## Exercise 1 B

#### Question 1

**Answer True (T) or False (F)**

**(i)** Subtraction is commutative for rational numbers. **F**

**(ii)** To subtract , we add the additive inverse of . **F**

**(iii)** 0 is its own additive inverse . **T**

**(iv)** The additive inverse of . **T**

**(v)** While subtracting three or more rational numbers , they can be grouped in any order . **F**

#### Question 2

**Add the following rational numbers**

**(i)**

Sol :

⇒

⇒

**(ii)**

Sol :

⇒

⇒

**(iii)**

Sol :

L.C.M of 4 and 10 is = 2×2×5=20

⇒⇒

⇒

**(iv)**

Sol :

⇒

L.C.M of 12 and 9 is = 2×2×3×3=36

⇒

⇒

⇒

**(v)**

Sol :

⇒

L.C.M of 10 and 15 is = 2×3×5=30

⇒⇒

⇒

**(vi)**

Sol :

⇒

⇒

⇒

⇒

⇒

**(vii)**

Sol :

⇒

L.C.M of 3 and 7 is 21

⇒

⇒

⇒

**(viii)**

Sol :

⇒

L.C.M of 6 and 12 is =2×2×3=12

⇒⇒

⇒

#### Question 3

**Simplify:**

**(i)**

Sol :

⇒

L.C.M of 4 , 7 and 14 is =2×2×3 =28

⇒⇒

⇒

⇒

**(ii)**

Sol :

⇒

L.C.M of 15 , 25 and 10 is =2×3×5×5 =150

⇒⇒

⇒

⇒

**(iii)**

Sol :

Denominator can not be negative

⇒

⇒

L.C.M of 3 , 9 and 6 is =2×3×3 =18

⇒⇒

⇒

⇒

**(iv)**

Sol :

⇒

L.C.M of 5 , 10 and 2 is =2×5 =10

⇒⇒

⇒

⇒

#### Question 4

**Verify the following.**

**(i)**

Sol :

They are equal to each other by commutative property

ALTERNATE METHOD

L.C.M of 8 and 3 is =2×2×2×3 =24

⇒⇒

⇒

**(ii)**

Sol :

They are equal to each other by commutative property

(by commutative property)

ALTERNATE METHOD

[denominator cannot be negative]

LCM of 11 and 22 is 22.

**(iii)**

Sol :

They are equal to each other by commutative property

ALTERNATE METHOD

#### Question 5

**Verify that:**

**(i)**

Sol :

They are equal to each other by associative property

ALTERNATE METHOD

**(ii)**

Sol :

They are equal to each other by associative property

ALTERNATE METHOD

(denominator can not be begative)

[L.C.M of 5 and 10 is 10]

[L.C.M of 5 and 10 is 10]

#### Question 6

**Find the additive inverse of each of the following.**

**(i)**

Sol :

⇒

**(ii)** 0

Sol :

0=0

**(iii)**

Sol :

⇒

**(iv)**

Sol :

⇒

⇒

**(v)**

Sol :

⇒

**(vi)**

Sol :

⇒

#### Question 7

**Arrange and simplify:**

**(i)**

Sol :

[L.C.M of 2 and 5 is 10]

**(ii)**

Sol :

**(iii)**

Sol :

L.C.M of 3 and 6 is 6

L.C.M of 5 and 15 is 15

L.C.M of 15 and 6 is 30

**(iv)**

Sol :

L.C.M of 5 and 3 is 15

**(v)**

Sol :

L.C.M of 5 and 3 is 15

**(vi)**

Sol :

L.C.M of 9,3,5 is 45

#### Question 8

Verify that -(-x)=x , when x= (i)

(ii)

Sol :

(i)

(ii)

#### Question 9

Verify that -(x+y)=(-x)+(-y) , when (i) (ii)

Sol :

(i)

(ii)

-(x+y)=(-x)+(-y)

#### Question 10

**Subtract:**

**(i)**

Sol :

**(ii)**

Sol :

LCM of 6,9 is 18

\begin{tabular}{c|c}

2 & 12,9 \\

\hline 2 & 6,9 \\

\hline 3 & 3,9 \\

\hline 3 & 1,3 \\

\hline & 1,1

\end{tabular}

**(iii)**

Sol:

**(iv)**

Sol :

LCM of 4,5 is 20

#### Question 11

**The sum of two rational numbers is . If one of the numbers is , find the other .**

Sol :

Sum of two rational numbers is

One of the number is and Let the other be x

LCM of 60 and 12 is 60

or

#### Question 12

**What number should be subtracted from to get ?**

Sol :

let be subtstaded from to get

or

LCM of 15 and 30 is 30

#### Question 13

**What should be subtracted from to get ?**

Sol :

LCM of 4,3,5,2 is 60