How to Divide Fractions?

Divide Fractions

Among mathematical operations possible, the division is one of the most commonly used operations. Similarly, among the many different kinds of numbers possible, fractions happen to be often involved in the day to day life. Thus, when it comes to dividing fractions , it is an important skill to have to do some basic mathematical operations.

Math worksheets are very helpful in learning these basic concepts of fractions in detail. Such practice worksheets are easily available online. Websites like Cuemath provide interactive and visually appealing websites to help students strengthen the understanding of the subject. These worksheets are based on a variety of topics covering all sorts of fractions; students will get familiar with working and understanding the different types of fractions. The partial fraction worksheets are easy to download and can be printed and used at home or classroom. Based on the age of the child, there are a variety of worksheets to choose from depending on their understanding level.

Division as an operation implies that how many times a number is equal to another number. So, another way of looking at it is that the division is the opposite of multiplication. Now when dealing with non-fractional numbers, it’s easy to notice that multiplication of two non-fraction numbers gives a bigger number than them both, and division of two numbers gives a smaller number. But in the case of the division of fractions, the resultant number can be bigger than both of the fractions.

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Fractions are special in the way that there are infinite fractions possible between any two numbers and also many infinite fractions possible between any two fractions. Compare it with whole numbers where while the total whole number count is infinite, the count of whole numbers between any two whole numbers is finite. Thus, fractions have a much wider variety than whole numbers as there are infinite series of each having many infinite fractions.

There are many different types of fractions like proper fractions, improper fractions, mixed fractions, equivalent fractions, like and unlike fractions. Between the proper and improper fractions, the difference is obvious. If the numerator is smaller than the denominator, then it is a proper fraction, and if the numerator is bigger than the denominator, then the fraction is improper. When two fractions have the same denominator, then they are called like fractions. In the case of the like fractions, addition and subtraction are easier as then we can keep the denominator constant and add or subtract the numerator.

Before we dive into the division of fractions, it is important to understand the reciprocal of the fraction. Let’s take an example of fraction, 3/4. If number 1 is divided by this fraction, it would be the same as the reciprocal of the fraction 3/4. So, 1 divided by 3/4 gives 4/3 as an answer. Now let us see how we can divide fractions by taking the example of two fractions, 3/4 and 2/3

3/4 divided by 2/3 

Let Y = 3/4 divided by 2/3

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Y = 3/4 multiplied by (1 divided 2/3)

Y = 3/4 multiplied by (3/2)

Y = 9/8

Note the result is bigger than any of the two fractions involved in the division.

Notice that in the division of fractions, it is, in fact  , the multiplication of one fraction with the reciprocal of the other.

Let us see some more examples of fraction division:

1/2 divided by 3/2

= 1/2 * 2/3

= 1/3

Above we divided a proper fraction with an improper fraction, but the method is the same.

Division of 8/9 and 6/7

= 8/9 * 7/6

= 56/54

= 28/27

When learning the division of fractions, keep in mind that the basic concept of division is to tell how many times a number, when added with itself, will give the other number.

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