Fractions Calculator
Add, subtract, multiply and divide fractions, or turn a decimal into a fraction, with the working shown.
How to Use the Fractions Calculator
Type a numerator and denominator into each box, choose whether you want to add, subtract, multiply or divide, and press Calculate. The tool returns the answer already reduced to lowest terms, along with its decimal value and, where one exists, the equivalent mixed number. The Show Step-by-Step button expands the full working, which is what makes this useful for checking homework rather than just getting an answer.
The second tab converts a decimal into a fraction. Enter something like 0.75 and it returns 3/4, showing how it got there.
The Four Fraction Operations
Adding and Subtracting Fractions
You can only add or subtract fractions that share a denominator. When they differ, cross-multiply to build a common one:
a/b + c/d = (a×d + c×b) / (b×d)
Worked example — 1/2 + 1/3:
- Common denominator: 2 × 3 = 6
- Numerator: (1 × 3) + (1 × 2) = 5
- Answer: 5/6 — the GCD of 5 and 6 is 1, so it is already in lowest terms
Subtraction works identically, with a minus in place of the plus: 3/4 − 1/6 becomes (3×6 − 1×4)/24 = 14/24, which simplifies to 7/12.
Multiplying Fractions
Multiplication is the easiest of the four — no common denominator required. Multiply straight across:
a/b × c/d = (a×c) / (b×d)
For 2/3 × 3/4: numerators give 6, denominators give 12, so the raw answer is 6/12. The GCD of 6 and 12 is 6, which reduces it to 1/2.
Dividing Fractions
To divide, flip the second fraction and multiply. The flipped fraction is called the reciprocal:
a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)
So 1/2 ÷ 1/4 becomes 1/2 × 4/1 = 4/2 = 2. This is why dividing by a fraction smaller than one makes the answer bigger — a result that surprises most students the first time they see it.
Simplifying: the Part Most People Get Wrong
A fraction is in lowest terms when the only number dividing both parts evenly is 1. To get there, divide the numerator and denominator by their greatest common divisor.
Take 18/24. The divisors shared by both are 1, 2, 3 and 6, so the GCD is 6. Dividing both by 6 gives 3/4. Halving repeatedly (18/24 → 9/12 → 3/4) reaches the same place; using the GCD just gets there in one move.
Converting Decimals to Fractions
For a terminating decimal, count the digits after the point, write the number over 1 followed by that many zeros, then simplify.
| Decimal | Written over a power of ten | Simplified |
|---|---|---|
| 0.5 | 5/10 | 1/2 |
| 0.25 | 25/100 | 1/4 |
| 0.75 | 75/100 | 3/4 |
| 0.2 | 2/10 | 1/5 |
| 0.125 | 125/1000 | 1/8 |
| 1.6 | 16/10 | 8/5 (mixed: 1 3/5) |
Repeating decimals such as 0.333… are a different case: they need an algebraic method and cannot be captured exactly by this power-of-ten approach. The nearest exact fraction for 0.333… is 1/3.
Common Fraction to Decimal Reference
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.3% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 2/3 | 0.666… | 66.7% |
| 3/4 | 0.75 | 75% |
| 5/8 | 0.625 | 62.5% |
Mistakes Worth Avoiding
- Adding denominators. 1/2 + 1/3 is not 2/5. Only the numerators are added, once the denominators match.
- Forgetting to simplify. 6/12 is arithmetically correct but will usually be marked down; 1/2 is the expected form.
- Flipping the wrong fraction when dividing. It is always the second one that is inverted.
- Leaving a negative on the denominator. Write −3/4 rather than 3/−4.
- Treating a repeating decimal as terminating. Rounding 0.333… to 0.33 gives 33/100, not 1/3.
Frequently Asked Questions
How do I add fractions with different denominators?
Multiply the denominators together to get a common denominator, cross-multiply each numerator by the other fraction’s denominator, add the results, then simplify. For 1/2 + 1/3 the common denominator is 6, the numerator becomes (1×3)+(1×2)=5, giving 5/6.
Why do you flip the second fraction when dividing?
Dividing by a number is the same as multiplying by its reciprocal. Since a/b divided by c/d asks how many c/d fit into a/b, inverting the second fraction converts the division into a multiplication that is far easier to compute.
What does it mean to simplify a fraction?
Simplifying means dividing the numerator and denominator by their greatest common divisor so no whole number other than 1 divides both. It does not change the value, only how it is written: 6/12 and 1/2 are the same quantity.
How do I turn a decimal into a fraction?
Count the digits after the decimal point, place the digits over 1 followed by that many zeros, then reduce. 0.75 has two decimal places, so it becomes 75/100, which simplifies to 3/4.
Can this calculator handle negative fractions?
Yes. Enter a minus sign on the numerator or the denominator and the calculator normalises the sign, always presenting the result with the negative on the numerator.
What is a mixed number?
A mixed number combines a whole number with a proper fraction, such as 1 1/2 instead of 3/2. When a result is larger than one, the calculator shows the mixed form alongside the improper fraction.