Question

1. On a number line, when we add a positive integer, we

(a) move to the right (b) move to the left

(c) do not move at all (d) none of these

2. On a number line, when we add a negative integer, we

(a) move to the right (b) move to the left

(c) do not move at all (d) none of these

3. On a number line, when we subtract a positive integer, we

(a) move to the right (b) move to the left

(c) do not move at all (d) none of these

4. On a number line, when we subtract a negative integer, we

(a) move to the right (b) move to the left

(c) do not move at all (d) none of these

5. When two positive integers are added, we get

(a) a positive integer (b) a negative integer

(c) sometimes a positive integer, sometimes a negative integer (d) none of these

6. When two negative integers are added, we get

(a) a positive integer (b) a negative integer

(c) sometimes a positive integer, sometimes a negative integer(d) none of these

7. Which of the following is true?

(а) (- 8) + (- 4) > (- 8) – (- 4) (b) (- 8) + (- 4) < (- 8) – (- 4)

(c) (- 8) + (- 4) = (- 8) – (- 4) (d) none of these

8. The product of two negative integers is

(a) a positive integer (b) a negative integer

(c) either a positive integer or a negative integer (d) none of these

9. The product of three negative integers is

(a) a positive integer (b) a negative integer

(c) either a positive integer or a negative integer(d) none of these

10. (- 1) × (- 1) × (- 1) × ……. 10 times is equal to

(a) 1 (b) – 1 (c) 1 or – 1 (d) none of these

11. (- 20) × (- 5) is equal to

(a) 100 (b) – 100 (c) 20 (d) 5

12. (- 30) × 20 is equal to

(a) 600 (b) – 600 (c) 50 (d) 10

13. 10 × (- 20) is equal to

(a) 200 (b) -200 (c) 30 (d) 10

14. (- 10) × 0 × (- 15) is equal to

(a) 0 (b) 10 (c) 15 (d) 150

15. The integer whose product with (- 1) is 0, is

(a) 1 (b) -1 (c) 0 (d) none of these​

Answer 1

1. On a number line, when we add a positive integer, we:

Solution:

On a number line, when we add a positive integer, we "move to the right".

Thus, the required option is a)

2. On a number line, when we add a negative integer, we:

Solution:

On a number line, when we add a negative integer, we "move to the left".

Thus, the required option is b)

3. On a number line, when we subtract a positive integer, we:

Solution:

On a number line, when we subtract a positive integer, we "move to the left.

Thus, the required option is b)

4. On a number line, when we subtract a negative integer, we:

Solution:

On a number line, when we subtract a negative integer, we "move to the right".

Thus, the required option is a)

5. When two positive integers are added, we get:

Solution:

When two positive integers are added, we get "always a positive integer".

Thus, the required option is a)

6. When two negative integers are added, we get:

Solution:

When two negative integers are added, we get "a negative integer".

Thus, the required option is b).

7. Check the options:

a) (- 8) + (- 4) > (- 8) – (- 4)

or, - 8 - 4 > - 8 + 4

or, - 12  > - 4, is not true.

b) (- 8) + (- 4) < (- 8) – (- 4)

or, - 8 - 4 < - 8 + 4

or, - 12  < - 4, is  true.

c) (- 8) + (- 4) = (- 8) – (- 4)

or, - 8 - 4 = - 8 + 4

or, - 12  = - 4, is not true.

Thus, the required is b).

8. The product of two negative integers is:

Solution:

The product of two negative integers is always positive integer.

For example: The two negative integers are - 2 and - 5

= (- 2) × (- 5)

= 10 [ ∵ ( - )× ( - ) = +]

Thus, the required option is a).

9. The product of three negative integers is:

Solution:

The product of three negative integers is negative integer.

For example: The three negative integers are - 2, - 4 and - 5

= (- 2) × (- 4) × (- 5)

= {(- 2) × (- 4)} × (- 5)

= 8 × (- 5) [ ∵ ( - ) × ( - ) = +]

= - 50 [ ∵ ( + ) × ( - ) =  - ]

Thus, the required option is b).

10. (- 1) × (- 1) × (- 1) × ……. 10 times is equal to:

Solution:

∴ (- 1) × (- 1) × (- 1) × ……. 10 times

= 1 [ ∵ 10 is even number. ]

Thus, the required option is a).

11. (- 20) × (- 5) is equal to:

Solution:

We have:

(- 20) × (- 5)

= 20 × 5 [ ∵ ( - ) × ( - ) = +]

= 100

Thus, the required option is a).

12. (- 30) × 20 is equal to:

Solution:

We have:

(- 30) × 20

= - 30 × 20 [ ∵ ( - ) × ( + ) =  -]

=  - 600

Thus, the required option is b).

13. 10 × (- 20) is equal to:

Solution:

We have:

10 × (- 20)

= - 10 × 20 [ ∵ ( + ) × ( - ) =  -]

=  - 200

Thus, the required option is b).

14. (- 10) × 0 × (- 15) is equal to:

Solution:

We have:

(- 10) × 0 × (- 15)

= 0 [∵ Zero is multiply by any number product is always zero]

Thus, the required option is a).

15. The integer whose product with (- 1) is 0, is:

Solution:

Let x be the integer.

x × ( - 1) = 0

⇒ x = $\dfrac{0}{-1}$

⇒ x = 0

Thus, the required option is c)

Answer 2

Answer:

1. On a number line, when we add a positive integer, we