Table of Contents
Exercise 5.1
Question: 1
Add the following rational numbers:
Solution:
We have,
We have,
We have,
We have,
Question: 2
Add the following rational numbers:
Solution:
If p/q and r/s are two rational numbers such that q and s do not have a common factor
If p/q and r/s are two rational numbers such that q and s do not have a common factor
LCM of 27 and 18 is 54
LCM of 4 and 8 is 4
Question: 3
Simplify
Solution:
LCM of 5 and 10 is 10
LCM of 16 and 24 is 48
LCM of 12 and 15 is 60
LCM of 19 and 57 is 57
Question: 4
Add and express the sum as a mixed fraction:
Solution:
LCM of 5 and 10 is 10
LCM of 7 and 4 is 28
Exercise 5.2
Question: 1
Subtract the first rational number from the second in each of the following:
Solution:
Question: 2
Evaluate each of the following:
Solution:
LCM of 3 and 5 is 15
LCM of 3 and 7 is 21
Question: 3
The sum of the two numbers is 5/9. If one of the numbers is 1/3, find the other.
Solution:
LCM of 3 and 9 is 9
Question: 4
The sum of two numbers is -1/3. If one of the numbers is -12/3, find the other.
Solution:
Let the required number be x
The required number is 11/3
Question: 5
The sum of two numbers is – 4/3. If one of the numbers is -5, find the other.
Solution:
Let the required number be x
The required number is 11/3
Question: 6
The sum of two rational numbers is – 8. If one of the numbers is – (15/7), find the other.
Solution:
Let the required number be x
The required number is – (41/7)
Question: 7
What should be added to – (7/8) so as to get 5/9?
Solution:
Let the required number be x
The required number is 103/72
Question: 8
What number should be added to (-5)/11 so as to get 26/33?
Solution:
Let the required number be x
The required number is 41/33
Question: 9
What number should be added to (-5)/7 to get (-2)/3?
Solution:
Let the required number be x
The required number is 1/21
Question: 10
What number should be subtracted from -5/3 to get 5/6?
Solution:
Let the required number be x
The required number is 15/6
Question: 11
What number should be subtracted from 3/7 to get 5/4?
Solution:
Let the required number be x
The required number is 23/28
Question: 12
Solution:
Let the required number be x
The required number is (-7)/5
Question: 13
Solution:
Let the required number be x
The required number is 59/30
Question: 14
Solution:
Let the required number be x
x = 1/4
The required number is ¼
Question: 15
Simplify:
Solution:
Question: 16
Fill in the blanks:
Solution:
Exercise 5.3
Question: 1
Multiply:
Solution:
Question: 2
Multiply:
Solution:
Question: 3
Simplify each of the following and express the result as a rational number in standard form:
Solution:
Question: 4
Simplify:
Solution:
Question: 5
Simplify:
Solution:
Exercise 5.4
Question: 1
Divide:
Solution:
Question: 2
Find the value and express as a rational number in standard form:
Solution:
Question: 3
The product of two rational numbers is 15. If one of the numbers is -10, find the other.
Solution:
Let the number to be found be x
x ×- 10 = 15
x = 15/(-10)
x = 3/(-2)
x = (-3)/2
Hence the number is x = (-3)/2
Question: 4
The product of two rational numbers is – 8/9. If one of the numbers is – 4/15, find the other.
Solution:
Let the number to be found be x
Hence the number is x = 10/3
Question: 5
By what number should we multiply -1/6 so that the product may be -23/9?
Solution:
Let the number to be found be x
Hence the number is x = 46/3
Question: 6
By what number should we multiply -15/28 so that the product may be -5/7?
Solution:
Let the number to be found be x
Hence the number is x = 4/3
Question: 7
By what number should we multiply -8/13 so that the product may be 24?
Solution:
Let the number to be found be x
x = – 39
Hence the number is x = – 39
Question: 8
By what number should -3/4 be multiplied in order to produce -2/3?
Solution:
Let the number to be found be x
x = 8/9
Hence the number is x = 8/9
Question: 9
Find (x + y) ÷ (x —y), if
Solution:
Question: 10
The cost of 7(2/3) metres of rope is Rs. 12(3/4). Find its cost per metre. 7(2/3) metres of rope cost = Rs. 12(3/4).
Solution:
Question: 11
The cost of 2(1/3) metres of cloth is Rs.75 1/4. Find the cost of cloth per metre. 2(1/3) metres of rope cost = Rs. 75(1/4)
Solution:
Question: 12
By what number should (-33)/16 be divided to get (-11)/4?
Solution:
x = 3/4
The number is x = 3/4
Question: 13
Divide the sum of (-13)/5 and 12/7 by the product of (-31)/7 and (-1)/2
Solution:
Question: 14
Divide the sum of 65/12 and 8/3 by their difference.
Solution:
Question: 15
If 24 trousers of equal size can be prepared in 54 metres of cloth, what length of cloth is required for each trouser?
Solution:
= 54/24
= 9/4 metres
9/4 metres of cloth is required to make each trouser
Exercise 5.5
Question: 1
Find six rational numbers between (-4)/8 and 3/8
Solution:
We know that
– 4, -3, -2, -1, 0, 1, 2, 3
Question: 2
Find 10 rational numbers between 7/13 and (- 4)/13
Solution:
We know that
76543210 -1 -2 -3 –4
Question: 3
State true or false:
(i) Between any two distinct integers there is always an integer.
(ii) Between any two distinct rational numbers there is always a rational number.
(iii) Between any two distinct rational numbers there are infinitely many rational numbers.
Solution:
(i) False
(ii) True
(iii) True
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