Fraction Calculator

1. Enter the numerator and denominator of each fraction.
2. Choose an operation: add, subtract, multiply or divide.
3. Read the result as a simplified fraction, a decimal and a percentage, all updating live.

Each output shows the same answer in a different form:

A fraction represents a part of a whole, written as one number over another. The bottom number, the denominator, says how many equal parts the whole is divided into, and the top number, the numerator, says how many of those parts you have. So 3/4 means three of four equal parts.

Fractions that look different can be equal: 2/4 and 1/2 describe the same amount. Reducing a fraction to lowest terms, by dividing top and bottom by their greatest common divisor, gives the simplest way to write it.

It combines the two fractions using the rule for the chosen operation, then reduces the answer with the greatest common divisor.

Adding or subtracting needs a common denominator, so both fractions are put over d1 * d2 first, as in n1/d1 + n2/d2 = (n1*d2 + n2*d1)/(d1*d2). Multiplying simply multiplies across, and dividing multiplies by the reciprocal of the second fraction.

1. Apply the rule for the chosen operation to get a single fraction.
2. Find the greatest common divisor of the new numerator and denominator.
3. Divide both by it to reduce the answer to lowest terms.

Keeping the denominator positive ensures the sign sits with the numerator, where it reads naturally.

Add one half and one third. Over a common denominator of 6, 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Since 5 and 6 share no factor, five sixths is already in lowest terms, about 0.833 or 83.33 percent.

Multiply three quarters by two fifths: 3/4 * 2/5 = 6/20 = 3/10, which reduces from six twentieths to three tenths.

Divide seven eighths by one eighth by flipping the second fraction: 7/8 / 1/8 = 7/8 * 8/1 = 7, a whole number.

Each operation follows its own rule, and mixing them up is the most common source of error.

To find a common denominator by hand, the LCM calculator gives the least common multiple of the two denominators.

The answer depends on the numbers and the operation, and a few details shape the final form.

The Operation Chosen

Add, subtract, multiply and divide give very different results from the same two fractions, so pick carefully.

Common Factors

When the result shares a factor top and bottom, it reduces; a numerator that is a multiple of the denominator becomes a whole number.

Negative Signs

A negative fraction keeps its sign with the numerator, so subtraction can flip the result below zero.

Order for Subtraction and Division

Unlike addition and multiplication, these depend on which fraction comes first.

Homework and Study

Check fraction arithmetic quickly and see the simplified form to confirm your own working.

Cooking and Measuring

Combine or scale recipe amounts written as fractions of a cup or a teaspoon.

Woodwork and DIY

Add and subtract fractional inch measurements without slipping a sixteenth.

1. Adding Across the Top and Bottom

You cannot add numerators and denominators directly. Use a common denominator first.

2. Forgetting to Flip When Dividing

Dividing by a fraction means multiplying by its reciprocal, so turn the second fraction upside down.

3. Leaving the Answer Unsimplified

Reduce by the greatest common divisor so six twentieths becomes three tenths.

4. Mishandling Negatives

Keep the sign with the numerator and mind the order when subtracting.

5. Using a Zero Denominator

A denominator of zero is undefined, and you cannot divide by a fraction that equals zero.

The arithmetic is exact using whole-number numerators and denominators, with no rounding until the decimal form.

Put both over a common denominator, then add the numerators. For 1/2 + 1/3, use sixths: 3/6 + 2/6 = 5/6. This calculator finds the common denominator for you.

Multiply the numerators together and the denominators together, then simplify. For 3/4 x 2/5 that is 6/20, which reduces to 3/10.

Multiply the first fraction by the reciprocal of the second, meaning you flip the second upside down. So 7/8 divided by 1/8 is 7/8 x 8/1 = 7.

Divide the numerator and denominator by their greatest common divisor. For 6/20 the GCD is 2, giving 3/10, the lowest terms.

Only fractions of the same size can be added or subtracted directly. A common denominator gives both fractions equal-sized parts so their numerators can combine.

Divide the numerator by the denominator. So 5/6 is 5 divided by 6, about 0.833. This calculator shows the decimal automatically.

Enter them as improper fractions. A mixed number like 1 and 1/2 is 3/2, so use 3 as the numerator and 2 as the denominator.

A fraction with a zero denominator is undefined, so the calculator asks you to enter a non-zero denominator instead.

No. The calculation runs in your browser, and nothing you enter is sent anywhere unless you Save a result, which stays on this device only.

• Adding fractions (Maths Is Fun).
• Fractions (Maths Is Fun).
• Fraction (mathematics) (Wikipedia).