Answer first
What this calculator tells you
Add, subtract, multiply or divide two fractions and get the answer in lowest terms plus its decimal value. Check homework or a recipe scaling by seeing the reduced fraction and the decimal side by side. Formula: a/b ± c/d = (ad ± bc) ÷ bd; a/b × c/d = ac ÷ bd; a/b ÷ c/d = ad ÷ bc; then divide top and bottom by their greatest common divisor. At the worked-example inputs, the simplified numerator is 19. Holding every other input steady, moving first numerator from 1 to 5 moves the result from 4 to 25.
Transparent method
The formula
Check homework or a recipe scaling by seeing the reduced fraction and the decimal side by side.
Worked example
Example inputs
How to interpret the result
Two fractions with different bottoms cannot be added until they share one. That is the whole reason 3/4 + 5/6 does not equal 8/10. The calculator finds the shared bottom, adds, then divides top and bottom by whatever they have in common, so 38/24 arrives as 19/12. Seeing the decimal beside it, 1.583, tells you whether a recipe or a cut list is in the right neighborhood before you trust the reduced form.
At the worked-example inputs the simplified numerator is 19. It rises with second denominator, first denominator and first numerator and falls as operation and second numerator increase.
These are exact mathematical formulas; results are limited only by floating-point precision, not by real-world estimation. Confirm the convention (rounding rule, sign, base) your assignment or application expects.
Before you rely on it
What to check
Estimate first. Three quarters plus five sixths must land a little under two, so 19/12 passes and 8/10 fails on sight.
The common error
Where people go wrong with fraction calculator
Adding tops and bottoms separately. It feels natural and gives an answer smaller than one of the inputs, which can never be right for a sum of positive fractions.
Sensitivity evidence
How first numerator changes the simplified numerator
Holding every other input at the worked-example value, moving first numerator from 1 to 5 moves the simplified numerator from 4 to 25: a spread of 21, or 111% of the worked-example result.
| First numerator | Simplified numerator | Simplified denominator | Decimal value |
|---|---|---|---|
| 1 | 13 | 12 | 1.1 |
| 2 | 4 | 3 | 1.3 |
| 3worked example | 19 | 12 | 1.6 |
| 4 | 11 | 6 | 1.8 |
| 5 | 25 | 12 | 2.1 |
Every input, tested
Which input moves the simplified numerator most
Of the 5 inputs, operation moves the simplified numerator most (10 across the range tested) and second numerator moves it least (10).
| Input | Tested from | To | Simplified numerator at each end | Swing |
|---|---|---|---|---|
| Operation | Add (+) | Divide (÷) | 19 to 9 | 10 (105%) |
| Second denominator | 4 | 8 | 2 to 11 | 9 (47%) |
| First denominator | 3 | 5 | 11 to 43 | 32 (168%) |
| First numerator | 2 | 4 | 4 to 11 | 7 (37%) |
| Second numerator | 4 | 6 | 17 to 7 | 10 (53%) |
Two variables at once
Simplified numerator by first numerator and first denominator
Across the grid the simplified numerator runs from 1 to 25. Moving first numerator from 1 to 5 shifts it by 12 at the middle column, and moving first denominator from 2 to 6 shifts it by 3 at the middle row, so first numerator is the bigger lever here.
| First numerator \ First denominator | 2 | 4 | 6 |
|---|---|---|---|
| 1 | 4 | 13 | 1 |
| 2 | 11 | 4 | 7 |
| 3 | 7 | 19 | 4 |
| 4 | 17 | 11 | 3 |
| 5 | 10 | 25 | 5 |
The highlighted cell is the worked example: 19.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| First numerator | 3 | The top number of the first fraction. |
| First denominator | 4 | The bottom number of the first fraction. It cannot be zero. |
| Operation | Add (+) | Choose add, subtract, multiply or divide. |
| Second numerator | 5 | The top number of the second fraction. |
| Second denominator | 6 | The bottom number of the second fraction. It cannot be zero. |
| Simplified numerator | 19 | |
| Simplified denominator | 12 | |
| Decimal value | 1.6 | |
Inputs, definitions and assumptions
First numerator
The top number of the first fraction. The prefilled worked-example value is 3.
