Students who would like to practice Questions on Comparison of Rational Numbers can make use of the Worksheet on Comparison of Rational Numbers. Solve numerous questions on the concept of Comparing Rational Numbers and get a good grip on the concept. For more information, refer to Rational Numbers Worksheets and clear all your queries easily.
Questions include finding the greater and smaller rational number among the given pair of rational numbers, arranging rational numbers in descending, ascending order, etc. Assess your preparation standards and concentrate on the areas you are lagging and improvise on them.
1. Which rational numbers in each of the following pairs of rational numbers is greater?
(i) 2/8 or 0
(ii) (-5)/8 or 0
(iii) (-2)/7 or 0
(iv) 2/3 or 0
(v) (-3)/4 or 2/4
(vi) (-4)/10 or 3/11
(vii) (-5)/7 or (-2)/7
Solution:
(i) 2/8 or 0
Between 2/8 and 0 2/8 is greater than 0
(ii) (-5)/8 or 0
Negative Numbers are Small when compared to 0.
0 is greater than -5/8
(iii) (-2)/7 or 0
Negative Numbers are Small when compared to 0.
0 is greater than -2/7
(v) (-3)/4 or 2/4
Between Negative and Positive Number, Positive Number is Greater
2/4 is greater than -3/4
(vi) (-4)/10 or 3/11
Between Negative and Positive Number, Positive Number is Greater
3/11 is greater than -4/10
(vii) (-5)/7 or (-2)/7
Between Negative Numbers, Smaller Number is Greater
-2/7 is greater than -5/7
2. Which of the rational numbers in each of the following pairs of rational numbers is smaller?
(i) -4/2 or -8/2
(ii) (-4)/(-13) or 7/13
(iii) 7/8 or -5/8
(iv) 16/(-4) or 3
Solution:
(i) -4/2 or -8/2
-4/2 < -8/2
(ii) (-4)/(-13) or 7/13
-4/-13<7/13
(iii) 7/8 or -5/8
-5/8<7/8
(iv) 16/(-4) or 3
16/-4 <3
3. Fill in the blanks with the symbol among >, = and <
(i) (-6)/4 ____ 7/13
(ii) (-3)/4 ____ (-5)/6
(iii)(-8)/3 ____ (-9)/10
(iv) 0 ____ (-4)/(-5)
(v) -2 ____ (-12)/5
Solution:
(i) (-6)/4 __<__ 7/13
(ii) (-3)/4 _>___ (-5)/6
(iii)(-8)/3 _<___ (-9)/10
(iv) 0 __>__ (-4)/(-5)
(v) -2 _>___ (-12)/5
The above symbols are given after checking the given rational numbers. The Logic is quite simple in the case of negative numbers the one with less value is greater.
4. Compare the fractions, and write >, < or = in the blank.
4/8 …… 7/10
Solution:
In order to compare the above rational numbers we need to find the LCM since the Denominators are not the same
LCM(8, 10) = 40
To make the denominator common use the LCM Obtained and express the rational numbers accordingly
4/8 = 4*5/8*5 = 20/40
7/10 = 7*4/10*4 = 28/40
Since Numerator 28 is greater the Rational Number 7/10 is greater
4/8 < 7/10.
5. Compare the fractions, and write >, < or = in the blank.
7/14 …..1/4
Solution:
In order to compare the above rational numbers we need to find the LCM since the Denominators are not the same
LCM(14, 4) = 28
To make the denominator common use the LCM Obtained and express the rational numbers accordingly
7/14 = 7*2/14*2 = 14/28
1/4 = 1*7/4*7 = 7/28
Since Numerator 14 is greater the Rational Number 7/14 is greater.
7/14 < 1/4
6. Arrange the following rational numbers in ascending order
2/3, 5/4, (-4)/(-8), 1/3
Solution:
Firstly check whether all the rational numbers given have a positive denominator or not
If not rearrange them to make them positive.
-4/-8 = -4*-1/-8*-1 = 4/8
Thus, Rational become 2/3, 5/4, 4/8, 1/3
LCM of(3, 4, 8, 3) = 24
2/3 = 2*8/3*8 = 16/24
5/4 =5*6/4*6 = 30/24
4/8 = 4*3/8*3 = 12/24
1/3 = 1*8/3*8 = 8/24
Therefore Rational Numbers arranged in Ascending Order is 1/3 < 4/8< 2/3< 5/4
7. Arrange the following rational numbers in descending order
(-3)/(-2), 17/30, (-8)/15, 7/(-10)
Solution:
Firstly check whether all the rational numbers given have a positive denominator or not
If not rearrange them to make them positive.
-3/-2 = -3*(-1)/-2*(-1) = 3/2
7/-10 = 7*(-1)/-10*(-1) = -7/10
Therefore, Rational Numbers are 3/2, 17/30, 8/15, -7/10
Find the LCM of denominators i.e. 2, 30, 15, 10
LCM(2, 30, 15, 10) =30
3/2 = 3*15/2*15 = 45/30
17/30 = 17*1/30*1 = 17/30
8/15 = 8*2/15*2 = 16/30
-7/10 = -7*3/10*3 = -21/30
Therefore Rational Numbers in Descending Order is 3/2> 17/30> 8/15> -7/10.