Simplify Fractions Calculator
A fraction is not finished until it is in lowest terms — the numerator and denominator sharing no common factor except 1. The fraction 12/18 is correct, but 2/3 is the finished answer, and every textbook, exam, and recipe expects the finished form. The simplify fractions calculator above reduces any fraction instantly and shows the greatest common divisor (GCD) it divided by, so you can see exactly how the simplification happened.
The method is one division: find the GCD of the numerator and denominator, then divide both by it. For 12/18, the GCD is 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving 2/3. For 8/12, the GCD is 4, giving 2/3 as well. The same two fractions in different clothes reduce to the same answer — which is the point of simplifying.
Whole (optional), then numerator / denominator
Whole (optional), then numerator / denominator
How to Simplify a Fraction
Simplifying has three steps, and the middle one is the whole skill:
Step 1 — Find the GCD. The greatest common divisor is the largest number that divides both the numerator and the denominator. For 12 and 18, the divisors of 12 are 1, 2, 3, 4, 6, 12; the divisors of 18 are 1, 2, 3, 6, 9, 18; the largest shared one is 6.
Step 2 — Divide both parts by the GCD. 12 ÷ 6 = 2 and 18 ÷ 6 = 3.
Step 3 — Write the result. 12/18 = 2/3, in lowest terms.
If you cannot see the GCD at once, simplify in stages: divide by any common factor you can spot, then repeat. 24/36 shares 6, giving 4/6, which shares 2, giving 2/3. Staging always works — each step makes the numbers smaller, and you stop when no common factor remains except 1. The calculator does it in one step and reports the GCD, which is useful for checking your own working.
Worked Examples
The table below simplifies a range of fractions, showing the GCD and the reduced form for each. Notice how many different fractions reduce to 2/3 — that is normal, and it is why simplifying matters: it reveals when two fractions are really the same number.
| Fraction | GCD | Simplified | Decimal |
|---|---|---|---|
| 12/18 | 6 | 2/3 | 0.667 |
| 8/12 | 4 | 2/3 | 0.667 |
| 15/25 | 5 | 3/5 | 0.6 |
| 24/36 | 12 | 2/3 | 0.667 |
| 10/15 | 5 | 2/3 | 0.667 |
| 18/24 | 6 | 3/4 | 0.75 |
| 21/28 | 7 | 3/4 | 0.75 |
| 100/1,000 | 100 | 1/10 | 0.1 |
| 7/11 | 1 | 7/11 (already simplest) | 0.636 |
The last row is the edge case: 7 and 11 share no factor except 1, so 7/11 is already in lowest terms and cannot be simplified. If the calculator reports a GCD of 1, the fraction is already finished. The same applies to any fraction whose numerator and denominator are both prime, or share no prime factor.
Why Simplifying Matters
Simplifying is not cosmetic — it changes what you can do next. Comparing fractions is nearly impossible before simplifying: is 12/18 bigger than 8/12? Both reduce to 2/3, so they are equal, and no cross-multiplication is needed. Adding fractions is easier after simplifying, because smaller numbers give a smaller common denominator. And in recipes and measurements, a simplified fraction is the one you can actually measure: 2/3 of a cup is a marking on the jug, 12/18 of a cup is not.
Where Simplifying Shows Up
- Comparing fractions. 15/25 and 18/30 are both 3/5 — equal, once simplified.
- Adding and subtracting. Smaller numbers mean a smaller common denominator and less arithmetic.
- Converting to decimals. 3/5 = 0.6 is obvious; 15/25 = 0.6 takes a division to see.
- Recipes and DIY. Measuring cups and rulers are marked in simplified fractions.
- Exams and homework. An unsimplified answer is usually marked wrong, even when it is numerically correct.
- Ratios. A ratio of 12:18 is the same as 2:3 — the ratio calculator reduces it the same way.
The connection to ratios is exact: a fraction and a ratio are the same relationship written two ways, and both are simplified by dividing by the GCD. The ratio calculator reduces ratios, and the percentage calculator turns a simplified fraction into a percentage — 2/3 is 66.67%.
Simplifying After an Operation
Every fraction operation ends with a simplification step, and the calculator shows it. Adding 3/4 + 1/2 gives 5/4, which is already simplest. Multiplying 2/3 × 3/4 gives 6/12, which simplifies by a GCD of 6 to 1/2. Dividing 3/4 by 2/5 gives 15/8, already simplest. Subtracting 2/3 − 1/4 gives 5/12, already simplest. The pattern is that multiplication often produces a simplifiable result — because the numerators and denominators share factors — while addition and subtraction often do not. Always check: divide numerator and denominator by their GCD, and if the GCD is 1, the fraction is finished. The Khan Academy — Fractions has free exercises on simplifying, including the visual models that make the GCD intuitive.
