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Fraction Calculator with Negatives

Reviewed by Calculator Editorial Team

This fraction calculator handles negative numbers, allowing you to perform addition, subtraction, multiplication, and division with fractions that include negative values. Learn how to work with negative fractions and understand the rules for combining them.

How to Use This Calculator

Enter two fractions with their numerators and denominators. The calculator will perform the selected operation (addition, subtraction, multiplication, or division) and display the result in its simplest form.

For negative fractions, simply enter negative numbers in the numerator or denominator fields. The calculator will handle the sign rules automatically.

Remember that a negative sign in front of a fraction is equivalent to a negative numerator. For example, -1/2 is the same as -1/2, while 1/-2 is also -1/2.

Adding Negative Fractions

When adding fractions with negative numbers, follow these steps:

  1. Find a common denominator for both fractions.
  2. Convert each fraction to have the common denominator.
  3. Add the numerators together.
  4. Simplify the result if possible.

For fractions a/b and c/d, the sum is (a*d + c*b)/(b*d).

Example: (-1/2) + (-3/4) = (-2/4) + (-3/4) = -5/4

Subtracting Negative Fractions

Subtracting a negative fraction is the same as adding its positive counterpart:

  1. Find a common denominator.
  2. Convert both fractions to have the common denominator.
  3. Subtract the second numerator from the first.
  4. Simplify the result.

For fractions a/b and c/d, the difference is (a*d - c*b)/(b*d).

Example: (-1/2) - (-3/4) = (-1/2) + (3/4) = (-2/4) + (3/4) = 1/4

Multiplying Negative Fractions

When multiplying fractions with negative numbers:

  1. Multiply the numerators together.
  2. Multiply the denominators together.
  3. Simplify the result.

For fractions a/b and c/d, the product is (a*c)/(b*d).

Example: (-1/2) * (-3/4) = (3/8)

Remember that a negative times a negative is positive.

Dividing Negative Fractions

Dividing fractions with negative numbers involves:

  1. Multiplying by the reciprocal of the second fraction.
  2. Simplifying the result.

For fractions a/b and c/d, the quotient is (a*d)/(b*c).

Example: (-1/2) / (-3/4) = (-1/2) * (-4/3) = (4/6) = (2/3)

Worked Examples

Operation Example Solution
Addition (-1/3) + (-2/5) -13/15
Subtraction (-3/4) - (-1/2) -1/4
Multiplication (-2/3) * (-5/6) 10/18 = 5/9
Division (-4/5) / (-2/3) 6/5

FAQ

Can I use this calculator for mixed numbers?

This calculator works with improper fractions. For mixed numbers, convert them to improper fractions first by multiplying the whole number by the denominator and adding the numerator, then use that as your numerator with the original denominator.

What happens if I enter a zero denominator?

The calculator will display an error message since division by zero is undefined in mathematics.

How do I simplify the result?

The calculator automatically simplifies the result by dividing both the numerator and denominator by their greatest common divisor (GCD).