Mixed Number Calculator

How to Calculate with Mixed Numbers

Mixed numbers are a combination of a whole number and a proper fraction. When performing operations with mixed numbers, we typically convert them to improper fractions first. Here's a comprehensive guide on how to use the mixed number calculator and understand the calculation process:

Mixed Number Operations Formulas

For mixed numbers \(a \frac{b}{c}\) and \(d \frac{e}{f}\):

• Addition: \(a \frac{b}{c} + d \frac{e}{f} = \frac{ac+b}{c} + \frac{df+e}{f}\)
• Subtraction: \(a \frac{b}{c} - d \frac{e}{f} = \frac{ac+b}{c} - \frac{df+e}{f}\)
• Multiplication: \(a \frac{b}{c} \times d \frac{e}{f} = \frac{ac+b}{c} \times \frac{df+e}{f}\)
• Division: \(a \frac{b}{c} \div d \frac{e}{f} = \frac{ac+b}{c} \times \frac{f}{df+e}\)

Calculation Steps

1. Convert mixed numbers to improper fractions.
2. Perform the operation using the improper fractions.
3. Simplify the result and convert back to a mixed number if necessary.

Example Calculation

Let's add 2 1/3 and 1 1/4:

1. Convert to improper fractions:
   • 2 1/3 = (2 × 3 + 1) / 3 = 7/3
   • 1 1/4 = (1 × 4 + 1) / 4 = 5/4
2. Add the fractions:

   7/3 + 5/4 = (7 × 4 + 5 × 3) / (3 × 4) = 43/12

3. Simplify and convert to mixed number:

   43/12 = 3 7/12

Visual Representation