OneTaskBy Tim King · Updated
Mixed Number Calculator
Adding, Subtracting, Multiplying and Dividing Mixed Numbers Such as 2 1/3
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How the Mixed Number Calculator works
This mixed number calculator adds, subtracts, multiplies and divides numbers such as 2 1/3 and 1 3/4. Type each one with a space between the whole number and the fraction. The answer comes back as a simplified mixed number, an improper fraction and a decimal, with every step written out.
A mixed number is a whole number and a fraction written together, like 3 1/2. Recipes, timber lengths and tape measures use them all the time, but they are awkward to work with directly. The reliable method is to turn each one into an improper fraction first, do the sum, then turn the answer back.
How the mixed number calculator works
The formula for the conversion is whole × denominator + numerator, all over the denominator, so 2 1/3 becomes 7/3. To add or subtract, the calculator finds the lowest common denominator and combines the numerators. To multiply, it multiplies tops and bottoms. To divide, it flips the second fraction and multiplies. Last, it simplifies and converts back to a mixed number.
First example. 2 1/3 + 1 3/4 becomes 7/3 + 7/4. Over twelfths that is 28/12 + 21/12 = 49/12, which is 4 1/12.
Second example. 3 1/2 ÷ 1 3/4 becomes 7/2 × 4/7 = 28/14, which simplifies to exactly 2.
How many 1 3/4 cup scoops fit in a 3 1/2 cup bag of flour? 3 1/2 ÷ 1 3/4 = 2, so exactly two.
Step-by-step working for 2 1/3 + 1 3/4
| Step | Working |
|---|---|
| Write as improper fractions | 2 1/3 = 7/3, 1 3/4 = 7/4 |
| Common denominator | The lowest common denominator of 3 and 4 is 12: 28/12 and 21/12 |
| Add the numerators | 28 + 21 = 49, so 49/12 |
| Back to a mixed number | 49/12 = 4 1/12 |
Common improper fractions as mixed numbers and decimals
| Improper fraction | Mixed number | Decimal |
|---|---|---|
| 9/8 | 1 1/8 | 1.125 |
| 6/5 | 1 1/5 | 1.2 |
| 5/4 | 1 1/4 | 1.25 |
| 4/3 | 1 1/3 | 1.(3) |
| 11/8 | 1 3/8 | 1.375 |
| 7/5 | 1 2/5 | 1.4 |
| 3/2 | 1 1/2 | 1.5 |
| 8/5 | 1 3/5 | 1.6 |
| 13/8 | 1 5/8 | 1.625 |
| 5/3 | 1 2/3 | 1.(6) |
| 7/4 | 1 3/4 | 1.75 |
| 9/5 | 1 4/5 | 1.8 |
| 15/8 | 1 7/8 | 1.875 |
| 17/8 | 2 1/8 | 2.125 |
| 11/5 | 2 1/5 | 2.2 |
| 9/4 | 2 1/4 | 2.25 |
| 7/3 | 2 1/3 | 2.(3) |
| 19/8 | 2 3/8 | 2.375 |
| 12/5 | 2 2/5 | 2.4 |
| 5/2 | 2 1/2 | 2.5 |
| 13/5 | 2 3/5 | 2.6 |
| 21/8 | 2 5/8 | 2.625 |
| 8/3 | 2 2/3 | 2.(6) |
| 11/4 | 2 3/4 | 2.75 |
| 14/5 | 2 4/5 | 2.8 |
| 23/8 | 2 7/8 | 2.875 |
Tips
- Use a space, not a plus. Type 2 1/3, not 2+1/3, so the calculator reads it as one number.
- Negatives go in front. Write −1 3/4 as -1 3/4; the minus applies to the whole mixed number.
- Plain fractions work too. 7/4 or a whole number like 3 can be mixed with mixed numbers.
FAQ
How do you add mixed numbers?
Convert both to improper fractions, give them a common denominator, add the numerators and simplify. For 1 1/2 + 2 2/3 that is 9/6 + 16/6 = 25/6, which is 4 1/6. You can also add the whole numbers and fractions separately, then carry any whole number the fractions make.
How do you subtract mixed numbers when the fraction is smaller?
Borrowing is the classroom method, but converting to improper fractions avoids it entirely. For 4 1/4 − 1 3/4, write 17/4 − 7/4 = 10/4, which simplifies to 2 1/2. The calculator always uses this route, so it never needs to borrow.
How do you multiply mixed numbers?
Never multiply the whole parts and fraction parts separately, because that misses the cross terms. Convert to improper fractions and multiply straight across: 1 1/2 × 2 2/3 = 3/2 × 8/3 = 24/6, which is exactly 4. Simplify at the end or cancel common factors first.
Why is dividing mixed numbers the same as multiplying by the reciprocal?
Dividing by a fraction asks how many of it fit into the first number. Flipping the divisor and multiplying gives the same answer, because a/b ÷ c/d = a/b × d/c. So 2 1/2 ÷ 1/4 is 5/2 × 4 = 10, which matches ten quarters fitting into two and a half.
See also: all Arithmetic tools, Number Theory, Algebra and Geometry, Statistics, Trigonometry and Calculus.
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