Exercise 4.1
1. Write down the numerator of each of the following rational numbers:
(i) -7/5
(ii) 15/(-4)
(iii) (- 17)/(- 21)
(iv) 8/9
(v) 5
Solution:
Numerators are:
(i) -7
(ii) 15
(iii) -17
(iv) 8
(v) 5
2. Write down the denominator of each of the following rational numbers:
(i) – 4/5
Solution:
Given (-4/5)
Denominators of (-4/5)
(ii) 11/(-34)
Solution:
Given (11/-34)
Denominators of (1/-34) is – 43
(iii) 15/82
Solution:
Given (-15/-82)
Denominators (15/-82) is -82
(iv) 15
Solution:
Given 15
Denominators of 15 is 1
(v) 0
Solution:
Given 0
Denominators of is any non-zero integer
3. Write down the rational number whose numerator is (-3) ×4, and whose denominator is (34 – 23) ×(7 – 4).
Solution:
According to the question:
Numerator = (-3) x 4 = – 12
Denominator = (34 – 23) x (7 – 4) =11 x 3 = 33
Therefore, Rational number = -12/32
4. Write the following rational numbers as integers:
Solution:
Integers are 7, -1, 34, -73 and 95
5. Write the following integers as rational numbers with denominator 1:
-15, 17, 85, -100
Solution:
Rational numbers of given integers with denominators 1 are
6. Write down the rational whose numerator is the smallest three digit number and denominator is the largest four digit number.
Solution:
Smallest three digit number = 100
Largest four digit numbers = 9999
Therefore the rational numbers is = 100/9999
7. Separate positive and negative numbers from the following rational number
Solution:
Positive rational numbers:-
A rational number is said to be positive is it numerator and denominators are either both are positive integers or both negative integers
Negative rational numbers is said to be negative if its numerators and denominators are such that one of them is positive integers and another one is a negative integers.
8. Which of the following rational numbers are positive:
(i) (- 8)/7
(ii) 9/8
(iii) 19/13
(iv) (- 21)/13
Solution:
The numbers can be rewritten as:
(i) (- 8)/7
(ii) 9/8
(iii) 19/13
(iv) -21/13
Positive rational numbers are (ii) and (iii), i.e., 9/8 and (-19)/(-13)
9. Which of the following rational numbers are negative?
(i) (- 3)/7
(ii) (- 5)/(- 8)
(iii) 9/(- 83)
(iv) 115/197
Solution:
Given (-3/7), (-5/-8), (9/-83), (-115/197)
A rational numbers is said to be negative integers if its numerator and denominator are such that one them is positive integer and another one is a negative integer.
Therefore negative rational numbers are (-3/7) and (9/-83)