# Converting Improper Fractions to Mixed Fractions and Vice Versa

In a previous lesson, we saw that there are three types of fractures:

• Proper Fractions: The numerator is less than the denominator. ()

Exemples: ; ;

• Improper Fractions: The numerator is greater than, or equal to, the denominator. ()

Exemples: ; ;

• Mixed numbers: There is a whole number and a fraction.

Exemples: ; ;

In this lesson, we will focus on the last two types, Improper Fractions and Mixed Fractions, so that we will see how to convert a mixed fraction to an improper fraction, and how to convert an improper fraction to a mixed fraction using a very simple rule. All you have to do, dear student, is to continue reading the lesson to the end, and re-perform the examples that we will see in this lesson.

## Converting Improper Fractions to Mixed Fractions

There are three very easy steps to convert an improper fraction to a mixed fraction, which are as follows:

• Divide the denominator by the numerator;

• Keep the obtained quotient as the whole part;

• Write the fraction part which the numerator is the remainder and the denominator is the original denominator;

• Write down the final result by combining the parts [Whole Part][Fraction Part];

### Info!

The fraction part is always a proper fraction.

### Examples of how to convert an improper fraction to a mixed fraction

#### Example1:

Convert to a mixed fraction.

#### Solution:

The denominator (28) is greater than the numerator (5), so is an improper fraction.

• Divide 28 by 5

• Quotient = 5 (then 5 is the whole part)

• Remainder = 3 (then is the fraction part)

Thus, the final answer is:

#### Example2:

Convert to a mixed fraction.

#### Solution:

The denominator (39) is greater than the numerator (4), so is an improper fraction.

• Divide 39 by 4

• Quotient = 9 (then 9 is the whole part)

• Remainder = 3 (then is the fraction part)

Thus, the final answer is:

#### Example3:

Convert to a mixed fraction.

#### Solution:

The denominator (85) is greater than the numerator (19), so is an improper fraction.

• Divide 85 by 19

• Quotient = 4 (then 4 is the whole part)

• Remainder = 9 (then is the fraction part)

Thus, the final answer is:

## Converting Mixed Fractions to Improper Fractions

For the reverse process, Converting a mixed fraction to an improper fraction is also easy, you just follow this three steps below.

### Note:

Let is a mixed fraction. To convert the mixed fraction to improper fraction we use the following formula:

Lets take some examples of converting the mixed fractions to improper fractions.

### Examples of how to convert an mixed fraction to a improper fraction

#### Example4:

Convert to an improper fraction.

#### Solution:

We can do the process in one go:

#### Example5:

Convert to an improper fraction.

#### Solution:

We can do the process in one go:

#### Example6:

Convert to an improper fraction.

#### Solution:

We can do the process in one go: