ML Aggarwal: Rational Numbers - 2
Q.1. Subtract:
(i) 
=
Taking L.C.M. we get,
=
= -106/35
=
Hence, the subtraction ofis
(ii) 
This can be written as,
=
=
Taking L.C.M. we get,
=
= 293/72
=
(iii) 
This can be written as,
=
=
=
Taking L.C.M. we get,
=
We get,
= -71/45
=
Q.2. Sum of two rational numbers is. 3/5. If one of them is. -2/7 , find the other.
Given
Sum of two rational numbers is 3/5
One of the number is -2/7
Hence, the other number is calculated as follows:
Other number =
=
Taking L.C.M. we get,
=
= 31/35
Therefore, the other number is 31/35
Q.3. What rational number should be added to -5/11 to get -7/8 ?
Given
According to the statement,
Sum of two numbers = -7/8
One number = -5/11
Hence, the other number is calculated as below:
Other number =
=
Taking L.C.M. we get,
=
= -37/88
Therefore, the other number is -37/88
Q.4. What rational number should be subtracted from 
to get 
?
The required number can be calculated as follows:
This can be written as,
On further calculation, we get
=
= -11/10
=
Therefore, the required number is
Q.5. Subtract the sum of -5/7 and -8/3 from the sum of 5/2 and -11/12 .
Sum of -5/7 and -8/3 can be calculated as,
-5/7 And -8/3 =
On further calculation, we get
=
= -17/21
Now,
Sum of 5/2 and -11/12 can be calculated as,
On simplification, we get,
=
= 19/12
Now,
=
Taking L.C.M. we get,
=
= 417/84
=
=
Q.6. If x = -4/7 and y = 2/5, then verify that x - y ≠ y - x
Given
x = -4/7 and y = 2/5
Now,
x - y =
=
Taking L.C.M. we get,
=
= -34/35
And
y - x =
=
Taking L.C.M. we get,
=
= 34/35
Therefore, x - y ≠ y - x
Q.7. If x = 4/9, y = -7/12 and z = -2/3 , then verify that x - (y - z) ≠ (x - y) - z
Given
x = 4/9, y = -7/12 and z = -2/3
x - (y - z) ≠ (x - y) - z
L.H.S. = x - (y - z)
=
=
On further calculation, we get
=
=
=
Taking L.C.M. we get,
=
= 13/36
Now,
R.H.S = (x - y) - z
=
=
On further calculation, we get
=
=
Again taking L.C.M. we get,
=
= 58/36
Therefore, x - (y - z) ≠ (x - y) - z
Q.8. Which of the following statement is true / false?
(i) 2/3 - 4/5 is not a rational number.
2/3 - 4/5
Taking L.C.M
=
= -2/15
Is a rational number
Hence, the given statement is false
(ii) -5/7 is the additive inverse of 5/7 .
The given statement is true.
(iii) 0 is the additive inverse of its own.
he given statement is true.
(iv) Commutative property holds for subtraction of rational numbers.
Let us take,
We know that,
Therefore, the given statement is false.
(v) Associative property does not hold for subtraction of rational numbers.
The given statement is true.
(vi) 0 is the identity element for subtraction of rational numbers.
Let us take,
7/8 - 0 = 7/8
But 0 - 7/8 = -7/8
7/8 ≠ -7/8
Therefore, the given statement is false.
