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- Question 1 of 9
##### 1. Question

- Write down a pair of integers whose

(a) sum is –3 (b) difference is –5

(c) difference is 2 (d) sum is 0

This response will be reviewed and graded after submission.

Grading can be reviewed and adjusted.Grading can be reviewed and adjusted.##### Hint

Ans:

(a) (–5) + 2 = –3

(b) (–9) – (– 4) = –5

(c) (–7) – (–9) =

(d) 5 + (–5) = 0

- Question 2 of 9
##### 2. Question

Fill in the blanks to make the following statements true:

(i) (–5) + (– 8) = (– 8) + (…………)

(ii) –53 + ………… = –53

(iii) 17 + ………… = 0

(iv) [13 + (– 12)] + (…………) = 13 + [(–12) + (–7)]

(v) (– 4) + [15 + (–3)] = [– 4 + 15] + …………

This response will be reviewed and graded after submission.

Grading can be reviewed and adjusted.Grading can be reviewed and adjusted.##### Hint

Ans: (i) –5 (ii) 0 (iii) –17 (iv) –7 (v) –3

- Question 3 of 9
##### 3. Question

Find each of the following products:

(i) (–18) × (–10) × 9 (ii) (–20) × (–2) × (–5) × 7

This response will be reviewed and graded after submission.

Grading can be reviewed and adjusted.Grading can be reviewed and adjusted.##### Hint

Ans:

(i) (–18) × (–10) × 9 = [(–18) × (–10)] × 9 = 180 × 9 = 1620

(ii) (–20) × (–2) × (–5) × 7 = – 20 × (–2 × –5) × 7 = [–20 × 10] × 7 = – 1400

- Question 4 of 9
##### 4. Question

- In a class test containing 15 questions, 4 marks are given for every correct answer and (–2) marks are given for every incorrect answer.
- Gurpreet attempts all questions but only 9 of her answers are correct. What is her total score?
- One of her friends gets only 5 answers correct. What will be her score?

This response will be reviewed and graded after submission.

Grading can be reviewed and adjusted.Grading can be reviewed and adjusted.##### Hint

Ans:

(i) Marks given for one correct answer = 4

So, marks given for 9 correct answers = 4 × 9 = 36

Marks given for one incorrect answer = – 2

So, marks given for 6 = (15 – 9) incorrect answers = (–2) × 6 = –12

Therefore, Gurpreet’s total score = 36 + ( –12) = 24

(ii) Marks given for one correct answer = 4

So, marks given for 5 correct answers = 4 × 5 = 20

Marks given for one incorrect answer = (–2)

So, marks given for 10 (=15 – 5) incorrect answers = (–2) × 10 = –20

Therefore, her friend’s total score = 20 + ( –20) = 0

- Question 5 of 9
##### 5. Question

Suppose we represent the distance above the ground by a positive integer and that below the ground by a negative integer, then answer the following:

(i) An elevator descends into a mine shaft at the rate of 5 metre per minute. What will be its position after one hour?

(ii) If it begins to descend from 15 m above the ground, what will be its position after 45 minutes?

This response will be reviewed and graded after submission.

Grading can be reviewed and adjusted.Grading can be reviewed and adjusted.##### Hint

Ans:

(i) Since the elevator is going down, so the distance covered by it will be represented by a negative integer.

Change in position of the elevator in one minute = – 5 m

Position of the elevator after 60 minutes = (–5) × 60 = – 300 m, i.e.,

300 m below down from the starting position of elevator.

- Change in position of the elevator in 45 minutes = (–5) × 45

= –225 m,

I.e., 225 m below ground level.

So, the final position of the elevator = –225 + 15 = –210 m, i.e., 210 m below ground level.

- Question 6 of 9
##### 6. Question

- Can we say [(–16) ÷ 4] ÷ (–2) is the same as (–16) ÷ [4 ÷ (–2)]?

This response will be reviewed and graded after submission.

Grading can be reviewed and adjusted.Grading can be reviewed and adjusted.##### Hint

Ans:

We know that [(–16) ÷ 4] ÷ (–2) = (– 4) ÷ (–2) = 2

And (–16) ÷ [4 ÷ (–2)] = (–16) ÷ (–2) = 8

So [(–16) ÷ 4] ÷ (–2) ¹ (–16) ÷ [4 ÷ (–2)]

- Question 7 of 9
##### 7. Question

- In a test (+5) marks are given for every correct answer and (–2) marks are given for every incorrect answer. (i) Radhika answered all the questions and scored 30 marks though she got 10 correct answers. Find the number of incorrect answers .

This response will be reviewed and graded after submission.

Grading can be reviewed and adjusted.Grading can be reviewed and adjusted.##### Hint

Ans:

Marks given for one correct answer = 5

So, marks given for 10 correct answers = 5 × 10 = 50

Radhika’s score = 30

Marks obtained for incorrect answers = 30 – 50 = – 20

Marks given for one incorrect answer = (–2)

Therefore, number of incorrect answers = (–20) ÷ (–2) = 10

- Question 8 of 9
##### 8. Question

- A shopkeeper earns a profit of 1 by selling one pen and incurs a loss of 40 paise per pencil while selling pencils of her old stock.

(i) In a particular month she incurs a loss of 5. In this period, she sold 45 pens. How many pencils did she sell in this period?

(ii) In the next month she earns neither profit nor loss. If she sold 70 pens, how many pencils did she sell?

This response will be reviewed and graded after submission.

Grading can be reviewed and adjusted.Grading can be reviewed and adjusted.##### Hint

Ans:

(i) Profit earned by selling one pen = 1

Profit earned by selling 45 pens = 45, which we denote by + 45

Total loss given = 5, which we denote by – 5

Profit earned + Loss incurred = Total loss

Therefore, Loss incurred = Total Loss – Profit earned

= (– 5 – 45) = (–50) = –5000 paise

Loss incurred by selling one pencil = 40 paise which we write as – 40 paise

So, number of pencils sold = (–5000) ÷ (– 40) = 125

(ii) In the next month there is neither profit nor loss.

So, Profit earned + Loss incurred = 0

I.e., Profit earned = – Loss incurred.

Now, profit earned by selling 70 pens = 70

Hence, loss incurred by selling pencils = 70 which we indicate by – 70

=– 7,000 paise.

Total number of pencils sold = (–7000) ÷ (– 40) = 175 pencils.

- Question 9 of 9
##### 9. Question

- Fill in the blanks:

(a) 369 ÷ _____ = 369 (b) (–75) ÷ _____ = –1

(c) (–206) ÷ _____ = 1 (d) – 87 ÷ _____ = 87

(e) _____ ÷ 1 = – 87 (f) _____ ÷ 48 = –1

(g) 20 ÷ _____ = –2 (h) _____ ÷ (4) = –3

This response will be reviewed and graded after submission.

Grading can be reviewed and adjusted.Grading can be reviewed and adjusted.##### Hint

Ans:

(a) 1 (b) 75 (c) – 206 (d) –1 (e) – 87 (f) – 48 (g) –10 (h) –12

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