# Fractions

Mathematics can be fun, that’s right. There’s maths all around us, every time we quantify something, there’s math involved. A fraction is a word that originated from Latin. In Latin, Fractus means broken. It is entirely too apt, the meaning fits beautifully with its purpose. Since a fraction represents the part of a whole, or more generally any number of equal parts. That well-known quote, that goes something like this, glass half full, or glass half empty” has also made use of fractions.

Fractions in maths are painful if you do not grasp the underlying concept behind it. Fractions form an important part of our daily lives. We have to willingly or unwillingly share that yummy pizza amongst our friends and families. Three people, four slices. Ouch.

If you learn and visualize fractions the easy way, it will be more fun and exciting. Slice an apple, and we get fractions.

Fill half a glass of water. What do you see? 1/2 glass is full. Or 1/2 glass is empty. This 1/2 is fractions where 1 is the Numerator that is, the number of parts we have. And 2 is the Denominator, the number of parts the whole glass is divided into. You can quickly add fractions with the same denominator. Just add the numerator, keeping the denominator same.

A fraction simply tells one, how many parts of a whole there are. It is symbolized by using a slash between two numbers. Like this 2/4. The number on top is the numerator, while the number below is the denominator. In the given example, the number on top 2 happens to be the numerator while, the number on the bottom, 4 will end up being the denominator. Now we shall visualize this fraction. Imagine a pie with four slices. Taking two slices of pie for yourself would mean that you have two out of the four. Hence, you represent it as 2/4. There is also a concept called proper fractions and improper fractions. The proper fractions are those where the numerator is more than the denominator and the improper fractions, as one can deduce, is the fractions where the numerator happens to be greater than the denominator. For example, 8/9 will be a proper fraction since numerator<denominator and 9/8 will be an improper fraction since denominator<numerator.

And then there’s the concept of like and unlike fractions. In this, like fractions are those fractions, as the name suggests, that are alike or same. While, on the other hand, the unlike fractions, are those that are dissimilar. For example, take ½ and 2/4; they are alike since if you simplify it mathematically, you will get the same fraction. And ½ and 1/3 are unlike fractions.

So, 1/2 +1/2 =2/2 that is one full glass, which is 100 %. Yes, if you are clear infractions then percentages are already covered. Just multiply the fraction with 100.

If the Denominator is the same, adding and subtracting fractions is an easy task. But how do you add 2/4 + 3/9?

Or how will you solve 6/12- 3/27? This is adding and subtracting fractions with unlike denominators.

Is 12/6 also a fraction? Yes, it is. It is called an improper fraction. But 6/12 is a proper fraction.

6/12 is an equivalent fraction to 3/6 as both equal to 1/2.  We can multiply fractions, divide fractions, divide fractions by fractions and so much more.

A lot of word problems on fractions appear in our textbooks to compare fractions, multiply mixed numbers and improper fractions, decimals, and fractions. Confusing? It will become easy if you visualize the number fractions and then solve systematically. Learn about types of fractions by visiting BYJU’S.

BYJU’S provides students with NCERT solutions for Fractions so that students can practice and solve problems easily. For NCERT solutions click here – Fractions

##### Fractions

Any part of a quantity into which it is divided is known as fraction. Generally, a fractions denotes the number of equal parts into which a quantity is divided.  For example, the slices of pizza are equally divided into parts and each part represents a fraction, each centimeter marked on a ruler represents a fraction of length.

##### Representation of Fractions:

You and your friends went to a pizza shop to buy a pizza. If you take 3 slices out of 4 slices of pizza, the fraction of pizza which you took is $$\frac{3}{4}$$.

$$\frac{3}{4}$$ means 3 parts out of 4 parts. Depending on how many slices you have taken, the fraction would be $$\frac{1}{4}\frac{2}{4}\frac{3}{4}$$ or $$\frac{4}{4}$$. In the last case, since you’ve taken up ‘ALL’ the slices, it means you have consumed the entire pizza, you no longer need the concept of dividing it, hence it can now be deduced to a whole number that is unity.

The bottom part of a fraction represents the total number of parts and is known as denominator. The top part of a fraction is the number of parts taken out of the total parts and is known as the numerator.

This implies that a fraction can be represented in the form of numerator and denominator where the denominator cannot be equal to zero.

We observe that the denominator is greater than the numerator in above cases. The fraction becomes a whole – a unit, i.e. 1, if the numerator is equal to the denominator.

What happens if the numerator is greater than the denominator? Is this possible? What if you have got 3 additional slices of the same kind of pizza after eating the first four slices? How would you represent this? You have eaten 7 slices from two pizzas which are made up of 4 slices each. That means, you’ve eaten up  $$\frac{7}{4}$$ of the pizza! Observe that you have eaten more than 1 pizza that had 3 extra slices. These 3 slices of another pizza would be represented as $$\frac{3}{4}$$. So, you’ve eaten 1 pie and another $$\frac{3}{4}$$ of another pie.

The inference is indeed true. The fractions such as these, where the numerator is greater than the denominator are known as improper fractions and the ones where the numerator is lesser than the denominator are known as proper fractions.

Improper fractions can be written as a combination of a whole number and a proper fraction. Such fractions are known as mixed fractions.

To convert a mixed fraction into an improper fraction following steps are followed:

##### Equivalent Fractions:

Every proper and improper fraction can have their equivalent fractions. Equivalent fractions can be obtained by multiplying or dividing the numerator and denominator of the given fraction by same number.