Comparing Fractions This class is mainly done as a preparation for competitive exams (eg BCS preparation, university entrance classes or university entrance preparation classes). But this lesson will also help those who are math students in other classes. Our lessons will help you sharpen your math skills at any moment in life.
Comparing Fractions
Comparing fractions means determining the larger and the smaller fraction between any two or more fractions. Since fractions are made up of two parts – a numerator and a denominator, they are compared using a certain set of rules. Let us learn more about comparing fractions in this page.
How to Compare Fractions?
Comparing fractions involves a set of rules related to the numerator and the denominator. When any two fractions are compared, we get to know the greater and the smaller fraction. We need to compare fractions in our everyday lives. For example, when we need to compare the ratio of ingredients while following a recipe or to compare the scores of exams, etc. So, let us go through the different methods of comparing fractions to understand the concept better.
What is a Fraction?
Before exploring the concept of comparing fractions, let us recall fractions. A fraction is a part of a whole and it consists of two parts – the numerator and the denominator. The numerator is the number on the upper part of the fractional bar and the denominator is located below the fractional bar.
Now, let us discuss more about comparing fractions.
Comparing Fractions with Same Denominators
For comparing fractions with the same denominators, it becomes easier to determine the greater or the smaller fraction. After checking if the denominators are the same, we can simply look for the fraction with the bigger numerator. If both the numerators and the denominators are equal, the fractions are also equal. For example, let us compare 6/17 and 16/17
- Step 1: Observe the denominators of the given fractions: 6/17 and 16/17. The denominators are the same.
- Step 2: Now, compare the numerators. We can see that 16 > 6.
- Step 3: The fraction with the larger numerator is the larger fraction. Therefore, 6/17 < 16/17.
Comparing Fractions with Unlike Denominators
For comparing fractions with unlike denominators, we need to convert them to like denominators, for which we should find the Least Common Multiple (LCM) of the denominators. When the denominators are made the same, we can compare the fractions easily. For example, let us compare 1/2 and 2/5.
- Step 1: Observe the denominators of the given fractions: 1/2 and 2/5. They are different. So, let us find the LCM of 2 and 5. LCM(2, 5) = 10.
- Step 2: Now, let us convert them in such a way that the denominators become the same. Let us multiply the first fraction with 5/5, that is, 1/2 × 5/5 = 5/10.
- Step 3: Now, let us multiply the second fraction with 2/2 that is, 2/5 × 2/2 = 4/10.
- Step 4: Compare the fractions: 5/10 and 4/10. Since the denominators are the same, we will compare the numerators, and we can see that, 5 > 4.
- Step 5: The fraction with the larger numerator is the larger fraction, that is, 5/10 > 4/10. Therefore, 1/2 > 2/5
It should be noted that if the denominators are different and the numerators are the same, then we can easily compare fractions by looking at their denominators. The fraction with a smaller denominator has a greater value and the fraction with a larger denominator has a smaller value. For example, 2/3 > 2/6.
Decimal Method of Comparing Fractions
In this method, we compare the decimal values of fractions. For this, the numerator is divided by the denominator and the fraction is converted into a decimal. Then, the decimal values are compared. For example, let us compare 4/5 and 6/8.
- Step 1: Write 4/5 and 6/8 in decimals. 4/5 = 0.8 and 6/8 = 0.75.
- Step 2: Compare the decimal values. 0.8 > 0.75
- Step 3: The fraction with a larger decimal value would be a larger fraction. Therefore, 4/5 > 6/8
Comparing Fractions in details :
Read more…