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.

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.

Example: Convert the improper fraction into a mixed number: 7/3

Solution: 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.

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.

Example: Let us convert the mixed number, \(5\dfrac{1}{7}\) to an improper fraction.

Solution: 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 an improper fraction to a mixed number is simple. 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 \(4\dfrac{1}{5}\)

Solution: 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 \(4\dfrac{1}{6}\)

Solution: 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 become the same. This means we will multiply 6/5 with 6/6, that is, 6/5 × 6/6 = 36/30. And we will multiply 25/6 with 5/5, that is, 25/6 × 5/5 = 125/30. Now, they can be added and written as (36 + 125)/30 = 161/30. Now, let us convert the improper fraction to a mixed number: 161/30 = \(5\dfrac{11}{30}\)

☛ Related Links

• Mixed Number to Improper Fraction
• Mixed Fraction to Decimal
• Types of Fractions
• Comparing Fractions
• Decimals and Fractions

Cuemath is one of the world's leading math learning platforms that offers LIVE 1-to-1 online math classes for grades K-12. Our mission is to transform the way children learn math, to help them excel in school and competitive exams. Our expert tutors conduct 2 or more live classes per week, at a pace that matches the child's learning needs.

How to Convert 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 \(7\dfrac{1}{3}\)