Common Mistakes
Most wrong fraction answers come from the same short list of errors. Check yours against it before trusting the result.
- Adding numerators and denominators. 1/2 + 1/3 is 5/6, not 2/5 — find a common denominator first.
- Forgetting to simplify. 6/12 is 1/2; an unsimplified answer is correct but unfinished.
- Multiplying by the wrong reciprocal. Dividing by 2/5 means multiplying by 5/2, not by 2/5.
- Mixing whole numbers and fractions. Convert mixed numbers to improper fractions before adding or multiplying.
- Dividing by zero. A denominator of zero has no meaning — check both denominators before calculating.
- Rounding a repeating decimal too early. 1/3 is 0.333…, not 0.33 — round only at the end, and say that it repeats.
Related Tools
Related tools on this site: the main simplify fractions calculator for any fraction sum, the ratio calculator for the ratio behind a fraction, the percentage calculator to turn a fraction into a percent, and the basic calculator for decimal arithmetic.
Key Takeaways
If you remember nothing else from this page, remember these five points.
- 3/4 + 1/2 = 5/4 = 1 1/4: find a common denominator, add the numerators, simplify.
- 12/18 simplifies to 2/3 — divide numerator and denominator by their GCD, which is 6.
- 3/4 as a decimal is 0.75: divide the numerator by the denominator.
- 1 1/2 is 3/2 as an improper fraction: 1 × 2 + 1 = 3, over 2.
- Dividing by a fraction means multiplying by its reciprocal: 3/4 ÷ 2/5 = 15/8.
Try It Yourself
- Enter the two fractions in the calculator above, whole parts included.
- Pick the operation and read the answer with the step-by-step working.
- Check the GCD shown to see how the answer was simplified.
- Convert the answer to a decimal or a mixed number as needed.
Quick Reminders
- Never add denominators — only numerators, and only after they match.
- Convert mixed numbers to improper fractions before multiplying or dividing.
- A denominator of zero has no meaning — check both denominators.
- 1/3 is 0.333…, repeating — round only at the end.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/3 | 0.333… | 33.33% |
Keep the fraction as a fraction for exact work and use the decimal only for measuring, money, or comparison — a rounded decimal is an approximation, and the fraction is the exact value.
More Fractions to Simplify
The same divide-by-the-GCD step simplifies any fraction. The table gives six more examples, including two that both reduce to 2/3 — different fractions can simplify to the same value.
| Fraction | GCD | Simplified | Decimal |
|---|---|---|---|
| 18/24 | 6 | 3/4 | 0.75 |
| 20/30 | 10 | 2/3 | 0.667 |
| 16/20 | 4 | 4/5 | 0.8 |
| 21/28 | 7 | 3/4 | 0.75 |
| 45/60 | 15 | 3/4 | 0.75 |
| 100/150 | 50 | 2/3 | 0.667 |
Three of these reduce to 3/4, which is a good check: if two fractions simplify to the same value, they were equal all along, just written with different denominators.
Frequently Asked Questions
How do you simplify a fraction?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For 12/18, the GCD is 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving 2/3. If the GCD is 1, the fraction is already in lowest terms.
What is 12/18 simplified?
2/3. The GCD of 12 and 18 is 6. Divide both parts by 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3. As a decimal, 2/3 is about 0.667.
What is the GCD and why does it matter?
The greatest common divisor is the largest number that divides both the numerator and denominator. Dividing by it reduces the fraction to lowest terms in a single step. For 24 and 36 the GCD is 12, so 24/36 simplifies directly to 2/3.
How do you simplify 8/12?
Divide both parts by their GCD, which is 4: 8 ÷ 4 = 2 and 12 ÷ 4 = 3, giving 2/3. You can also simplify in stages — divide by 2 to get 4/6, then by 2 again to get 2/3.
Can every fraction be simplified?
No. A fraction is already in lowest terms when its numerator and denominator share no common factor except 1 — for example 7/11, 3/5, or 5/6. The calculator reports a GCD of 1 in that case, which means the fraction is finished as it is.
What is 15/25 in simplest form?
3/5. The GCD of 15 and 25 is 5: 15 ÷ 5 = 3 and 25 ÷ 5 = 5. As a decimal, 3/5 is 0.6, and as a percentage it is 60%.
What is 20/30 simplified?
2/3. The GCD of 20 and 30 is 10: 20 ÷ 10 = 2 and 30 ÷ 10 = 3. As a decimal that is about 0.667.
How do you simplify a fraction with a calculator?
Enter the fraction in the calculator above — it divides numerator and denominator by their greatest common divisor and shows the GCD it used, so you can check the working.
Disclaimer: This calculator is for general information and education. Fractions are exact arithmetic, but measurements and quantities you enter should be checked against the original source.