# 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:

1. Multiply the whole number by the denominator of the fractional part:

• $3 \times 4 = 12$
2. Add the result to the numerator of the fractional part:

• $12 + 1 = 13$
3. 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:

1. Multiply the whole number part of the mixed number by the denominator of the fractional part.
2. Add the result from step 1 to the numerator of the fractional part.
3. 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:

1. 3 x 4 = 12
2. 12 + 1 = 13
3. The improper fraction is 13/4.

Method 2: Least Common Multiple (LCM)

1. Find the least common multiple (LCM) of the denominators of the whole and fractional parts of the mixed number.
2. Multiply the whole number by the LCM divided by the denominator of the whole number.
3. Multiply the numerator and denominator of the fractional part by the LCM divided by the denominator of the fractional part.
4. Add the results from step 2 and 3.
5. 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:

1. LCM of 3 and 3 is 3.
2. 3 x (3/3) = 3
3. 1 x (3/3) = 3
4. 3 + 3 = 6
5. 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.

Tags Mixed Numbers , Improper Fractions

• ### How do you convert a mixed number to an improper fraction?

– Convert the mixed number or numbers to improper fraction Step 2 – Change the division sign to multiplication Step 3 – Change the fraction following the multiplication sign to its reciprocal (flip the fraction around so the old denominator is the new numerator and the old numerator is the new denominator) Step 4 - Multiply the numerators
Learn the process of converting mixed numbers to improper fractions through a step-by-step guide. Understand how to simplify fractions and perform mathematical conversions effectively. ...Continue reading

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Mathematics