Class 7 Exam > Class 7 Notes > Mathematics (Maths) Class 7 > RD Sharma Solutions: Rational Numbers (Exercise 4.1)
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Page 1
Exercise 4.1 page no: 4.3
1. Write down the numerator of each of the following rational numbers:
(i) (-7/5)
(ii) (14/-4)
(iii) (-17/-21)
(iv) (8/9)
(v) 5
Solution:
(i) Given (-7/5)
Numerator of (-7/5) is -7
(ii) Given (14/-4)
Numerator of (14/-4) is 1
(iii) Given (-17/-21)
Numerator of (-17/-21) is -17
(iv) Given (8/9)
Numerator of (8/9) is 8
(v) Given 5
Numerator of 5 is 5
2. Write down the denominator of each of the following rational numbers:
(i) (-4/5)
(ii) (11/-34)
(iii) (-15/-82)
(iv) 15
(v) 0
Solution:
(i) Given (-4/5)
Denominator of (-4/5) is 5
(ii) Given (11/-34)
Page 2
Exercise 4.1 page no: 4.3
1. Write down the numerator of each of the following rational numbers:
(i) (-7/5)
(ii) (14/-4)
(iii) (-17/-21)
(iv) (8/9)
(v) 5
Solution:
(i) Given (-7/5)
Numerator of (-7/5) is -7
(ii) Given (14/-4)
Numerator of (14/-4) is 1
(iii) Given (-17/-21)
Numerator of (-17/-21) is -17
(iv) Given (8/9)
Numerator of (8/9) is 8
(v) Given 5
Numerator of 5 is 5
2. Write down the denominator of each of the following rational numbers:
(i) (-4/5)
(ii) (11/-34)
(iii) (-15/-82)
(iv) 15
(v) 0
Solution:
(i) Given (-4/5)
Denominator of (-4/5) is 5
(ii) Given (11/-34)
Denominator of (11/-34) is -43
(iii) Given (-15/-82)
Denominator of (15/-82) is -82
(iv) Given 15
Denominator of 15 is 1
(v) Given 0
Denominator of 0 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:
Given numerator = (-3) × 4 = -12
Denominator = (34 – 23) × (7 - 4)
= 11 × 3 = 33
Therefore the rational number = (-12/33)
4. Write down the rational numbers as integers: (7/1), (-12/1), (34/1), (-73/1), (95/1)
Solution:
Given (7/1), (-12/1), (34/1), (-73/1), (95/1)
Integers of (7/1), (-12/1), (34/1), (-73/1), (95/1) are 7, -12, 34, -73, 95
5. Write the following integers as rational numbers: -15, 17, 85, -100
Solution:
Given -15, 17, 85, -100
The rational numbers of given integers are (-15/1), (17/1), (85/1) and (-100/1)
6. Write down the rational number whose numerator is the smallest three digit
number and denominator is the largest four digit number.
Solution:
Smallest three digit number = 100
Page 3
Exercise 4.1 page no: 4.3
1. Write down the numerator of each of the following rational numbers:
(i) (-7/5)
(ii) (14/-4)
(iii) (-17/-21)
(iv) (8/9)
(v) 5
Solution:
(i) Given (-7/5)
Numerator of (-7/5) is -7
(ii) Given (14/-4)
Numerator of (14/-4) is 1
(iii) Given (-17/-21)
Numerator of (-17/-21) is -17
(iv) Given (8/9)
Numerator of (8/9) is 8
(v) Given 5
Numerator of 5 is 5
2. Write down the denominator of each of the following rational numbers:
(i) (-4/5)
(ii) (11/-34)
(iii) (-15/-82)
(iv) 15
(v) 0
Solution:
(i) Given (-4/5)
Denominator of (-4/5) is 5
(ii) Given (11/-34)
Denominator of (11/-34) is -43
(iii) Given (-15/-82)
Denominator of (15/-82) is -82
(iv) Given 15
Denominator of 15 is 1
(v) Given 0
Denominator of 0 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:
Given numerator = (-3) × 4 = -12
Denominator = (34 – 23) × (7 - 4)
= 11 × 3 = 33
Therefore the rational number = (-12/33)
4. Write down the rational numbers as integers: (7/1), (-12/1), (34/1), (-73/1), (95/1)
Solution:
Given (7/1), (-12/1), (34/1), (-73/1), (95/1)
Integers of (7/1), (-12/1), (34/1), (-73/1), (95/1) are 7, -12, 34, -73, 95
5. Write the following integers as rational numbers: -15, 17, 85, -100
Solution:
Given -15, 17, 85, -100
The rational numbers of given integers are (-15/1), (17/1), (85/1) and (-100/1)
6. Write down the rational number 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 number = 9999
Therefore the rational number is = 100/9999
7. Separate positive and negative rational numbers from the following rational
numbers:
(-5/-7), (12/-5), (7/4), (13/-9), 0, (-18/-7), (-95/116), (-1/-9)
Solution:
Given (-5/-7), (12/-5), (7/4), (13/-9), 0, (-18/-7), (-95/116), (-1/-9)
A rational number is said to be positive if its numerator and denominator are either
positive integers or both negative integers.
Therefore positive rational numbers are: (-5/-7), (-18/-7), (7/4), (-1/-9)
A rational number is said to be negative integers if its numerator and denominator are
such that one of them is positive integer and another one is a negative integer.
Therefore negative rational numbers are: (12/-5), (13/-9), (-95/116)
8. Which of the following rational numbers are positive:
(i) (-8/7)
(ii) (9/8)
(iii) (-19/-13)
(iv) (-21/13)
Solution:
Given (-8/7), (9/8), (-19/-13), (-21/13)
A rational number is said to be positive if its numerator and denominator are either
positive integers or both negative integers.
Therefore the positive rational numbers are (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 number is said to be negative integers if its numerator and denominator are
Page 4
Exercise 4.1 page no: 4.3
1. Write down the numerator of each of the following rational numbers:
(i) (-7/5)
(ii) (14/-4)
(iii) (-17/-21)
(iv) (8/9)
(v) 5
Solution:
(i) Given (-7/5)
Numerator of (-7/5) is -7
(ii) Given (14/-4)
Numerator of (14/-4) is 1
(iii) Given (-17/-21)
Numerator of (-17/-21) is -17
(iv) Given (8/9)
Numerator of (8/9) is 8
(v) Given 5
Numerator of 5 is 5
2. Write down the denominator of each of the following rational numbers:
(i) (-4/5)
(ii) (11/-34)
(iii) (-15/-82)
(iv) 15
(v) 0
Solution:
(i) Given (-4/5)
Denominator of (-4/5) is 5
(ii) Given (11/-34)
Denominator of (11/-34) is -43
(iii) Given (-15/-82)
Denominator of (15/-82) is -82
(iv) Given 15
Denominator of 15 is 1
(v) Given 0
Denominator of 0 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:
Given numerator = (-3) × 4 = -12
Denominator = (34 – 23) × (7 - 4)
= 11 × 3 = 33
Therefore the rational number = (-12/33)
4. Write down the rational numbers as integers: (7/1), (-12/1), (34/1), (-73/1), (95/1)
Solution:
Given (7/1), (-12/1), (34/1), (-73/1), (95/1)
Integers of (7/1), (-12/1), (34/1), (-73/1), (95/1) are 7, -12, 34, -73, 95
5. Write the following integers as rational numbers: -15, 17, 85, -100
Solution:
Given -15, 17, 85, -100
The rational numbers of given integers are (-15/1), (17/1), (85/1) and (-100/1)
6. Write down the rational number 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 number = 9999
Therefore the rational number is = 100/9999
7. Separate positive and negative rational numbers from the following rational
numbers:
(-5/-7), (12/-5), (7/4), (13/-9), 0, (-18/-7), (-95/116), (-1/-9)
Solution:
Given (-5/-7), (12/-5), (7/4), (13/-9), 0, (-18/-7), (-95/116), (-1/-9)
A rational number is said to be positive if its numerator and denominator are either
positive integers or both negative integers.
Therefore positive rational numbers are: (-5/-7), (-18/-7), (7/4), (-1/-9)
A rational number is said to be negative integers if its numerator and denominator are
such that one of them is positive integer and another one is a negative integer.
Therefore negative rational numbers are: (12/-5), (13/-9), (-95/116)
8. Which of the following rational numbers are positive:
(i) (-8/7)
(ii) (9/8)
(iii) (-19/-13)
(iv) (-21/13)
Solution:
Given (-8/7), (9/8), (-19/-13), (-21/13)
A rational number is said to be positive if its numerator and denominator are either
positive integers or both negative integers.
Therefore the positive rational numbers are (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 number is said to be negative integers if its numerator and denominator are
such that one of them is positive integer and another one is a negative integer.
Therefore negative rational numbers are (-3/7) and (9/-83)
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FAQs on Rational Numbers (Exercise 4.1) RD Sharma Solutions - Mathematics (Maths) Class 7
| 1. What are rational numbers? |  |
Ans. Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. They can be positive, negative, or zero.
| 2. How do you identify a rational number? | |
Ans. A number can be identified as a rational number if it can be written in the form of p/q, where p and q are integers and q is not equal to zero.
| 3. What is the difference between a rational number and an irrational number? | |
Ans. Rational numbers can be expressed as fractions, whereas irrational numbers cannot be expressed as fractions. Irrational numbers are non-repeating and non-terminating decimals.
| 4. How can you represent rational numbers on a number line? | |
Ans. To represent rational numbers on a number line, we can mark the position of the whole number and then divide the gap between two consecutive whole numbers into equal parts. We can then locate the rational number on the number line based on its fractional value.
| 5. How can you compare rational numbers? | |
Ans. Rational numbers can be compared by converting them into a common denominator and then comparing the numerators. If the numerators are equal, the rational numbers are equal. If the numerators are not equal, we can compare them based on their size.
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