If a whole thing is divided into equal parts then each part is said to be a fraction. In other words, a fraction is a part of the whole. A fraction is formed up of two parts - numerator and denominator.
Expressed as - numerator/denominator.
The numerator tells us how many of the total parts are taken and the denominator tells us the total number of equal parts.
For example, in ¼ the top number ‘1’ is said to be the numerator and ‘4’ is said to be the denominator. Here we can say that 1 is taken from 4 equal whole parts. Fractions are very important to understand as it is used in our daily life.
Depending on the numerator and denominator, fractions are divided into different types. These types are given as below:
Here let us understand the concept of Like fractions and Unlike fractions in detail.
What is like a fraction?
In two or more fractions or a group of fractions when the denominator is exactly the same then they are said to be like fractions. Or you can say that fractions have the same number at the bottom.
Like fraction example - 2/4, 6/4, 8/4, 10/4.
Here we can see that the denominator of all the fractions is 4, so these fractions are called as like fractions.
Fractions like 2/8, 25/20, 9/12, 8/32 are also like fractions though they have different denominators because when they are written in the simplest form such as ¼, 5/4, ¾, ¼, we get the same denominator here 4.
Fractions like 4/2, 4/6, 4/10, 4 /13 are not like fractions. Here the numerators are the same but the denominators are different.
Natural numbers like 2, 5, 6, 8 are called fractions because they have the same denominator 1. They are written as 2/1, 5/1, 6/1, 8/1.
Like fraction example
Mathematical operations like addition and subtraction can be carried out easily with Like fractions. As the denominator is the same we have to just add or subtract the numerator accordingly.
When the denominators of two or more fractions are different then they are said to be unlike fractions. We can define it as fractions with different denominators are called,unlike fractions. Or you can say that fractions that have different numbers in the denominator are called unlike fractions.
Unlike fraction example, ⅜, 1/13, 5/16, are called unlike fractions.
Unlike fraction example
Mathematical operations like addition and subtraction are not as easy as like fractions. Because the denominator of unlike fractions are different. To carry out addition and subtraction with unlike fractions first we have to convert unlike fractions into like fractions.
There are two methods to convert unlike fractions to like fractions they are:
Cross multiplication method.
Cross multiplication method
To perform addition or subtraction of two unlike fractions, first, we have to simplify the fraction into simplest form and make the denominators as coprime or relatively prime, then we have to follow the steps explained below in cross multiplication method.
Step 1: Multiply the numerator of the first fraction by the denominator of the second fraction.
Step 2: Multiply the numerator of the second fraction by the denominator of the first fraction.
Step 3: Multiply the denominators of both fractions and take it as a common denominator for the results of step 1 and step 2.
Step 4: After simplification, we will get the fractions with the same denominators and now we can carry out the given operation.
Example: Add 2/5 and 4/3
2/5 + 4/3
Applying cross multiplication method, we get;
= [(2 x 3) + (4 x 5)]/5 x 3
= (6 + 20)/15
To perform addition or subtraction of two unlike fractions, first, check if denominators of the fractions are not coprime (there is a common divisor other than 1), then we have to apply this method. We have to follow these steps to use the LCM method.
Step 1: Find the least common multiple of the denominators of the given fractions.
Step 2: Using the least common multiple, make all the fractions like fractions.
Step 3: Now the denominator of all the fractions will be the same. So we can carry out the necessary operations.
Example: Add 5/8 and 9/12
5/10 + 9/12
Now take the LCM of 10 and 12, we get;
LCM (10, 12) = 2 x 2 x 5 x 3 = 60
Now multiply the given fractions to get the denominators equal to 60, such that;
=[(5 x 6)/(10 x 6)] + [(9 x 5) + (12 x 5)]
=(30/60) + (45/60)
Add 2/21 and ⅓.
2/21 + ⅓
Now take the L.C.M of 21 and 3, we get
L.C.M(21, 3) = 3 x 7 = 21
Now multiply the numbers to get the denominators equal to 21, such that,
=[(2 x 1)/(21 x 1) + [(1 x 7)/(3 x 7)]
=(2/21) + (7/21)
Subtract 2/7 from 5/7.
5/7 - 2/7
Now the denominators of these numbers are already equal.
So we can subtract 2/7 from 5/7 very easily.
= 5/7 - 2/7
i] 30/15 and 31/15
ii] 6/11 and 7/33
i] 10/8 from 21/8
ii] ½ from 5/8
How to convert unlike fractions to like fractions?
To carry out the mathematical operations like addition and subtraction we need to convert the unlike fractions to like fractions.
Let us convert 1/2, 3/4, 5/9, and 7/12 into like fractions.
Steps for conversion:
Find the LCM of the denominators 2, 4, 9,12 we get 36.
Calculate the fractions to make the denominators the same.
1/2 = (1×18)/(2 x 18) = 18/36
3/4 = (3 x 9)/(4 x 9) = 27/36
5/9 = (5 x 4)/(9 x 4) = 20/36
7/12 = (7 x 3)/(12 x 3) = 21/36
½, 3/4, 5/9, 7/12 which are unlike fractions can be represented as 18/36, 27/36, 20/36, and 21/36 which are like fractions.
How to find LCM of two numbers?
LCM stands for the least common multiple. The least common multiple is the smallest number that is the common multiple of all the given numbers. To find the LCM of given numbers first we have to write all the factors of the given numbers. Now multiply a
each factor the maximum number of times it occurs in either number. You will get the LCM of the numbers.
example: Let us find the LCM of 30 and 50
First, calculate the prime factors
30 = 2 x 3 x 5
50 = 2 x 5 x 5
Now, LCM = 2 x 5 x 3 x 5