Improper Fraction to Mixed Number
In order to convert an improper fraction to a mixed number, we need to divide the numerator by the denominator. After the division, the mixed number is formed in such a way that the quotient that is obtained becomes the whole number, the remainder becomes the new numerator and the denominator remains the same. Let us learn more about converting an improper fraction to mixed number in this lesson.
1.  Conversion of Improper Fraction to Mixed Number 
2.  Conversion of Mixed Number to Improper Fraction 
3.  Adding Improper Fraction to Mixed number 
4.  FAQs on Improper Fraction to Mixed Number 
Conversion of Improper Fraction to Mixed Number
An improper fraction is a fraction in which the denominator is always less than the numerator. For example, 9/2 is an improper fraction. A mixed fraction or a mixed number is a combination of a whole number and a proper fraction. For example, \(2\dfrac{1}{7}\) is a mixed number where 2 is the whole number and 1/7 is the proper fraction.
To convert an improper fraction to a mixed number, we need to divide the numerator by the denominator and then find out the remainder and the quotient. Now, the quotient becomes the whole number of the resultant mixed fraction, the remainder becomes the numerator part of the mixed fraction and the denominator part remains the same.
For example, 7/3 is an improper fraction. Let us change this into a mixed number.
On dividing 7 by 3, we get 2 as the quotient and 1 as the remainder. Thus, 7/3 will be written as \(2\dfrac{1}{3}\) as a mixed number.
Conversion of Mixed Number to Improper Fraction
As we already know that an improper fraction is a fraction where the numerator is more than the denominator and a mixed number consists of a whole number and a proper fraction. So, while converting a mixed number into an improper fraction we multiply the denominator by the whole number then add the product with the numerator.
Let us convert the mixed number, \(5\dfrac{1}{7}\) to an improper fraction.
We will multiply the number 7 by 5 and the product is 7 × 5 = 35. To this, we will add the numerator 1, which makes it 35 + 1 = 36. Now, 36 becomes the new numerator and the denominator 7 remains the same. Therefore, \(5\dfrac{1}{7}\) is changed to an improper fraction and is written as 36/7.
Adding Improper Fraction to Mixed number
Adding an improper fraction to a mixed number is simple and easy. We need to convert the mixed number into an improper fraction and then we need to check the denominators of the given fractions which should be the same. In case they are the same, then the numerators can be added while the denominator remains the same. However, if the denominators are different, then they need to be changed to a common denominator. This is done by finding the LCM of the denominators and then the fractions can be added.
When the denominators are same
Example: Add 6/5 and \(4\dfrac{1}{5}\)
We will convert \(4\dfrac{1}{5}\) into an improper fraction
\(4\dfrac{1}{5}\) = 21/5
Now, add the numerators: 6/5 and 21/5
(6 + 21)/5 = 27/5. Now, we will finally convert this improper fraction to a mixed number = \(5\dfrac{2}{5}\)
When the denominators are not the same
Example: Add 6/5 and \(4\dfrac{1}{6}\)
We will convert \(4\dfrac{1}{6}\) into an improper fraction
\(4\dfrac{1}{6}\) = 25/6
Now, add 6/5 and 25/6
Since the denominators are different, we will make their values equal. For this, we need to find the Least Common Multiple (LCM) of the denominators. The LCM of 5 and 6 is 30. Now, we multiply both the fractions with such a number so that the denominators remain the same. This results in (36 + 125)/30 = 161/30. Now, let us convert the improper fraction to a mixed number: 161/30 = \(5\dfrac{11}{30}\)
Related Links
Check out the following pages related to the conversion of an improper fraction to mixed number.
Improper Fraction to Mixed Number Examples

Example 1: Convert the given improper fraction to a mixed number: 8/3
Solution: To convert the given improper fraction to mixed number we will divide 8 by 3 and write the remainder as the new numerator and quotient as the whole number.
8/3 = \(2\dfrac{2}{3}\)

Example 2: Write the steps to convert the given improper fraction to a mixed number: 23/11
Solution: To convert an improper fraction to a mixed number we use the following steps:
 We divide the numerator by the denominator. In this case, 23 is divided by 11, After the division, we get 2 as the quotient and 1 as the remainder.
 This quotient becomes the whole number for the resultant mixed number, and the remainder becomes the new numerator. The denominator remains the same.
23/11 = \(2\dfrac{1}{11}\)

Example 3: Add the improper fraction 31/5 to a mixed number \(2\dfrac{2}{5}\).
Solution: To add an improper fraction to a mixed number we will first convert \(2\dfrac{2}{5}\) into an improper fraction.
\(2\dfrac{2}{5}\) = 12/5
Now, we can add the fractions 31/5 and 12/5
Since the denominators are the same, (31+12)/5 = 43/5
Finally, we change the improper fraction to mixed number, 43/5 = \(8\dfrac{3}{5}\)
FAQs on Improper Fraction to Mixed Number
How to Convert an Improper Fraction to a Mixed Number?
In order to convert an improper fraction to a mixed number, we need to divide the numerator by the denominator and find out the quotient and the remainder. Now, the quotient becomes the whole number of the resultant mixed fraction and the remainder becomes the numerator part of the mixed fraction while the denominator part remains the same. For example, to convert 9/5 to a mixed number, we divide 9 by 5. After the division, we get 1 as the quotient and 4 as the remainder. So, 1 becomes the whole number and 4 becomes the new numerator of the resultant mixed fraction, thus, making it \(1\dfrac{4}{5}\)
How do you Convert a Mixed Number to an Improper Fraction?
In order to convert a mixed number to an improper fraction, we multiply the denominator of the mixed number by the whole number. After getting the product, we add the product and the numerator which will make it into an improper fraction. For example, let us convert \(8\dfrac{3}{5}\) to an improper fraction. We will multiply 5 by 8 and then the product 40 will be added to 3. The resultant improper fraction will be 43/5.
How to Change the Improper Fraction 34/8 to a Mixed Number?
First, we will divide the numerator 34 by 8 and then find the remainder and the quotient. On dividing 34 by 8, we get 4 as the quotient and 2 as the remainder. Thus, the quotient 4 becomes the whole number and 2 becomes the new numerator of the resultant mixed number, thus, making it \(4\dfrac{2}{8}\)
How to Convert a Negative Improper Fraction to a Mixed Number?
A negative improper fraction can be changed to a mixed number in the same way as we do any other positive improper fraction. The only change is the negative sign that will go along the converted mixed fraction. For example, let us convert 13/4 to a mixed number. We will first divide 13 by 4, which will give the quotient as 3 and the remainder as 1. Therefore, the mixed number will be written as \(3\dfrac{1}{4}\)
What is the First Step to convert 22/3 from an Improper Fraction to a Mixed Number?
The first step to convert an improper fraction to a mixed number is to divide the numerator by the denominator. After this step, the quotient that is obtained becomes the whole number, the remainder becomes the new numerator and the denominator remains the same. In this case, 22/3 need to be converted to a mixed number. So, the first step is to divide 22 by 3. 22 ÷ 3 gives 7 as the quotient and 1 as the remainder. The resultant mixed number will be written as \(7\dfrac{1}{3}\)