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IBPS PO Mains Preparation . 738526
Last Modified 26-03-2025
IBPS PO Mains Preparation Guidelines
March 26, 2025
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Comparison of Fractions With the Same Denominator
Comparing fractions means figuring out which of two or more fractions is greater and which is smaller. As fractions include two elements – a numerator and a denominator – we must compare them according to a set of rules. In this article, we will learn more about comparing fractions.
It is also possible that a piece or section of any quantity is also known as a fraction. It is represented by the ‘/’ sign, as in a/b. For example, 2/4 is a fraction with the numerator in the upper part and the denominator in the lower part. We will learn the definition of fractions in mathematics, the many types of fractions, how to convert fractions to decimals, and numerous solved problems with detailed explanations in this post.
What Is the Definition of a Fraction?
Let us review fractions before moving on to the concept of comparing fractions. A fraction is a subset of a whole that has two parts: the numerator and the denominator. The numerator is the number on the fractional bar’s upper half, while the denominator is the number on the fractional bar’s lower half.
Let us talk about fraction comparisons in more detail now.
How to Compare Fractions?
When two fractions are compared, we can determine which is greater and which is smaller. In our daily lives, we must compare fractions. For example, while comparing the proportions of ingredients while following a recipe or comparing exam grades, etc. So, to further comprehend the notion, let us go over the various methods of comparing fractions.
1/2 x 1/3= 3/6 and 1/3 x 1/2 = 2/6.
3/6 > 2/6. Therefore, 1/2 > 1/3
Comparing Fractions Using the Same Denominator Method
Every fraction, as we all know, is made up of two terms: the numerator and the denominator. The numerator is at the top, while the denominator is at the bottom. Consider the fraction 3/4 as an example. The numerator is 3 and the denominator is 4.
Using the Same Denominator Method to Compare Fractions Example:
Like fractions can be simply compared because their denominators are the same, but unlike fractions must be changed to like fractions before being compared. Let us look at the comparison procedure for both of these categories.
When two fractions have the same denominator, comparing them is simple.
- 1st Step: Consider the following two fractions: 3/4 and 1/4.
- 2nd Step: 3/4 denotes three of the four sections. The required fraction is represented by the shaded region displayed below.
- 3rd Step: Because the denominator is the same, the greater fraction can be determined solely by comparing the numerator.
- 4th Step: The numerator of the fraction 3/4 is greater than the numerator of the fraction 1/4, i.e. the numerator 3 of the fraction 3/4 is greater than the numerator 1 of the fraction 1/4.
- 5th Step: When two fractions have the same denominator, this is a way to compare them.
Using the Unlike Denominator Method to Compare Fractions Example:
We must convert unlike denominators to like denominators before comparing fractions. To do so, we must find the Least Common Multiple (LCM) of the denominators. We can simply compare fractions when the denominators are the same. Let us look at 1/2 and 2/5 as an example.
- 1st Step: Look at the denominators of the fractions given: 1/2 and 2/5. They are not the same. Let us look for the LCM of 2 and 5. 10. LCM(2, 5) = LCM(2, 5) = LCM(2, 5) = L
- 2nd Step: Now let us convert them such that the denominators are all the same. Let us multiply the first fraction by 5/5, which equals 1/2 5/5 = 5/10.
- 3rd Step: Multiply the second fraction by 2/2, which equals 2/5 2/2 = 4/10.
- 4th Step: Make a comparison between the fractions 5/10 and 4/10. We will compare the numerators because the denominators are the same, and we can see that 5 > 4.
- 5th Step: The fraction with the larger numerator, 5/10 > 4/10, is the larger fraction. As a result, 1/2 > 2/5
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