COMPARING RATIONAL NUMBERS EXAMPLES

About "Comparing Rational Numbers Examples"

Comparing Rational Numbers Examples :

Here we are going to see some practice questions on comparing rational numbers.

Comparing Rational Numbers Examples - Practice questions

Question 1 :

Compare the following pairs of rational numbers.

(i)  −11/5, -21/8

Solution :

To decide which rational number is greater, we must have the same denominators. For that let us take L.C.M for 5 and 8.

L.C.M (5, 8) is 40

(-11/5) ⋅ (4/4)  =  -44/20

(-21/8) ⋅ (5/5)  =  -105/40

(-44/20) > (-105/40)

(-11/5) > (-21/8)

(ii)  3/(-4) , -1/2

Solution :

-3/4 , -1/2

L.C.M (4, 2) is 4

(-3/4) ⋅ (1/1)  =  -3/4

(-1/2) ⋅ (2/2)  =  -2/4

(-2/4) > (-3/4)

(-1/2) > (-3/4)

(iii)   2/3, 4/5

Solution :

2/3, 4/5

L.C.M (3, 5) is 15

(2/3) ⋅ (5/5)  =  10/15

(4/5) ⋅ (3/3)  =  12/15

(12/15) > (10/15)

(4/5) > (2/3)

Arranging the Rational Numbers in Ascending order and Descending order

Question 1 :

Arrange the following rational numbers in ascending and descending order.

(i)  -5/12, -11/8, -15/24, -7/(-9), 12/36

Solution :

L.C.M (12, 8, 24, 9, 36)  =  144

(-5/12) ⋅ (12/12)  =  -60/144

(-11/8) ⋅ (18/18)  =  -198/144

(-15/24) ⋅ (6/6)  =  -90/144

(-7/(-9)) ⋅ (16/16)  =  112/144

(12/36) ⋅ (4/4)  =  48/144

(-198/144) > (-90/144) > (-60/144) > (48/144) > (112/144)

Ascending order :

(-11/8), (-15/24), (-5/12), (12/36), (7/9)

Descending order :

(7/9), (12/36), (-5/12), (-15/24), (-11/8)

(ii)  -17/10, -7/5, 0, -2/4, -19/20

Solution :

L.C.M (10, 5, 4, 20)  =  20

(-17/10) ⋅ (2/2)  =  -34/20

(-7/5) ⋅ (4/4)  =  -28/20

(-2/4) ⋅ (5/5)  =  -10/20

(-19/20) ⋅ (1/1)  =  -19/20

(-34/20) > (-28/20) > (-19/20) > (-10/20) > 0

Ascending order :

(-17/10), (-7/5), (-19/20), (-2/4), 0

Descending order :

0, (-2/4),

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