Subtracting Fractions Calculator

How to Subtract Fractions

Subtracting fractions follows the same principle as adding fractions — you need a common denominator before you can operate on the numerators.

Fraction Subtraction Formula

The shortcut formula for subtracting two fractions is:

a/b − c/d = (a×d − c×b) / (b×d)

This works by cross-multiplying to get matching denominators automatically. However, it's often easier to find the LCD first for smaller numbers.

Step One: Find a Common Denominator

Find the Least Common Denominator (LCD) of both denominators, then convert each fraction to an equivalent fraction with that denominator.

Example: Subtract 1/2 − 1/3.

• LCD(2, 3) = 6
• 1/2 = 3/6 (multiply by 3/3)
• 1/3 = 2/6 (multiply by 2/2)

Step Two: Subtract the Numerators

With matching denominators, subtract the second numerator from the first. Keep the denominator.

• 3/6 − 2/6 = (3 − 2) / 6 = 1/6

Step Three: Simplify

Simplify the result by dividing both numerator and denominator by their GCD. Convert to a mixed number if it's improper.

• 1/6 — GCD(1, 6) = 1, already simplified ✓

Subtracting Mixed Numbers

To subtract mixed numbers, first convert them to improper fractions, then follow the same steps.

Example: 3 1/4 − 1 2/3

1. Convert: 3 1/4 = 13/4, 1 2/3 = 5/3
2. LCD(4, 3) = 12
3. 13/4 = 39/12, 5/3 = 20/12
4. 39/12 − 20/12 = 19/12
5. As mixed number: 1 7/12

What if the Result is Negative?

When you subtract a larger fraction from a smaller one, the result is negative. This is perfectly valid.

Example: 1/4 − 1/2

• 1/4 = 1/4, 1/2 = 2/4
• 1/4 − 2/4 = −1/4

Frequently Asked Questions

Can you subtract fractions with different denominators?

Not directly — you must first convert them to equivalent fractions with a common denominator. Once the denominators match, subtract the numerators and keep the denominator.

What are the three rules for subtracting fractions?

1) Find the LCD and convert both fractions. 2) Subtract the numerators, keeping the denominator. 3) Simplify the result using the GCD.

Why can't you subtract the denominators?

Denominators represent the size of each piece, not a quantity. Subtracting them would change the piece size, which doesn't make mathematical sense. You can only subtract numerators (the number of pieces) once the pieces are the same size.

Can you subtract fractions and decimals together?

Yes, but first convert everything to the same format. Either convert the decimal to a fraction or convert the fraction to a decimal, then subtract.

What if the fractions already have the same denominator?

Even easier! Skip Step One and just subtract the numerators directly. For example, 5/8 − 3/8 = (5 − 3)/8 = 2/8 = 1/4.