Fraction Calculator for Negatives and Positives

How to Use This Calculator

Using our fraction calculator is simple. Follow these steps:

1. Enter the first fraction in the format "a/b" where a is the numerator and b is the denominator.
2. Select the operation you want to perform (+, -, ×, ÷).
3. Enter the second fraction in the same format.
4. Click "Calculate" to see the result.
5. Review the detailed calculation steps and simplified result.

The calculator will show you the full calculation process, including how to handle negative fractions, and present the final result in its simplest form.

Basic Fraction Operations

Adding Fractions

To add two fractions, follow these steps:

1. Find a common denominator by multiplying the denominators.
2. Convert each fraction to have the common denominator.
3. Add the numerators together.
4. Simplify the resulting fraction if possible.

Subtracting Fractions

The process for subtracting fractions is similar to adding:

1. Find a common denominator.
2. Convert each fraction to have the common denominator.
3. Subtract the numerators.
4. Simplify the result.

Multiplying Fractions

Multiplying fractions is straightforward:

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

Dividing Fractions

Dividing fractions involves multiplying by the reciprocal:

1. Find the reciprocal of the second fraction (swap numerator and denominator).
2. Multiply the first fraction by this reciprocal.
3. Simplify the result.

Working with Negative Fractions

Negative fractions follow the same rules as positive fractions but require careful attention to signs:

• When adding or subtracting fractions with the same sign, keep the sign and perform the operation.
• When adding or subtracting fractions with different signs, subtract the smaller absolute value from the larger and keep the sign of the larger fraction.
• When multiplying or dividing fractions, the sign of the result is positive if both fractions have the same sign, and negative if they have different signs.

Worked Examples

Example 1: Adding Positive Fractions

Calculate 1/4 + 1/6:

1. Find common denominator: 4 × 6 = 24
2. Convert fractions: (1×6)/24 + (1×4)/24 = 6/24 + 4/24
3. Add numerators: 6/24 + 4/24 = 10/24
4. Simplify: 10/24 = 5/12

Example 2: Subtracting Negative Fractions

Calculate -3/5 - (-2/5):

1. Subtracting a negative is the same as adding: -3/5 + 2/5
2. Add numerators: (-3 + 2)/5 = -1/5

Example 3: Multiplying Mixed Sign Fractions

Calculate -2/3 × 3/4:

1. Multiply numerators: -2 × 3 = -6
2. Multiply denominators: 3 × 4 = 12
3. Result: -6/12 = -1/2