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Fraction guide

The Fraction Calculator has four modes: fraction operations (add, subtract, multiply, divide), simplifying fractions, decimal-to-fraction, and fraction-to-decimal. Each mode shows the exact simplified result and its decimal approximation.

Worked examples

Add two fractions (1/2 + 1/3)

  1. Open the "Fraction Operations" tab.
  2. Enter 1 in the first numerator and 2 in the first denominator.
  3. Select + as the operator.
  4. Enter 1 in the second numerator and 3 in the second denominator.
  5. Click Calculate.
Result: 1/2 + 1/3 = 5/6

A common denominator of 6 is found first (3/6 + 2/6), then the numerators are added. The result is reduced to its simplest form.

Simplify 24/36

  1. Open the "Simplify Fraction" tab.
  2. Enter 24 as the numerator and 36 as the denominator.
  3. Click Calculate.
Result: 24/36 = 2/3

The GCD of 24 and 36 is 12, so both numbers are divided by 12.

Convert 0.75 to a fraction

  1. Open the "Decimal to Fraction" tab.
  2. Enter 0.75 in the decimal field.
  3. Click Calculate.
Result: 0.75 = 3/4

0.75 has 2 decimal places, so it becomes 75/100, then simplifies to 3/4 using the GCD of 25.

Tips

  • •The denominator can never be zero — the calculator rejects that input.
  • •For division, flip the second fraction and multiply (e.g., 1/2 ÷ 1/4 = 1/2 × 4/1 = 2).
  • •Fractions with denominators containing primes other than 2 and 5 produce repeating decimals.

Frequently asked questions

What is the Greatest Common Divisor (GCD)?
The largest number that divides evenly into both the numerator and denominator. For 24 and 36, the GCD is 12.
Why do fractions need a common denominator before adding?
Because you can only add parts of the same size. 1/2 and 1/3 cannot be added directly because halves and thirds are different sizes. Converting both to sixths (3/6 and 2/6) lets you add the numerators.
How do I divide fractions?
Keep the first fraction, flip the second fraction (its reciprocal), and multiply. For example, 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3.
Can a fraction have a negative denominator?
Yes, but the calculator normalises it. A fraction like 3/(−4) is rewritten as −3/4 so the denominator is always positive.
What is an improper fraction?
A fraction where the numerator is greater than or equal to the denominator (e.g., 5/4). The calculator handles improper fractions without issue.
Why does 1/3 produce a repeating decimal?
Because 3 is not a factor of any power of 10. Dividing 1 by 3 gives 0.333… repeating indefinitely. The calculator rounds to 4 decimal places.
How do I convert a mixed number (e.g., 2 1/2) to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and keep the same denominator. So 2 1/2 = (2×2+1)/2 = 5/2.
Can I enter decimals as fractions?
Not directly in the fraction fields — they accept integers only. Use the "Decimal → Fraction" tab instead, which converts any terminating decimal.
What happens if I enter a denominator of 0?
The calculator rejects the input with an error message. Division by zero is undefined in mathematics.
How do I know the fraction is fully simplified?
When the GCD of the numerator and denominator is 1. The calculator always does this final step automatically.
Is the decimal result exact or rounded?
Rounded to 4 decimal places. For fractions with denominators of 2 or 5, the decimal is exact. For others, it may be a rounded approximation of a repeating decimal.
Can I copy the result to use in another app?
Yes. Every result card has a Copy button. You can paste the fraction directly into Excel, Google Sheets, or a document.
What is the reciprocal of a fraction?
Swapping the numerator and denominator. The reciprocal of 3/4 is 4/3. Multiplying a fraction by its reciprocal gives 1.
Can I use this for mixed numbers?
Convert the mixed number to an improper fraction first (e.g., 2 1/2 → 5/2). The calculator works with proper and improper fractions.
How does the calculator simplify the final fraction?
It computes the GCD of the numerator and denominator, then divides both by that number.
Are negative fractions supported?
Yes. Enter a negative numerator and the sign carries through the calculation.
Is my calculation stored on a server?
No. Guest calculations stay in your browser and clear on reload. Signed-in users can sync history across devices.
What is the fastest way to convert a fraction to a decimal?
Divide the numerator by the denominator. 3 ÷ 4 = 0.75. The "Fraction → Decimal" tab does this instantly.
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