General
Fraction Calculator
Works fraction arithmetic, where the operation decides whether denominators matter.
Result
Numerators and denominators are rounded to whole numbers, since a fraction of a fraction is better entered as a single fraction.
Get a Free Business AuditHow the calculation works
Addition and subtraction require a common denominator; multiplication multiplies numerators and denominators directly; division multiplies by the reciprocal. Results are simplified by dividing both parts by their greatest common divisor, and improper fractions convert to mixed numbers by division.
What moves the number
- Which operation, since the rules differ.
- Whether a common denominator is needed.
- Whether the result should be simplified or exact.
- Mixed numbers, which convert before operating.
Where this one goes wrong
Adding numerators and denominators separately is the classic error and it produces a result that is not a sum at all, which is why addition and subtraction need the common denominator first while multiplication does not. The other practical point is that fractions are exact where decimals are not: a third is exactly a third as a fraction and a rounded approximation as a decimal, which matters in any calculation chained from it.
Before you quote
- Find a common denominator before adding or subtracting.
- Convert mixed numbers before operating on them.
- Keep fractions exact rather than converting to decimals early.
Questions
About this calculator
Why do I need a common denominator to add fractions?
Because the denominator defines the size of the parts, and parts of different sizes cannot be counted together. Adding numerators and denominators separately produces something that is not a sum at all.
How do I divide by a fraction?
Multiply by its reciprocal, meaning turn it upside down and multiply. Dividing by a half is the same as multiplying by two, which is why dividing by a fraction less than one produces a larger result.
Should I convert fractions to decimals?
Not early, because fractions are exact and decimals frequently are not. A third as a decimal is a rounded approximation, and chaining calculations from a rounded value accumulates error that the fraction form avoids.
The formula
a/b + c/d = (ad + cb) ÷ bd, then reduce by the greatest common divisor
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How to use this calculator
- First fraction: numerator. Enter your own figure; the page starts at 3.
- First fraction: denominator. Enter your own figure; the page starts at 4.
- Operation. Enter your own figure; the page starts at Add (+).
- Second fraction: numerator. Enter your own figure; the page starts at 5.
- Second fraction: denominator. Enter your own figure; the page starts at 6.
The result updates as you type, so you can try a figure, see what it does to result, and change it back. Nothing you enter is sent anywhere or saved.
A worked example
These are the figures the calculator opens with. Every number in the results column below is produced by the same calculation the page runs, so you can follow it through before putting your own figures in.
What goes in
| Input | Value |
|---|---|
| First fraction: numerator | 3 |
| First fraction: denominator | 4 |
| Operation | Add (+) |
| Second fraction: numerator | 5 |
| Second fraction: denominator | 6 |
What comes out
| Result | Value |
|---|---|
| Result main result | 19/12 |
| As a mixed number | 1 7/12 |
| As a decimal | 1.5833 |
| As a percentage | 158.33% |
3/4 + 5/6 = 19/12 (1.5833).
How sensitive the answer is
Holding everything else steady and changing only first fraction: numerator, this is what happens to result. It is worth knowing which of your inputs the answer actually hinges on, and which barely move it.
| First fraction: numerator | Result |
|---|---|
| 2 | 4/3 |
| 2 | 4/3 |
| 3 example above | 19/12 |
| 5 | 25/12 |
| 6 | 7/3 |
Every other input is held at the example value while this one changes, which is not how a real job behaves. Treat it as a guide to which number matters most, not as five separate quotes.
What each figure means
- First fraction: numerator
- A number, starting at 3.
- First fraction: denominator
- A number, starting at 4.
- Operation
- Choose from Add (+), Subtract (−), Multiply (×), Divide (÷).
- Second fraction: numerator
- A number, starting at 5.
- Second fraction: denominator
- A number, starting at 6.
What the results tell you
| Result | What it is |
|---|---|
| Result | The headline result. A category or planning selection, rather than a measured quantity. |
| As a mixed number | A category or planning selection, rather than a measured quantity. |
| As a decimal | A number. |
| As a percentage | A percentage. |
Keep going
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