# Converting a Mixed Number to an Improper Fraction: Fraction Conversion

_{December 10, 2023 by JoyAnswer.org, Category : Mathematics}

How do you convert a mixed number into an improper? Discover how to convert a mixed number into an improper fraction. This article explains the steps for this conversion in mathematics.

## How do you convert a mixed number into an improper?

To convert a mixed number to an improper fraction, follow these steps:

### Example:

Let's use the mixed number 3 1/4 as an example.

### Steps:

**Multiply the whole number by the denominator of the fractional part:**- $3 \times 4 = 12$

**Add the result to the numerator of the fractional part:**- $12 + 1 = 13$

**Place the sum obtained in step 2 as the new numerator, and retain the denominator:**- The result is $13/4$.

### Conclusion:

So, the improper fraction equivalent of the mixed number 3 1/4 is $13/4$.

### General Formula:

If you have a mixed number $a \frac{b}{c}$, the corresponding improper fraction is given by:$\text{Improper Fraction} = \frac{(a \times c) + b}{c}$

In this formula:

- $a$ is the whole number,
- $b$ is the numerator of the fractional part, and
- $c$ is the denominator of the fractional part.

Simply follow these steps, and you can easily convert any mixed number into an improper fraction.

## How can you transform a mixed number into an improper fraction?

There are two main ways to transform a mixed number into an improper fraction:

**Method 1: Multiply and Add**

**Multiply the whole number part of the mixed number by the denominator of the fractional part.****Add the result from step 1 to the numerator of the fractional part.****Write the sum as the numerator of the improper fraction, and keep the denominator the same.**

**Example:**

Convert the mixed number 3 1/4 into an improper fraction.

**Solution:**

- 3 x 4 = 12
- 12 + 1 = 13
- The improper fraction is 13/4.

**Method 2: Least Common Multiple (LCM)**

**Find the least common multiple (LCM) of the denominators of the whole and fractional parts of the mixed number.****Multiply the whole number by the LCM divided by the denominator of the whole number.****Multiply the numerator and denominator of the fractional part by the LCM divided by the denominator of the fractional part.****Add the results from step 2 and 3.****Write the sum as the numerator of the improper fraction, and the LCM as the denominator.**

**Example:**

Convert the mixed number 3 1/3 into an improper fraction.

**Solution:**

- LCM of 3 and 3 is 3.
- 3 x (3/3) = 3
- 1 x (3/3) = 3
- 3 + 3 = 6
- The improper fraction is 6/3.

Both methods are valid for transforming mixed numbers into improper fractions. Choose whichever method you find easier and more convenient.