Fraction Subtraction Calculator

Q: How do I subtract fractions with different denominators?

Find the LCD, convert both fractions, then subtract numerators. Example: 5/6 − 1/4 → LCD=12 → 10/12 − 3/12 = 7/12.

Q: Is subtraction of fractions commutative?

No. The order matters. a/b − c/d is NOT the same as c/d − a/b. Changing the order changes the sign of the result.

Subtract any two fractions with full step-by-step solutions. See LCD conversion, numerator subtraction, and automatic simplification with interactive visuals.

📐 Fraction Subtraction Calculator

Result

Visual Diagram

Definition

What is Fraction Subtraction Calculator?

A Fraction Subtraction Calculator subtracts one fraction from another, showing the complete step-by-step process including LCD conversion, numerator subtraction, and simplification.

Fraction subtraction follows the same common-denominator principle as addition. The key difference: subtract the numerators instead of adding them. When the result is negative, the answer is a negative fraction.

Fraction subtraction is used in measuring remaining quantities, finding differences between measurements, calculating changes in values, and solving algebraic equations.

Interactive Visualization

Formula

Fraction Subtraction Calculator Formula

Same Denominator: a/c − b/c = (a − b)/c

Different Denominators:

Find the LCD of the two denominators
Convert each fraction to the LCD
Subtract the numerators
Simplify the result

General formula: a/b − c/d = (a×d − c×b) / (b×d)

Example: 3/4 − 1/3 = 9/12 − 4/12 = 5/12

Examples

Worked Examples

3/4 − 1/3

LCD(4,3) = 12. Convert: 9/12 − 4/12 = 5/12. Result: 5/12.

5/6 − 1/4

LCD(6,4) = 12. Convert: 10/12 − 3/12 = 7/12. Result: 7/12.

7/8 − 3/8

Same denominator: (7−3)/8 = 4/8 = 1/2.

1/3 − 2/3

Same denominator: (1−2)/3 = −1/3. Result: −1/3.

FAQ

Frequently Asked Questions

Common questions about the fraction subtraction calculator.

How do I subtract fractions with different denominators?

Find the LCD, convert both fractions, then subtract numerators. Example: 5/6 − 1/4 → LCD=12 → 10/12 − 3/12 = 7/12.

Can the result of fraction subtraction be negative?

Yes. If the first fraction is smaller than the second, the result is negative. Example: 1/4 − 3/4 = −2/4 = −1/2.

How do I subtract mixed numbers?

Convert to improper fractions first, then subtract. Example: 3 1/2 − 1 3/4 → 7/2 − 7/4 → LCD=4 → 14/4 − 7/4 = 7/4 = 1 3/4.

What if the numerator becomes zero after subtraction?

If the numerator is zero, the result is 0, regardless of the denominator. Example: 5/8 − 5/8 = 0/8 = 0.

Is subtraction of fractions commutative?

No. The order matters. a/b − c/d is NOT the same as c/d − a/b. Changing the order changes the sign of the result.