A fraction is a number that represents a part of a whole thing or a group of objects. It is defined by two integers, one at the top and one at the bottom of a fraction bar, known as the numerator and denominator. We divide two or more fractions into Like Fractions and Unlike Fractions based on the similarity of the denominator. They are also known as similar fractions and dissimilar fractions at times.
Like means the same as opposed to unlike, which denotes dissimilar. Here, let’s learn to perform the arithmetic operations on both the type of fractions, as well as how to convert an unlike fraction into a like fraction with examples.
Like Fractions are a set of two or more fractions that have the same denominator. Alternatively, Like fractions are those that have the same integers in their denominators. For example, 1/7, 2/7, 5/7, and 6/7 are all fractions with denominators of 7.
Like fractions, mathematical operations like addition and subtraction are simple to perform. While performing both operations, the denominators do not need to be neutralised. Let’s use examples to better understand.
Addition and Subtraction of Like Fractions
When we add or subtract like fractions, the denominator remains constant and only the numerators are added or subtracted. Here are some instances.
Example 1: Add 2/5 and 4/5
Solution: 2/5 + 4/5 = (2+ 4)/5= 6/5
Example 2: Subtract 1/3 from 11/3.
Solution: 14/3 – 2/3 = (14-2)/3 = 12/3 = 4
Unlike fractions are fractions having different denominators. The denominators of fractions have various values in this case. 2/3, 4/9, 6/67, and 9/89 are all unlike fractions.
Since the denominators are different, it is difficult to add or subtract such fractions. To perform arithmetic operations such as addition and subtraction, unlike fractions must first be converted into like fractions. Then we carry out the necessary operation.
Addition and Subtraction of Unlike Fractions
When we add and subtract two dissimilar fractions, we must first make the denominator equal before doing the appropriate operation. There are two methods for making the denominator equal. They are as follows:
- Cross-Multiplication Method
- LCM Method
We cross multiply the numerator of the first fraction by the denominator of the second fraction in the cross multiplication method. Then divide the denominator of the first fraction by the numerator of the second fraction. Multiply both denominators and use the result as the common denominator. The fractions can now be added or subtracted.
Conversion of Unlike to Like Fraction
Like fractions make fraction comparison easier. As a result, it is frequently necessary to convert dissimilar fractions to them.
Let us convert the fractions 1,2/5, 9/10, and 1/2 into like fractions. Conversion process:
- Determine the denominators’ LCM. The LCM of 1, 5, 10, and 2 is 10.
- Calculate the LCM of their comparable fractions with the same denominator.
1/1 = (1×10)/(1×10) = 10/10
2/5 = (2×2)/(5×2) = 4/10
9/10 = (9×1)/(10×1) = 9/10
1/2 = (1×5)/(2×5) = 5/10
1, 2/5, 9/10, and 1/2 are unlike fractions, whereas 10/10, 8/10, 7/10, and 5/10 are like fractions.
It should be noted that the fractions can be compared once the denominators are equal. You would be unable to respond to the largest among 1, 2/5, 9/10, and 1/2. However, if converted to 10/10, 4/10, 9/10, and 5/10, they can be easily arranged in ascending order of 5/10, 4/10, 9/10, and 10/10.