Chapter 1 Rational Numbers Ex 1.2 Solutions
Question - 1 : - Find five rational numbers between.
(i) 2/3 and 4/5
(ii) -3/2 and 5/3
(iii) 1/4 and 1/2
Answer - 1 : -
(i) 2/3 and 4/5
Let us make the denominators same, say 60
i.e., 2/3 and 4/5 can be written as:
2/3 = (2 ├Ч 20)/(3 ├Ч 20) = 40/60
4/5 = (4 ├Ч 12)/(5 ├Ч 12) = 48/60
Five rational numbers between 2/3 and 4/5 = five rational numbers between 40/60 and 48/60
Therefore, Five rational numbers between 40/60 and 48/60 = 41/60, 42/60, 43/60, 44/60, 45/60
(ii) -3/2 and 5/3
Let us make the denominators same, say 6
i.e., -3/2 and 5/3 can be written as:
-3/2 = (-3 ├Ч 3)/(2├Ч 3) = -9/6
5/3 = (5 ├Ч 2)/(3 ├Ч 2) = 10/6
Five rational numbers between -3/2 and 5/3 = five rational numbers between -9/6 and 10/6
Therefore, Five rational numbers between -9/6 and 10/6 = -1/6, 2/6, 3/6, 4/6, 5/6
(iii) ┬╝ and ┬╜
Let us make the denominators same, say 24.
i.e., ┬╝ and ┬╜ can be written as:
┬╝ = (1 ├Ч 6)/(4 ├Ч 6) = 6/24
┬╜ = (1 ├Ч 12)/(2 ├Ч 12) = 12/24
Five rational numbers between ┬╝ and ┬╜ = five rational numbers between 6/24 and 12/24
Therefore, Five rational numbers between 6/24 and 12/24 = 7/24, 8/24, 9/24, 10/24, 11/24
Question - 2 : - Write five rational numbers which are smaller than 2.
Answer - 2 : -
The number 2 can be written as 20/10
Hence, we can say that, the five rational numbers which are smaller than 2 are:
2/10, 5/10, 10/10, 15/10, 19/10
Question - 3 : - Write five rational numbers greater than -2.
Answer - 3 : -
-2 can be written as тАУ 20/10
Hence, we can say that, the five rational numbers greater than -2 are
-10/10, -5/10, -1/10, 5/10, 7/10
Question - 4 : - Represent these numbers on the number line.
(i) 7/4
(ii) -5/6
Answer - 4 : -
(i) 7/4
Divide the line between the whole numbers into 4 parts. i.e., divide the line between 0 and 1 to 4 parts, 1 and 2 to 4 parts and so on.
Thus, the rational number 7/4 lies at a distance of 7 points away from 0 towards positive number line.
(ii) -5/6
Divide the line between the integers into 4 parts. i.e., divide the line between 0 and -1 to 6 parts, -1 and -2 to 6 parts and so on. Here since the numerator is less than denominator, dividing 0 to тАУ 1 into 6 part is sufficient.
Thus, the rational number -5/6 lies at a distance of 5 points, away from 0, towards negative number line
Answer - 5 : -
Divide the line between the integers into 11 parts.
Thus, the rational numbers -2/11, -5/11, -9/11 lies at a distance of 2, 5, 9 points away from 0, towards negative number line respectively.
Question - 6 : - Find the rational numbers between -2/5 and 1/2.
Answer - 6 : -
Let us make the denominators same, say 50.
-2/5 = (-2 ├Ч 10)/(5 ├Ч 10) = -20/50
┬╜ = (1 ├Ч 25)/(2 ├Ч 25) = 25/50
Ten rational numbers between -2/5 and ┬╜ = ten rational numbers between -20/50 and 25/50
Therefore, ten rational numbers between -20/50 and 25/50 = -18/50, -15/50, -5/50, -2/50, 4/50, 5/50, 8/50, 12/50, 15/50, 20/50
Question - 7 : - Find ten rational numbers between 3/5 and 3/4,
Answer - 7 : -
Let us make the denominators same, say 80.
3/5 = (3 ├Ч 16)/(5├Ч 16) = 48/80
3/4 = (3 ├Ч 20)/(4 ├Ч 20) = 60/80
Ten rational numbers between 3/5 and ┬╛ = ten rational numbers between 48/80 and 60/80
Therefore, ten rational numbers between 48/80 and 60/80 = 49/80, 50/80, 51/80, 52/80, 54/80, 55/80, 56/80, 57/80, 58/80, 59/80