Rational Numbers can be expressed in the form of fractions. In this article, we will solve different types of problems on basis of comparison between rational numbers. Learn the different methods for solving problems on comparing rational numbers. Comparing the Fractions depends on the kind of fraction we have to compare such as like and unlike fractions.
How to Compare Two Rational Numbers?
Follow the simple steps listed below to compare rational numbers. There are 2 scenarios in general while comparing between rational numbers. They are as such
Like Fractions: These are the fractions that have the same denominator. As the fractions have the same denominator we need to simply check the numerator and the one having a larger numerator is the greater of the two fractions.
Unlike Fractions: The fractions having different denominators are called Unlike Fractions. Firstly, we need to make the denominators equal in unlike fractions and the rest of the process is the same as like fractions.
Also, See:
- Comparison between Two Rational Numbers
- Problems on Rational numbers as Decimal Numbers
- Rational Numbers Between Two Unequal Rational Numbers
Comparison of Rational Numbers Examples
Example 1.
Compare Rational Numbers 3/5 and 8/5?
Solution:
Given Rational Numbers are 3/5 and 8/5
The above fractions are like fractions so we need to check the numerators and the one which is having a larger numerator is the greater fraction.
8>3
Therefore, 8/5 is the greater rational number.
Example 2.
Compare the Rational Numbers 4/7 and 6/4?
Solution:
Given Rational Numbers are 4/7 and 6/4
the above fractions are unlike fractions. So we need to make the denominators the same i.e. by using the LCM Method.
LCM(7, 4) = 28
4/7 = 4*4/7*4 = 16/28
6/4 = 6*7/4*7 = 42/28
Now, since the denominators are equal we will continue the process the same as like fractions. Compare the numerators of the fractions i.e. 42>16
Therefore, 6/4 is greater than 4/7
Example 3.
Compare 4/6 and 2/6?
Solution:
Given Rational Numbers are 4/6 and 2/6
The above fractions are like fractions so we need to check the numerators and the one which is having a larger numerator is the greater fraction.
4>2
Therefore, 4/6 is the greater rational number.
Example 4.
Compare and arrange the following fractions into ascending order 3/5, 4/15, 7/9, 12/10?
Solution:
Given Rational Numbers are 3/5, 4/15, 7/9, 12/10
Since the fractions given are unlike fractions we need to first make the denominators the same. To do so we will take the LCM of Denominators and then equate them.
LCM(5, 15, 9, 10) = 90
3/5 = 3*14/5*14 = 42/90
4/15 = 4*6/15*6 = 24/90
7/9 = 7*10/9*10 = 70/90
12/10 = 12*9/10*9 = 108/90
Since the denominators are the same let us check the numerators and the one having the larger numerator is the larger fraction.
Since 24<42<70<108
4/15<3/5<7/9<12/10
Therefore, 4/15<3/5<7/9<12/10 is the ascending order of given fractions.
Example 5.
Compare and arrange the following in descending order 2/3, 4/15, 5/7, and 7/12?
Solution:
Given Rational Numbers are 2/3, 4/15, 5/7, and 7/12
Since the fractions given are unlike we need to make the denominators the same. Find the LCM of the denominators and then equate them
LCM(3, 15, 7,12) = 420
2/3 = 2*140/3*140 = 280/420
4/15 = 4*28/15*28 = 112/420
5/7 = 5*60/7*60 = 300/420
7/12 = 7*35/12*35 = 245/420
Since the denominators are the same we will check the numerators and then decide which fraction is larger
300>280>245>112
5/7>2/3>7/12>4/15
Therefore, 5/7>2/3>7/12>4/15 is the descending order of given fractions.