6 and 4 is 12, so 8/6 = 16/12 and 9/4 = 27/12. Then 16/12 + 27/12 = 43/12 = 3 7/12.
Subtracting
Same as adding, but subtract the numerators: 16/12 − 27/12 = −11/12. The answer is negative because 2 1/4 is bigger than 1 2/6.
Multiplying
a/b × c/d = (a × c) / (b × d)
Multiply the tops and multiply the bottoms, with no common denominator needed: 8/6 × 9/4 = 72/24, which simplifies to 3.
Dividing
a/b ÷ c/d = a/b × d/c
Multiply by the reciprocal (flip the second fraction): 8/6 ÷ 9/4 = 8/6 × 4/9 = 32/54, which simplifies to 16/27. You can’t divide by 0, because 0 has no reciprocal.
Common mistakes
- Multiplying the parts separately. 1 1/2 × 2 1/2 is not 2 × 1/4 = 2 1/4. The correct answer is 3/2 × 5/2 = 15/4 = 3 3/4. Always convert to improper fractions first.
- Adding denominators. 1/2 + 1/3 is not 2/5. Find a common denominator: 3/6 + 2/6 = 5/6.
- Flipping the wrong fraction. When dividing, flip only the second fraction (the divisor), not the first.
- Misplacing the minus sign. −1 1/2 is −(1 + 1/2) = −3/2, not −1 + 1/2 = −1/2.
- Forgetting to simplify. 4 5/10 is correct but not finished; 4 1/2 is the simplest form.
Frequently asked questions
How do you add mixed numbers?
Turn each mixed number into an improper fraction, rewrite both over a common denominator, add the numerators, then simplify and turn the answer back into a mixed number. For example, 1 2/6 + 2 1/4 = 16/12 + 27/12 = 43/12 = 3 7/12.
How do you convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The quotient is the whole number and the remainder becomes the new numerator over the same denominator. For 14/3, 14 ÷ 3 = 4 remainder 2, so 14/3 = 4 2/3.
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 denominator. For 3 2/5, 3 × 5 + 2 = 17, so 3 2/5 = 17/5.
Can I multiply the whole numbers and fractions separately?
No. 1 1/2 × 2 1/2 is not 2 1/4. Each mixed number is a sum, so you must convert both to improper fractions first: 3/2 × 5/2 = 15/4 = 3 3/4.
How do negative mixed numbers work?
The minus sign applies to the whole mixed number, so −1 1/2 means −(1 + 1/2) = −3/2, not −1 + 1/2. In this calculator, type the minus sign in the Whole box.