If you would like to practice questions on Comparing Rational Numbers then the Worksheet on Comparison between Rational Numbers can be extremely helpful for you. Comparing Rational Numbers Worksheet will have problems on arranging rational numbers in ascending order, descending order, finding the greatest or smallest rational number, etc. Identify your knowledge gap and improve on the areas you are lagging accordingly by solving the problems from the Comparison of Rational Numbers Practice Worksheet PDF.
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Comparing and Ordering Rational Numbers Worksheet Answer Key PDF
Example 1.
Compare 4/3 and 8/3?
Solution:
Given Rational Numbers are 4/3 and 8/3
Since the above rational numbers are like fractions we just need to simply check the numerator and the one having a larger numerator is greater.
8>4
Therefore, 8/3 is greater.
Example 2.
Akbar and Suhas are taxi drivers. Akbar started his journey at 7:30 a.m. and stopped at 8:30 a.m. by covering a distance of 30 km. On the other hand, Suhas traveled 40 km in 2 hours. Assuming that they travel at a constant speed, compare the distances traveled by them in the first hour of their journey.
Solution:
Since Akbar traveled for 1 hr we need not do any calculation further
Suhas traveled a distance of 40 km in 2hr thus for 1 hr he travels 20 Km
Akbar travels a distance of 30km in 1st 1 hr of the journey
Suhas travels a distance of 20km in 1st 1 hr of the journey.
Therefore, Akbar traveled more distance compared to Suhas.
Example 3.
Compare and order the rational numbers 3/7, 4/10, 7/11 in ascending order?
Solution:
Given Rational Numbers are 3/7, 4/10, 7/11
Firstly, let us make the denominators equal to compare the given unlike fractions.
LCM(7,10,11) = 770
Equating the denominators we have
3/7 = 3*110/7*110 = 330/770
4/10 = 4*77/10*77 = 308/770
7/11 = 7*70/11*70 = 490/770
Now compare the numerators of the fractions obtained.
308<330<490
Thus, 4/10 <3/7 <7/11
Example 4.
Compare the rational numbers 4/6 and 3/-4?
Solution:
Given Rational Numbers are 4/6 and 3/-4
Let us make the denominators positive by multiplying both numerator and denominator with -1 i.e. 3/-4 = 3*-1/-4*-1 = -3/4
Since the given fractions are unlike fractions let us find the LCM of Denominators
LCM(6, 4) = 12
4/6 = 4*2/6*2 = 8/12
-3/4 = -3*3/4*3 = -9/12
Compare the numerators
8>-9
Thus, 4/6 is greater.
Example 5.
Compare each pair of rational numbers with > < =?
(i)6/7 ………9/7
(ii)8/9 ……..6/4
(iii)4/6 ………2/3
Solution:
(i)6/7 ………9/7
Given Rational Numbers are Like Fractions. To check which one is greater let us see the numerators.
6<9
Therefore, 6/7 is less than 9/7 i.e. 6/7……<…….9/7
(ii)8/9 ……..6/4
Given Rational Numbers are Unlike Fractions. We have to equate the denominators to tell which one is greater or smaller.
LCM(9, 4) = 36
8/9 = 8*4/9*4 = 32/36
6/4 = 6*9/4*9 = 54/36
Comparing Numerators we can say 8/9 ……<…… 6/4
(iii)4/6 ………2/3
Given Rational Numbers are 4/6 and 2/3
4/6 reduced gives the same fraction 2/3
Thus, 4/6 ……=…… 2/3
Example 6.
Compare the rational numbers 0, -5/4, 3/2 and arrange them from smallest to largest?
Solution:
Given Rational Numbers are 0, -5/4, 3/2
-5/4 is a negative number
3/2 is a positive number
-5/4 <0 <3/2 is the rational numbers from smallest to largest.
Example 7.
Which of the following rational numbers in each of the following pairs is smaller
(i)(-6)/(-13) or 9/13
(ii)7/8 or -8/8
Solution:
(i) (-6)/(-13) or 9/13
Given Rational Numbers are (-6)/(-13) or 9/13
Since both are like fractions the one with a lesser numerator is a smaller fraction.
Since 6 <9, (-6)/(-13) is smaller than 9/13 i.e. (-6)/(-13) <9/13
(ii) 7/8 or -8/8
Given Rational Numbers are 7/8 or -8/8
Since both are like fractions we will check the numerator.
-8 <7
Therefore, -8/8 is a smaller fraction.
Example 8.
Which rational numbers in each of the following pairs of rational numbers are greater?
(i) 3/8 or 0
(ii) (-6)/8 or 0
(iii) (-4)/7 or 0
(iv) 5/3 or 0
(v) (-3)/2 or 2/2
Solution:
(i) 3/8 or 0
3/8 is greater than 0
(ii) (-6)/8 or 0
In a negative number and zero, 0 is greater. Therefore (-6)/8 < 0
(iii) (-4)/7 or 0
In a negative number and zero, 0 is greater. Therefore (-4)/7 < 0
(iv) 5/3 or 0
5/3 >0
(v) (-3)/2 or 2/2
2/2 >-3/2