Improper Fractions

Fractions are written in the form p/q, every fraction has two parts: that is the numerator and the denominator. A fraction where the numerator is greater than the denominator is known as an improper fraction. For example, 9/5, where 9 is the numerator and 5 is the denominator. 

As we discussed, there are different types of fractions. In this section, let's talk about the difference between improper and proper fractions.

A whole number and a proper fraction make a mixed fraction. It is written as a p/q where a = whole number, p, q are integers, q≠0. Converting improper fractions to mixed fractions is referred below:

Step 1: First, we divide the numerator by the denominator

Step 2: When converting an improper fraction to a mixed fraction, we consider the quotient as the whole number of the mixed fraction, and the remainder as the numerator and denominator will be the same for the proper fraction. That is the quotient (remainder/denominator). 

Step 3: Arrange the values as in step 2. 

For example, to convert 8/5 to a mixed fraction 

Dividing 8 by 5, the quotient is 1 and the remainder is 3

So, 8/5 can be written as 1 3/5

As we learned how to convert an improper fraction to a mixed fraction, now let’s discuss the conversion of the mixed fraction to an improper fraction in the following steps -

Step 1:  First, multiply the denominator by the whole number of the mixed fraction

Step 2: Then add the product from step 1 to the numerator 

Step 3: The sum from step 2 is the numerator, and the denominator will be the same as in the mixed fraction

Now let’s see how to convert 2 3/5 to an improper fraction

Step 1: Multiplying the denominator by the whole number, that is, 5 × 2 = 10

Step 2: Adding the product in Step 1 with the numerator, that is 10 + 3 = 13

Step 3: 2 3/5 can be written as 13/5

The most common way to represent a part of a whole is by using fractions and decimals. For dividing the numerator by the denominator, convert the improper fraction to a decimal. For example, let’s convert 11/5 to a decimal. 

Dividing 11 by 5, that is, 11 ÷ 5 = 2.2

So, 11/5 in decimal can be written as 2.2. 

Solving the improper fraction means performing the arithmetic operations, and the answer is simplified further and written as a mixed fraction. There are four basic arithmetic operations: addition, subtraction, multiplication, and division. 

Let’s solve the improper fraction: 7/5 + 6/5 

As both the fractions have the same denominator, so, we add the numerators. That is 7 + 5 = 12, so 7/5 + 6/5 = 13/5.

It can be written as 2 3/5 

In our everyday life, we use fractions in different fields such as finance, cooking, construction, and so on. These are the few real-life applications of fractions.

• To split the bills among the friends, we use fractions. That is, if the total cost is $15 and there are 5 people, the bill per person is $15/5 = $3.  

• In cooking, to adjust the ingredients according to the number of servings, we use fractions. 

• In construction, to measure the materials, floor, and so on, we use fractions.

• To represent the distances in road signs, we use fractions such as ½ mile.