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# S.chand books class 8 maths solution chapter 1 Rational Numbers exercise 1 B

## 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

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