Let us compare two like fractions:
3
and
8
8
Answers
Step-by-step explanation:
examples.
Example 1: Add 2/3 and 5/3
Solution: 2/3 + 5/3 = (2+5)/3 = 7/3
Example 2: Subtract 1/2 from 11/2.
Solution: 11/2 – 1/2 = (11-1)/2 = 10/2 = 5
Points to Remember
2/4, 4/8, 1/2, etc. are not like fractions, although when simplified, they all result in 1/2.
6/16 and 6/26 are not like fractions. The numerators are the same but denominators are not.
2, 3, 4 are like fractions since their denominators are considered as 1, which implies these fractions are 2/1, 3/1 and 4/1.
Unlike Fractions
Fractions with different denominators are called, unlike fractions. Here the denominators of fractions have different values. For example, 2/3, 4/9, 6/67, 9/89 are unlike fractions.
Unlike Fractions
Unlike Fractions
Since the denominators here are different, therefore it is not easy to add or subtract such fractions. To perform arithmetic operations like addition and subtraction in case of unlike fractions, we have to covert the unlike fractions into like fractions first. Then we perform the required operation.
Addition and Subtraction of Unlike Fractions
When we add and subtract two unlike fractions, we have to make the denominator equal first and then perform the respective operation. There are two methods by which we can make the denominator equal. They are:
Cross-Multiplication Method
LCM Method
In the cross multiplication method, we cross multiply the numerator of the first fraction by the denominator of the second fraction. Then multiply the numerator of the second fraction by the denominator of the first fraction. Now, multiply both the denominators and take it as a common denominator. Hence we can add or subtract the fractions now.
Example: Add 1/3 and 3/4
Solution: 1/3 + 3/4
By cross multiplication method, we get;
[(1 x 4) + (3 x 3)]/3 x 4
(4 + 9)/12
13/12 (Ans)
In the LCM method, first, we need to take the LCM of denominators of the given fractions. Now using this LCM, make all the fractions as like fractions. Then we can simplify the numerator.
Example: Add 3/8 and 5/12
Solution: 3/8 + 5/12
Now take the LCM of 8 and 12, we get;
LCM (8, 12) = 2 x 2 x 2 x 3 = 24
Now multiply the given fractions to get the denominators equal to 24, such that;
[(3 x 3)/(8 x 3)] + [(5 x 2) + (12 x 2)]
(9/24) + (10/24)
(9+10)/24
19/24. (Ans)
Conversion of Unlike to Like Fraction
Like fractions facilitate the comparison of fractions. So there is often a need to convert unlike fractions to them.
Let us convert 1, 4/5, 7/10 and 1/2 into like fractions. Steps for conversion:
Find the LCM of the denominators. LCM of 1, 5, 10 and 2 is 10.
Calculate their equivalent fractions with the same denominator, that is, the LCM.
1/1 = (1×10)/(1×10) = 10/10
4/5 = (4×2)/(5×2) = 8/10
7/10 = (7×1)/(10×1) = 7/10
1/2 = (1×5)/(2×5) = 5/10
1, 4/5, 7/10 and 1/2 which are unlike fractions can be represented as 10/10, 8/10, 7/10 and 5/10 which are like fractions.
It is to be noted that when the denominators become equal, the fractions can be compared. You would not be able to answer the largest among 1, 4/5, 7/10 and 1/2. But once they have been converted to 10/10, 8/10, 7/10 and 5/10, you can arrange them in the ascending order of 5/10, 7/10, 8/10 and 10/10 very conveniently.
Types of Fractions
There are majorly three types of fractions, they are:
Proper Fraction
Improper Fraction
Mixed Fraction
Proper and Improper Fractions
Similar to like and unlike fractions, we have another type of fractions, which are known as proper and improper fractions.
A proper fraction is a fraction that has a value less than 1. Or we can say, when the value of the numerator is less than the denominator, then such fractions are called proper fractions. For example, 1/2, 1/3, 4/5, 6/7, 8/