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Fractions Calculator with Negatives and Mixed Numbers

Reviewed by Calculator Editorial Team

This fractions calculator handles negative numbers and mixed numbers with precision. Whether you're adding, subtracting, multiplying, or dividing fractions, this tool provides accurate results with clear explanations.

How to Use This Calculator

Using this fractions calculator is straightforward. Follow these steps:

  1. Select the operation you want to perform (addition, subtraction, multiplication, or division).
  2. Enter the first fraction in the provided fields. You can enter mixed numbers by specifying the whole number, numerator, and denominator.
  3. Enter the second fraction in the same way.
  4. Click the "Calculate" button to see the result.
  5. Review the detailed explanation and any additional information provided.

The calculator will display the result in its simplest form and provide a step-by-step explanation of how the calculation was performed.

Formulas Used

The calculator uses standard fraction arithmetic formulas:

Addition

To add two fractions, find a common denominator and add the numerators:

a/b + c/d = (a×d + b×c)/(b×d)

Subtraction

To subtract two fractions, find a common denominator and subtract the numerators:

a/b - c/d = (a×d - b×c)/(b×d)

Multiplication

To multiply two fractions, multiply the numerators together and the denominators together:

a/b × c/d = (a×c)/(b×d)

Division

To divide two fractions, multiply by the reciprocal of the second fraction:

a/b ÷ c/d = (a×d)/(b×c)

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

Worked Examples

Here are some examples of how to use the calculator:

Example 1: Adding Fractions

Calculate 1/2 + 1/3:

  1. Find a common denominator: 6
  2. Convert fractions: 3/6 + 2/6 = 5/6
  3. Result: 5/6

Example 2: Subtracting Fractions

Calculate 3/4 - 1/2:

  1. Find a common denominator: 4
  2. Convert fractions: 3/4 - 2/4 = 1/4
  3. Result: 1/4

Example 3: Multiplying Fractions

Calculate 2/3 × 3/4:

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

Example 4: Dividing Fractions

Calculate 1/2 ÷ 3/4:

  1. Multiply by reciprocal: 1/2 × 4/3 = 4/6
  2. Simplify: 4/6 = 2/3
  3. Result: 2/3

Frequently Asked Questions

Can this calculator handle negative fractions?

Yes, this calculator can handle negative fractions. Simply enter a negative number in the numerator or denominator field, and the calculator will process it correctly.

How does the calculator simplify fractions?

The calculator simplifies fractions by dividing both the numerator and denominator by their greatest common divisor (GCD). This ensures the result is in its simplest form.

Can I use mixed numbers with this calculator?

Yes, you can enter mixed numbers by specifying the whole number, numerator, and denominator. The calculator will convert them to improper fractions for calculation and then back to mixed numbers if needed.

What if I enter a zero in the denominator?

The calculator will display an error message if you enter a zero in the denominator, as division by zero is undefined in mathematics.