Improper Fractions

Fractions are written in the form \(p\over q\). Every fraction has two parts: the numerator and the denominator. A fraction where the numerator is greater than the denominator is known as an improper fraction. For example, \(9\over 5\), where 9 is the numerator and 5 is the denominator. 

In this section, we will discuss the difference between improper and proper fractions.

A whole number and a proper fraction make a mixed fraction. It is written as  \(a{p\over q}\) where a = whole number, p, q are integers, \(q \neq 0\). 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. The mixed fraction is written as the quotient, followed by the proper fraction: quotient \((remainder ÷ denominator)\).
 

Step 3: Arrange the values as in step 2. 

For example, to convert \(8 \over 5\) to a mixed fraction 

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

So, \(8 \over 5\) can be written as \({1}{3\over5}\)

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 result from Step 1 to the numerator. 

Step 3: The sum from Step 2 becomes the numerator, and the denominator remains the same as in the mixed fraction.
 

Now let’s see how to convert \({2}{3\over 5}\)to an improper fraction.
 

Step 1: Multiplying the denominator by the whole number, that is, \(5 \times 2 = 10\).
 

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

Step 3: \({2} {3\over 5}\) can be written as \(13\over 5\).
 

Fractions and decimals are the most common ways to represent parts of a whole. For dividing the numerator by the denominator, convert the improper fraction to a decimal. For example, let’s convert \(11\over 5\) to a decimal. 

Dividing 11 by 5, that is, \(11 \div 5 = 2.2\)

So, \(11\over 5\) 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. 

Students often consider fractions as tricky. To master improper fractions, we will learn a few tips and tricks. It helps students to convert, simplify, and use improper fractions in real life. 

• Understand the concept of the improper fraction, that is, an improper fraction is a fraction where the numerator is equal to or greater than the denominator. 
   
• When converting the improper fraction to a mixed number, remember: \({mixed number} = {numerator\over denominator} = {{quotient} {remainder\over denominator}}  \)
   
• To convert a mixed number to an improper fraction, first multiply the whole number by the denominator, then ass the numerator. 
   
• Simplify the fraction whenever possible, so after calculation, check if the fraction can be simplified, whether the numerator and denominator have any common factors or not. 
   
• Memorize that if the numerator is greater than the denominator, then it's an improper fraction, and if the numerator is smaller than the denominator, then it's a proper fraction.

In our everyday life, we use fractions in different fields such as finance, cooking, construction, and more. 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 \(\frac{15}{5} = 3 \).  

• 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 \(1 \over 2\) mile. 
   
• To share quantities we use the improper fraction, for example, when dividing pizza, cakes, or any item into unequal portions.