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Negative Fractions Calculator

Reviewed by Calculator Editorial Team

A negative fraction is a fraction with a negative numerator, denominator, or both. This calculator helps you perform operations with negative fractions, including addition, subtraction, multiplication, and division.

What is a Negative Fraction?

A negative fraction is any fraction where either the numerator or the denominator (or both) is negative. For example, -3/4 is a negative fraction because the numerator is negative. Similarly, 3/-4 is also a negative fraction because the denominator is negative.

Negative fractions are used in various mathematical contexts, including algebra, calculus, and physics. They represent quantities that are less than zero but are expressed as parts of a whole.

How to Calculate Negative Fractions

Calculating with negative fractions follows the same rules as working with positive fractions, but you must carefully consider the signs. Here's how to perform each operation:

Addition and Subtraction

To add or subtract negative fractions, follow these steps:

  1. Find a common denominator for the fractions.
  2. Convert each fraction to have the common denominator.
  3. Add or subtract the numerators while keeping the denominator the same.
  4. Simplify the resulting fraction if possible.

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

1. Common denominator: 4

2. Convert: (-3/4) + (-2/4)

3. Add: (-3 - 2)/4 = -5/4

4. Simplified: -5/4

Multiplication

To multiply negative fractions, multiply the numerators together and the denominators together. The result will be negative if there's an odd number of negative signs.

Example: (-3/4) × (-2/3)

1. Multiply numerators: -3 × -2 = 6

2. Multiply denominators: 4 × 3 = 12

3. Result: 6/12 = 1/2 (positive because two negatives multiply to positive)

Division

To divide negative fractions, multiply the first fraction by the reciprocal of the second fraction. Remember that dividing by a negative number is the same as multiplying by its positive counterpart.

Example: (-3/4) ÷ (-2/3)

1. Find reciprocal of second fraction: 3/-2

2. Multiply: (-3/4) × (3/-2) = (-3 × 3)/(4 × -2) = -9/-8 = 9/8

Examples

Here are some examples of calculations with negative fractions:

Addition Example

Calculate (-5/6) + (-1/3):

  1. Common denominator: 6
  2. Convert: (-5/6) + (-2/6)
  3. Add: (-5 - 2)/6 = -7/6

Subtraction Example

Calculate (-7/8) - (-3/4):

  1. Common denominator: 8
  2. Convert: (-7/8) - (-6/8)
  3. Subtract: (-7 + 6)/8 = -1/8

Multiplication Example

Calculate (-4/5) × (-3/7):

  1. Multiply numerators: -4 × -3 = 12
  2. Multiply denominators: 5 × 7 = 35
  3. Result: 12/35 (positive)

Division Example

Calculate (-9/10) ÷ (-3/5):

  1. Reciprocal of second fraction: 5/-3
  2. Multiply: (-9/10) × (5/-3) = (-9 × 5)/(10 × -3) = -45/-30 = 3/2

FAQ

How do you add negative fractions?
To add negative fractions, find a common denominator, convert the fractions, add the numerators, and simplify the result if possible.
Can you multiply negative fractions?
Yes, you can multiply negative fractions by multiplying the numerators and denominators. The result will be negative if there's an odd number of negative signs.
What happens when you divide negative fractions?
When you divide negative fractions, multiply the first fraction by the reciprocal of the second fraction. The result will be positive if there's an even number of negative signs.
How do you simplify negative fractions?
To simplify negative fractions, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by the GCD.
What is the difference between a negative fraction and a negative decimal?
A negative fraction is a fraction with a negative numerator or denominator, while a negative decimal is a decimal number less than zero. Negative fractions can be converted to negative decimals by dividing the numerator by the denominator.