**Integers**

**Exercise 1.1**

(*) 1). Write down a pair of integers whose:

(a) sum is –7

(b) difference is –10

(c) sum is 0

Answer:

(a) sum is –7

3 + (-10)

(b) difference is –10

(-17) – (-7)

(c) sum is 0

5 + (-5)

2). (a) Write a pair of negative integers whose difference gives 8.

Ans: (-10) – (-18)

(b) Write a negative integer and a positive integer whose sum is –5.

Ans: 13 + (-18)

(c) Write a negative integer and a positive integer whose difference is –3.

Ans: -1 – (2)

3). In a quiz, team A scored – 40, 10, 0 and team B scored 10, 0, – 40 in three successive rounds. Which team scored more? Can we say that we can add integers in any order?

Scores of team A are -40,10 and 0.

Total score of team A = -40 +10 + 0

= -30 + 0

= -30

Scores of team B are 10,0 and -40

Total score of team B = 10 + 0 + (-40)

= 10 + 0 – 40

= 10 – 40

= -30.

Ans: Both the team scored equally.

4). Fill in the blanks to make the following statements true:

(i) (–5) + (– 8) = (– 8) + (…………)

Ans: (–5) + (– 8) = (– 8) + (-5)

(ii) –53 + ………… = –53

Ans: –53 + 0 = –53

(iii) 17 + ………… = 0

Ans: 17 + (-17) = 0

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

Ans: [13 + (– 12)] + (-7) = 13 + [(–12) + (–7)]

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

Ans: (– 4) + [15 + (–3)] = [– 4 + 15] + (-3)

Additional Examples for Practice

1). Following number line shows the temperature in degree celsius (°C) at different places on a particular day.

(a) Observe this number line and write the temperature of the places marked on it.

Place Temperature

Lahulspiti -8^{0 }C

Srinagar -2^{0 }C

Shimla 5^{0 }C

Ooty 14^{0 }C

Bengaluru 22^{0 }C

(b) What is the temperature difference between the hottest and the coldest places among the above?

Temperature of the hottest place = 22^{0} C

Temperature of the coldest place = -8^{0 }C

Difference = 22- (-8)

= 22 + 8

= 30

Ans: temperature difference between the hottest and the coldest places among the above = 30^{0} C.

(c) What is the temperature difference between Lahulspiti and Srinagar?

Temperature of Lahulspiti = -8^{0} C

Temperature of Srinagar = -2^{0 }C

Difference = (-2) – (-8)

= -2 + 8

= 6

Ans: temperature difference between Lahulspiti and Srinagar = 6^{0} C.

(d) Can we say the temperature of Srinagar and Shimla taken together is less than the temperature at Shimla? Is it also less than the temperature at Srinagar?

Temperature of Shimla= 5^{0} C

Temperature of Srinagar = -2^{0 }C

temperature of Srinagar and Shimla taken together = 5 + (-2)

= 5 – 2

= 3

3 < 5

temperature of Srinagar and Shimla taken together is less than the temperature at Shimla.

3 > -2

temperature of Srinagar and Shimla taken together is not less than the temperature at Srinagar.

2). In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers. If Jack’s scores in five successive rounds were 25, – 5, – 10, 15 and 10, what was his total at the end?

Jack’s score in five successive rounds = 25, – 5, – 10, 15 and 10

Total of the scores = 25+ (– 5) + (– 10) + 15 +10

= 25 – 5 -10 + 15 + 10

= 20 -10 + 15 + 10

= 10 +15 + 10

= 25 + 10

= 35

Ans: Jack’s total score at the end = 35

3). At Srinagar temperature was – 5^{0}C on Monday and then it dropped by 2°C on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4^{0}C. What was the temperature on this day?

The temperature of Srinagar on Monday = – 5^{0} C

The temperature of Srinagar on Tuesday = dropped by 2

= -5 – 2

= -7

The temperature of Srinagar on Wednesday = raised by 4^{0} C

= – 7 + 4

= – 3

Ans: The temperature of Srinagar on Tuesday and Wednesday is -7^{0} C and -3^{0} C respectively.

4). A plane is flying at the height of 5000 m above sea level. At a particular point, it is exactly above a submarine floating 1200 m below sea level. What is the vertical distance between them?

