Mixed Fraction Calculator

Understanding Mixed Fraction Operations

What are Mixed Fractions?

A mixed fraction, also known as a mixed number, is a combination of a whole number and a proper fraction. It represents a number between two whole numbers. For example, 2 3/4 is a mixed fraction that represents 2 whole units plus 3/4 of a unit.

Formulas and Representation

To perform operations on mixed fractions, we typically convert them to improper fractions first. The formula for this conversion is:

\[a \frac{b}{c} = \frac{ac + b}{c}\]

Where:

• \(a\) is the whole number part
• \(b\) is the numerator of the fractional part
• \(c\) is the denominator of the fractional part

Basic Operations on Mixed Fractions

1. Addition and Subtraction:

   \[\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}\]

2. Multiplication:

   \[\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}\]

3. Division:

   \[\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}\]

Calculation Steps

1. Convert mixed fractions to improper fractions
2. Perform the desired operation using the appropriate formula
3. Simplify the resulting fraction
4. Convert back to a mixed fraction if necessary

Example and Visual Representation

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

This diagram illustrates the addition of 2 1/2 and 1 3/4. The result is 4 1/4, which is approximately 4.25 in decimal form.