Exercise 5.2
1. Subtract the first rational number from the second in each of the following:
(i) 3/8, 5/8
(ii) -7/9, 4/9
(iii) -2/11,-9/11
(iv) 11/13, -4/13
Solution:
2. Evaluate each of the following:
3. The sum of the two numbers is 5/9. If one of the numbers is 1/3, find the other.
Solution:
4. The sum of two numbers is -1/3. If one of the numbers is -12/3, find the other.
Solution:
5. The sum of two numbers is – 4/3. If one of the numbers is -5, find the other.
Solution:
Given sum of two numbers = (-4/3)
One of them is -5
Let the required number be x
X + (-5) = (-4/3)
LCM OF 1 and 3 is 3
(-5/1) = (-5/1)×(3/3) = (-15/3)
On substituting
X+ (-15/3) = (-4/3)
X = (-4/3) – (015/3)
X = (-4/3) + (15/3)
X = (11/3)
6. The sum of two rational numbers is – 8. If one of the numbers is – (15/7), find the other.
Solution:
7. What should be added to – (7/8) so as to get 5/9?
Solution:
Given (-7/8)
Let the required number be x
X + (-7/8) = (5/9)
The LCM of 8 and 9 is 71
X = (5/9) – (-7/8)
X = (5/9) + (-7/8)
Consider (5/9) = (5/9) ×(8/8) = (40/71)
Again (7/8) = (7/8) ×(9/8) = (63/72)
On substituting
X = (40/71) + (63/72)
X = (40+63)/ 72
X = (103/72)
8. What number should be added to (-5)/11 so as to get 26/33?
Solution:
9. What number should be added to (-5)/7 to get (-2)/3?
Solution:
10. What number should be subtracted from -5/3 to get 5/6?
Solution:
Given (-5/3)
Let the required number be x
(-5/3) – x = (5/6)
– x = (5/6) – (-5/3)
– x = (5/6) – (-5/3)
– x = (5/6) + (5/3)
Consider (5/3) = (5/3) ×(2/2) = (10/6)
On substituting
– x = (5/6) + (10/6)
– x = (15/6)
X = (-15/6)
11. What number should be subtracted from 3/7 to get 5/4?
Solution:
12. What should be added to ((2/3) + (3/5) to get (-2/15)?
Solution:
Given ((2/3) + (3/5))
Let the required number be x
((2/3) + (3/5) + x = (-2/15)
Consider (3/5) = (2/3) ×(5/5) = (10/15)
Again (3/5) = (3/5) × (3/3) = (9/15)
On substituting
((10/15) + (9/15)) + x = (-2/15)
X = (-2/15) – ((10/15) + (9/15)
X = (-2/15)- (19/15)
X = (-2-19)/15
X = (-21/15)
X = (-7/5)
13.
Required number =
14. What should be subtracted from ((3/4) – (2/3)) to get (-1/6)?
Solution:
Given ((3/5) – (2/3)))
Let the required number be x
((3/4) – (2/3)) – x = (-1/6)
– x = (-1/6) – ((3/4) – (2/3)
Consider (3/4) = (3/4) ×(3/3) = (9/12)
(2/3) = (2/3) ×(4/4) = (8/12)
On substituting
– x = (-1/6) – ((9/12) – ((8/12))
– x = (-1/6) – (1/12)
(1/6) = (1/6) ×*2/2) = (2/12)
– x = (-2/12) – (1/12)
– x = (-3/12)
-x = (-3/12)
X = (1/4)
Solution: 15
16. Fill in the blanks:
(i) (-4/13) – (-3/26)= ….
(ii) (-9/14) + …. = = -1
(iii) (-7/9) + ….. = 3
(iv) ….. + (15/23) = 4
Solution:
(i) (-5/26)
Definition:
Consider (-4/13) – (-3/26)
(-4/13) = (-4/13) ×(2/2) = (-8/26)
(-\4/13) – (-3/26) = (-8/26) – (-3/26)
= (-5/26)
(ii) (-5/14)
Definition:
Given (-9/14) + ….=-1
(-9/14) + 1= ….
(-9/14) + (14/14) = (5/14)
(-9/14) – (-5/15) = – 1
(iii) (34/9)
Definition:
Given (-7/09) +……. = 3
(-7/9) + x = 3
X = 3 + (7/9)
(3/1) = (3/1) ×(9/9) = (27/9)
X = (27/9) + (7/9) = (34/9)
(iv) (77/23)
Definition:
Given ….+ (15/23) = 4
X + (15/23) = 4
X + = 4 – (15/23)
(4/1) = (4/1) ×(23/23) = (92/23)
X = (92/23) – (25/23)
= (77/23)