Cal11 calculator
Search calculator...

3 Fraction Calculator with Negatives and Positives

Reviewed by Calculator Editorial Team

This calculator handles operations with three fractions, including both positive and negative values. It performs addition, subtraction, multiplication, and division of fractions while maintaining proper mathematical formatting.

How to Use This Calculator

To use the 3 fraction calculator:

  1. Enter the three fractions you want to calculate with. Each fraction has a numerator and denominator field.
  2. Select the operation you want to perform (addition, subtraction, multiplication, or division).
  3. Click "Calculate" to see the result.
  4. Review the simplified result and the step-by-step calculation process.

The calculator will automatically simplify the result to its lowest terms and handle negative values correctly.

Formulas Used

The calculator uses standard fraction arithmetic formulas:

Addition

a/b + c/d + e/f = (adf + bcf + bde)/(bdf)

Subtraction

a/b - c/d - e/f = (adf - bcf - bde)/(bdf)

Multiplication

a/b × c/d × e/f = (ace)/(bdf)

Division

a/b ÷ c/d ÷ e/f = (adf)/(bce)

After performing the operation, the result is simplified by dividing both numerator and denominator by their greatest common divisor (GCD).

Worked Examples

Example 1: Addition

Calculate 1/2 + 1/3 + 1/4:

  1. Find common denominator: 12
  2. Convert fractions: 6/12 + 4/12 + 3/12 = 13/12
  3. Simplify: 13/12 (already in simplest form)

Example 2: Subtraction

Calculate 5/6 - 1/3 - 1/4:

  1. Find common denominator: 12
  2. Convert fractions: 10/12 - 4/12 - 3/12 = 3/12
  3. Simplify: 1/4

Example 3: Multiplication

Calculate 2/3 × 3/4 × 4/5:

  1. Multiply numerators: 2 × 3 × 4 = 24
  2. Multiply denominators: 3 × 4 × 5 = 60
  3. Result: 24/60
  4. Simplify: 2/5

Example 4: Division

Calculate 3/4 ÷ 2/3 ÷ 1/2:

  1. Convert divisions to multiplications: 3/4 × 3/2 × 2/1
  2. Multiply numerators: 3 × 3 × 2 = 18
  3. Multiply denominators: 4 × 2 × 1 = 8
  4. Result: 18/8
  5. Simplify: 9/4

FAQ

Can this calculator handle negative fractions?
Yes, the calculator properly handles negative fractions in all operations. The sign of the result will be determined by the number of negative fractions in the operation.
What if I enter a denominator of zero?
The calculator will display an error message if you try to enter a denominator of zero, as division by zero is undefined in mathematics.
Can I perform mixed operations (like addition and multiplication together)?dt>
No, this calculator performs only one operation at a time. You would need to perform the operations separately and then combine the results.
Is the result always simplified to lowest terms?
Yes, the calculator automatically simplifies the result by dividing both the numerator and denominator by their greatest common divisor (GCD).
Can I use this calculator for decimal numbers?
No, this calculator is specifically designed for fractions. For decimal calculations, please use our decimal calculator instead.