First denominator
The bottom number of the first fraction. It cannot be zero. The prefilled worked-example value is 4.
Operation
Choose add, subtract, multiply or divide. The prefilled worked-example value is Add (+).
Second numerator
The top number of the second fraction. The prefilled worked-example value is 5.
Second denominator
The bottom number of the second fraction. It cannot be zero. The prefilled worked-example value is 6.
How to use this calculator
- 1Verify the inputs. Gather first numerator, first denominator, operation, second numerator and second denominator from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the simplified numerator at 19. Store your own version of it as Scenario A.
- 3Test one change. Start with operation, the input with the biggest effect here: switching operation changes the simplified numerator: add (+) gives 19; subtract (−) gives -1; multiply (×) gives 5; divide (÷) gives 9.
- 4Check the boundary. Read the interpretation boundary above before acting on the result.
People also ask
Frequently asked questions
How do you calculate fraction?
a/b ± c/d = (ad ± bc) ÷ bd; a/b × c/d = ac ÷ bd; a/b ÷ c/d = ad ÷ bc; then divide top and bottom by their greatest common divisor. At the worked-example inputs the simplified numerator is 19.
What does the fraction result mean?
Check homework or a recipe scaling by seeing the reduced fraction and the decimal side by side. At the worked-example inputs the simplified numerator is 19. It rises with second denominator, first denominator and first numerator and falls as operation and second numerator increase.
How much does first numerator change the simplified numerator?
Holding every other input at the worked-example value, moving first numerator from 1 to 5 moves the simplified numerator from 4 to 25, a spread of 21.
What are the limits of this fraction calculator?
These are exact mathematical formulas; results are limited only by floating-point precision, not by real-world estimation. Confirm the convention (rounding rule, sign, base) your assignment or application expects. The tables on this page test first numerator only from 1 to 5; a value outside that range is not tabulated here.
Which input moves the simplified numerator most in the fraction calculator?
Ranked by how far each moves the simplified numerator across the range tested: operation (10, 105%), second denominator (9, 47%), first denominator (32, 168%) and first numerator (7, 37%).
How much does first denominator matter in the fraction calculator?
The worked example uses 4. With the other inputs left at the worked example, moving first denominator from 3 to 5 takes the simplified numerator from 11 to 43, a swing of 168% of the worked-example figure.
How much does operation matter in the fraction calculator?
The worked example uses Add (+). Holding every other input at its worked-example value, switching operation changes the simplified numerator: add (+) gives 19; subtract (−) gives -1; multiply (×) gives 5; divide (÷) gives 9.
How much does second numerator matter in the fraction calculator?
The worked example uses 5. With the other inputs left at the worked example, moving second numerator from 4 to 6 takes the simplified numerator from 17 to 7, a swing of 53% of the worked-example figure.
How much does second denominator matter in the fraction calculator?
The worked example uses 6. Holding every other input at its worked-example value, moving second denominator from 4 to 8 takes the simplified numerator from 2 to 11, a swing of 47% of the worked-example figure.
Which inputs change the simplified denominator in the fraction calculator?
At the worked-example inputs it is 12. First numerator takes it from 3 to 6, first denominator takes it from 6 to 30, operation takes it from 12 to 10 and second numerator takes it from 12 to 4.
Which inputs change the decimal value in the fraction calculator?
At the worked-example inputs it is 1.6. First numerator takes it from 1.3 to 1.8, first denominator takes it from 1.8 to 1.4, operation takes it from 1.6 to 0.9 and second numerator takes it from 1.4 to 1.8.
What's the difference between a root and an exponent?
An exponent raises a value to a power (2³ = 8). A root reverses that operation, asking what value raised to a power gives the result (the cube root of 8 is 2). A root is the same as raising to a fractional exponent: the cube root of x equals x^(1/3).
Sources and evidence
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