Dividing Fractions in Mathematical Terms!

Have you ever thought about it mathematically, if you take half of a pizza and further divide it into two equal parts then each portion shall be a quarter of the whole pizza.


This is called Dividing Fractions.

Division means sharing an item equally in n parts. Division can be of whole numbers, fractions or decimals.

Equivalent Fractions

Any two fractions having the same value are called Equivalent fractions. Also equivalent fractions can have different values in their numerator and denominator but have the same value. By multiplying or dividing numerator and denominator with the same number we can make equivalent fractions.

Different Methods for Determining Equivalent Fractions

       Method 1: Making the Denominators the same.

       Method 2: Cross multiplying the fractions.

       Method 3: Converting to decimals

 Forming Equivalent Fractions:

1. Multiplying numerator and denominator by the same number.

If we take a fraction ⅓ , by multiplying top and bottom by 2 it will become 2/6. These two fractions ⅓ and 2/6 are equivalent fraction.

2. Dividing the numerator and the denominator by the same number.

Let's take 6/9. if instead of multiplying we divide top and bottom by 3 we will get ⅔. These two fractions 6/9 and ⅔ are also equivalent fractions.

Steps to Divide Fractions:

       Keep the first fraction as it is.

       Reciprocate the second fraction(which we want to divide) i.e; upside down.

       Now, multiply the first fraction by its reciprocal.

       If needed, simplify the fraction.

Dividing Fractions by Fractions

As we learned above, for dividing fractions here we will apply the same rule.

steps included are as follows :-

       Reciprocate the 2nd fraction.

       Now, multiply this flipped fraction with the 1st fraction which is unchanged.

       If needed, simplify the result.

Dividing a Fraction by a Whole Number

We know that a number when divided by 1 is the number itself.

Following are the steps for division of fractions by a whole number:

       Convert the whole number into a fraction by dividing with 1.

       Reciprocate this number.

       Multiply the reciprocal value with the fraction.

       Simplify the result.

Dividing Fractions With Decimals

Decimal numbers are a fraction to base 10 and we can convert decimal into fractions.

Following are the steps for dividing Fractions with decimals:

       Convert the given decimal into fraction by putting 10^n in the denominator.

       Divide both the fractions.

Dividing Fractions Used in Everyday Life

       In shopping - When we go shopping and we have to calculate the cost of the product after discount, we must have knowledge of division of fractions.

       In cooking - When we bake something or are making some dishes we require an exact amount of each ingredient and here we need to know dividing fractions.

       Eating out with someone - Have you ever gone out to dine with friends? Here also we need to use fractions for dividing the bill.

       Shopping of Grocery items - When we see invoices for shopping,sales tax and coupons all use fractions.

       In understanding the purity of the jewellery.

       Time - Time is also measured in fractions like a quarter of an hour, half of an hour.

Some Interesting Facts About Fractions

       The word Fraction means a part of the whole and this word fraction is derived from the Latin word "Fractio" which means to break.

       The line in between the numerator and the denominator is called a vinculum, which also means a ligament that limits the movement of an organ or part.

       Pi,golden ratio are examples of irrational numbers which can not be expressed as fractions.

       The numerator of fraction tells us how many equal parts of the collection are taken.(For example, if you divide an apple in 6 slices and take 4 slices then the numerator would be 4).

       The denominator shows the total number of equal parts in the collection.(For example, an apple has a total of 6 slices,the denominator of the fraction would be 6).