The word ‘fraction’ literally means broken, and the origin of the name comes from the Latin word ‘fractus.’ By a fraction, we mean a part of something that forms a whole. So, before getting into the details of how to divide fractions, you must know the detailed explanation for what a fraction means. In simple English, when we say a fraction of something, we mean a part of it. For example, we ½, or ¾ of a round cake means a fraction of it.
There are various types of fractions, out of which we will first talk about common, simple, and vulgar fractions. In all of these cases, the representation is simply a number on either side of a small line that divides them. For example, if we say 20/50, it merely means 20 parts of something whole that consists of 50 total pieces. In the equation, 20 is known as the numerator and 50 as the denominator. The concept of these two terms remains the same with other types of fractions, too, such as compound, mixed, and complex fractions.
When you want to know more about how to divide fractions, it is a must that you get into the smaller details of the same. For example, the denominator of a number cannot be zero. According to mathematical laws and rules, anything divided by zero results in ‘undefined.’ When we are discussing fractions, the denominator or the whole cannot be zero because speaking, you cannot divide something that is a zero into any number of parts. Moreover, a fraction can be represented in other forms too. For example, 1/100 can be represented in the decimal form as 0.001 or ¾ can be described as 3:4 in a ratio form.
Forms of fractions in details
You will know how to divide fractions better when you know about the different forms of fractions too. The list below gives a summarized version of the same.
1. Simple, common or vulgar fractions
All three terms are used for the same form of fractions. In this case, a rational number is represented as ‘a/b’ in which both the alphabets a and b are integer numbers. As mentioned earlier, the denominator cannot be a ‘zero.’ Besides, a simple or common fraction can be both negative and positive. Other forms of fractions, such as compound, mixed, and complex fractions, along with decimals, do not fall under this category of pure fractions. However, people often confuse the two concepts.
2. Improper and proper fractions
the solution of how to divide fractions becomes complicated when we do not know the details about the idea. We will now move on to improper and proper fractions that are parts of simple or common fractions. To define the concept of these two forms of portions, we can take an example of a fraction of two positive numbers.
Now, if the numerator is lower than the denominator, it is a proper fraction, and in case it is the opposite, you can term it as an improper fraction. The latter form is sometimes also called a top-heavy fraction.
3. Invisible denominator and reciprocals
When you exchange the position of the denominator and numerator with each other, they are called reciprocals of each other. For example, if you represent 3/7 as 7/3, the fractions are said to be reciprocals of each other. Another way of verification of the concept is that when you multiply a fraction with its reciprocal, a fraction, the reduced solution will always be ‘1’. For example, (3/7 x 7/3) = 21/21, which is the ultimate ‘1’.
Now, the second part of the section is about ‘invisible denominator,’ and it is one of the most straightforward concepts of all. Whenever the denominator of a certain fraction is ‘1’, it is equivalent to being invisible. For example, if you say 3/1, isn’t it the same as ‘3’? It is because any number divided by ‘1’ remains the same.
How to divide fractions by fractions?
Now, we have come to an essential part of the entire article in which you will learn how to divide fractions by fractions. Further, you will get a step by step demonstration of dividing fractions examples.
When you try to divide a fraction with another fraction, it may be a bit of confusion in the beginning. However, once you learn the technique, you will understand that it is one of the easiest parts of working with fractions.
1. Understand the meaning of the fraction
Suppose, the fraction for you to solve is two ÷ ½. So, the literal meaning of the question is for you to answer, “how many halves are there if the whole is two?” The simple answer to the equation is four. The logic is that if you take the entire equation as a cake and cut it into two parts, how many halves can you make out of each part. The answer is two halves out of each, and there are two more significant parts. So, the total comes to four.
What we find out in simple mathematics is that if you take the equations and numbers in the form of examples through objects that you see around you, the solution becomes easier. For instance, in this, we took the case of a cake, and it seemed to be so simple.
2. Differentiation of division with multiplication
As mentioned earlier, a reciprocal of a fraction is also called the ‘multiplicative inverse’ of it. So, the division of a fraction is the same as the multiplication of it with the reciprocal of the same. For example, let us take the same example of 2 ÷ 1/2. If we do the reciprocal, we get 2 x 2/1, which is the same as 2 x 2= 4. So, the answer comes to four in both ways you do it.
3. Memorizing the necessary steps of dividing one fraction by another one
The essential steps are as follows:
- Leave alone the first fraction in the entire equation
- Try to convert the division sign into that of multiplication
- Find the inverse or reciprocal of the second fraction
- Multiply both the numerators to get the final one.
- Do the same with the denominators.
- Now simplify and reduce the fraction to its simplest form.
Mathematics is often considered one of the most complicated subjects, and fractions are a crucial part of it all. Through this article, you can learn the basic concept of the lesson and also how to divide fractions most easily.