Simplifying Negative Fractions Calculator

What is a Negative Fraction?

A negative fraction is any fraction where either the numerator (top number) or denominator (bottom number) is negative. For example:

• -3/4 (negative numerator)
• 3/-4 (negative denominator)
• -3/-4 (both negative)

Negative fractions can represent quantities less than zero, such as negative temperatures, debts, or measurements below a reference point.

How to Simplify Negative Fractions

Simplifying a negative fraction follows the same steps as simplifying a positive fraction, but with special attention to the negative sign:

1. Identify the greatest common divisor (GCD) of the absolute values of the numerator and denominator.
2. Divide both the numerator and denominator by the GCD.
3. Place the negative sign in the simplified fraction according to these rules:
   • If both original numbers were negative, the simplified fraction will be positive.
   • If only one original number was negative, the simplified fraction will be negative.

Worked Examples

Example 1: Simplifying -6/9

Step 1: Find the GCD of 6 and 9, which is 3.

Step 2: Divide numerator and denominator by 3: -6 ÷ 3 = -2, 9 ÷ 3 = 3.

Step 3: The simplified form is -2/3.

Example 2: Simplifying 8/-12

Step 1: Find the GCD of 8 and 12, which is 4.

Step 2: Divide numerator and denominator by 4: 8 ÷ 4 = 2, -12 ÷ 4 = -3.

Step 3: The simplified form is -2/3.

Example 3: Simplifying -4/-6

Step 1: Find the GCD of 4 and 6, which is 2.

Step 2: Divide numerator and denominator by 2: -4 ÷ 2 = -2, -6 ÷ 2 = -3.

Step 3: The simplified form is 2/3 (both signs cancel out).