Fractions Calculator

Using the calculator is straightforward. Select the operation you want to perform, enter the numerator and denominator for each fraction, then hit calculate. The result appears instantly, already reduced to its simplest form.

• For two-fraction operations (add, subtract, multiply, divide), fill in both fraction fields.
• For simplification, enter just one fraction and choose the simplify option.
• For conversion, enter your fraction or decimal in the appropriate field and select convert.

If you enter a zero in the denominator, the calculator will flag it. Division by zero is undefined, so that's expected behavior, not a bug.

Adding fractions requires a common denominator. If the denominators are already the same, you simply add the numerators and keep the denominator. When they're different, you need to find the least common denominator (LCD) first.

Here's the general process:

1. Find the LCD of the two denominators.
2. Convert each fraction so it has the LCD as its denominator.
3. Add the numerators together.
4. Simplify the result if possible.

For example, to add 1/3 and 1/4, the LCD is 12. Convert to 4/12 and 3/12, then add to get 7/12. That's already in its simplest form, so you're done.

Subtracting fractions works the same way as adding them, just with a minus sign. You still need a common denominator before you can subtract the numerators.

1. Find the LCD of both denominators.
2. Rewrite each fraction with the LCD.
3. Subtract the second numerator from the first.
4. Simplify the result.

Take 3/4 minus 1/6 as an example. The LCD is 12. That gives you 9/12 minus 2/12, which equals 7/12. Watch the sign carefully when the result is negative: if you're subtracting a larger fraction from a smaller one, you'll end up with a negative value, and that's completely valid.

Multiplication is actually the easiest fraction operation. No common denominator needed. You multiply straight across: numerator times numerator, denominator times denominator.

So 2/3 times 3/5 becomes (2×3)/(3×5), which is 6/15. Reduce that and you get 2/5.

One handy trick is to simplify before you multiply. If there's a common factor between any numerator and any denominator, cancel it out first. It keeps the numbers smaller and makes reducing the final answer easier. For instance, in the example above, you could cancel the 3s before multiplying and arrive at 2/5 directly without needing to reduce afterward.

Dividing fractions trips people up, but the method is consistent and simple once you know it. The key idea: dividing by a fraction is the same as multiplying by its reciprocal. That single rule covers every case.

A fraction is fully simplified when the numerator and denominator share no common factors other than 1. This is called being in lowest terms. Simplified fractions are easier to read, compare, and work with in further calculations.

The process always comes down to one thing: finding the GCF and dividing it out. The calculator does this automatically, but understanding the steps helps when you need to check your work by hand.

A mixed number combines a whole number and a fraction, like 2 3/4. An improper fraction has a numerator larger than (or equal to) its denominator, like 11/4. They represent the same value, just written differently.

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and put the result over the original denominator. So 2 3/4 becomes (2×4 + 3)/4 = 11/4.

Going the other direction, divide the numerator by the denominator. The quotient is the whole number part, and the remainder becomes the new numerator. So 11 ÷ 4 = 2 remainder 3, which gives you 2 3/4.

The calculator accepts both formats and converts between them as needed.

Converting a fraction to a decimal is simple: divide the numerator by the denominator. That's it. 3/4 becomes 3 ÷ 4 = 0.75. 1/3 becomes 0.3333... (a repeating decimal).

Some fractions convert to terminating decimals (they end cleanly), while others produce repeating decimals (a digit or group of digits repeats forever). Whether a fraction terminates depends on its denominator. If the denominator, in its simplest form, has only 2s and 5s as prime factors, the decimal terminates. Any other prime factor in the denominator means it repeats.

For practical use, repeating decimals are usually rounded to two or three decimal places. The calculator will show you the full decimal value and indicate if it repeats.

Going from a decimal back to a fraction takes a few more steps, but it's not complicated.

1. Write the decimal over 1 (e.g., 0.75/1).
2. Multiply both numerator and denominator by 10 for each digit after the decimal point. For 0.75, multiply by 100: you get 75/100.
3. Simplify the fraction. The GCF of 75 and 100 is 25, so 75/100 reduces to 3/4.

Repeating decimals require a slightly different approach using algebra, but for most everyday decimals with one to four decimal places, this method works perfectly. The calculator handles repeating decimals automatically if you enter them in the standard notation.

Here's a quick reference for the formulas behind each operation. All variables represent integers, with the denominators never equal to zero.

After applying any of these formulas, simplify the result by dividing numerator and denominator by their GCF. For addition and subtraction, using the product of the denominators (bd) as a common denominator always works, though finding the LCD first will give you smaller numbers to work with.

Here are a few worked examples covering each operation so you can see exactly how the math plays out.

• Addition: 2/5 + 1/3. LCD is 15. Convert: 6/15 + 5/15 = 11/15. No further simplification needed.
• Subtraction: 7/8 - 1/4. LCD is 8. Convert: 7/8 - 2/8 = 5/8. Already in lowest terms.
• Multiplication: 3/7 × 14/9. Cancel 7 and 14 (factor of 7), and 3 and 9 (factor of 3): you get 1/1 × 2/3 = 2/3.
• Division: 5/6 ÷ 2/3. Flip the second fraction: 5/6 × 3/2 = 15/12. Simplify by dividing by 3: 5/4, or 1 1/4 as a mixed number.
• Simplify: 36/48. GCF is 12. Divide both: 36÷12 = 3, 48÷12 = 4. Result: 3/4.

These examples follow the same steps every time. Once the pattern clicks, fractions become a lot less intimidating.