Mixed Number to Improper Fraction Calculator

Understanding Mixed Numbers and Improper Fractions

What is a Mixed Number?

A mixed number is a combination of a whole number and a proper fraction. It represents a number that is between two whole numbers. For example, 3 1/4 is a mixed number that represents three and one-quarter.

What is an Improper Fraction?

An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). For example, 7/4 is an improper fraction.

Formula for Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we use the following formula:

\[a \frac{b}{c} = \frac{(a \times c) + b}{c}\]

Where:

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

Steps for Conversion

1. Multiply the whole number by the denominator of the fraction
2. Add this result to the numerator of the fraction
3. Write this sum over the original denominator

Example with Visual Representation

Let's convert 3 1/4 to an improper fraction:

1. \[3 \frac{1}{4} = \frac{(3 \times 4) + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}\]

This diagram visually represents the equivalence of 3 1/4 and 13/4.