Height of the plane above sea level = 5000 m

Depth of the submarine below sea level = -1200 m

Vertical difference between plane and submarine = 5000 – (-1200)

= 5000 + 1200

= 6200 m

Ans: The vertical difference between plane and submarine= 6200m

5). Mohan deposits 2,000 in his bank account and withdraws 1,642 from it, the next day. If the withdrawal of amount from the account is represented by a negative integer, then how will you represent the amount deposited? Find the balance in Mohan’s account after the withdrawal.

withdrawal of the amount from the account is represented by a negative integer

then the deposit of the amount is represented by positive integer.

The amount deposited by Mohan in the bank = Rs 2000

The amount withdrawn by Mohan next day = – Rs 1642

Balance in the Mohan’s account = 2000 + (- 1642)

= 2000 – 1642

= 358

Ans: Balance in the Mohan’s account after withdrawl = Rs 358

6). Rita goes 20 km towards east from a point A to the point B. From B, she moves 30 km towards west along the same road. If the distance towards the east is represented by a positive integer then, how will you represent the distance travelled towards the west? By which integer will you represent her final position from A?

If the distance towards the east is represented by a positive integer then, the distance travelled towards the west is represented by a negative integer.

Rita travells from point A to the point B = 20 km

Rita travels a distance to the west = -30 km

Final position of Rita = 20 + (-30)

= 20 – 30

= -10

Ans: The integer to represent final position of Rita is -10 km.

7). Verify *a *– (– *b*) = *a *+ *b *for the following values of *a *and *b*.

(i) *a *= 21, *b *= 18 (ii) *a *= 118, b = 125

(iii) *a *= 75, *b *= 84 (iv) *a *= 28, *b *= 11

Answer:

(i) *a *= 21, *b *= 18

* a *– (– *b*) = *a *+ *b*

L H S = a – (-b) = 21 – (-18) = 21 + 18 = 39

R H S = a + b = 21 + 18 = 39

L H S = R H S

a- (-b) = a + b

(ii) *a *= 118, b = 125

*a *– (– *b*) = *a *+ *b*

L H S = a – (-b) = 118 – (-125) = 118 + 125 = 243

R H S = a + b = 118 + 125 = 243

L H S = R H S

a- (-b) = a + b

(iii) *a *= 75, *b *= 84

*a *– (– *b*) = *a *+ *b*

L H S = a – (-b) = 75 – (-84) = 75 + 84 = 159

R H S = a + b = 75 + 84 = 159

L H S = R H S

a- (-b) = a + b

(iv) *a *= 28, *b *= 11

*a *– (– *b*) = *a *+ *b*

L H S= a – (-b) = 28 – (-11) = 28 + 11 = 39

R H S = a + b = 28 + 11 = 39

L H S = R H S

a- (-b) = a + b

8). Use the sign of >, < or = in the box to make the statements true.

(a) (– 8) + (– 4) (–8) – (– 4)

(b) (– 3) + 7 – (19) 15 – 8 + (– 9)

(c) 23 – 41 + 11 23 – 41 – 11

(d) 39 + (– 24) – (15) 36 + (– 52) – (– 36)

(e) – 231 + 79 + 51 –399 + 159 + 81

Answer:

(a) (– 8) + (– 4) (–8) – (– 4)

L H S = (– 8) + (– 4) = – 8 – 4 = -12

R H S = (– 8) – (– 4) = – 8 + 4 = -4

-12 < – 4

L H S < R H S

Ans: (– 8) + (– 4) < (– 8) – (– 4)

(b) (– 3) + 7 – (19) 15 – 8 + (– 9)

L H S = (– 3) + 7 – (19) = – 3 +7- 19 = 4 – 19 = -15

R H S = 15 – 8 + (– 9) = 15 – 8 – 9 = 7 – 9 = – 2

-15 < – 2

L H S < R H S

Ans: (– 3) + 7 – (19) < 15 – 8 + (– 9)

(c) 23 – 41 + 11 23 – 41 – 11

L H S = 23 – 41 + 11 = – 18 + 11 = -7

R H S = 23 – 41 – 11= – 18 – 11 = – 29

-7 > – 29

L H S > R H S

Ans: 23 – 41 + 11 > 23 – 41 – 11

(d) 39 + (– 24) – (15) 36 + (– 52) – (– 36)

L H S = 39 + (– 24) – (15) = 39 – 24 – 15 = 15 – 15 = 0

R H S = 36 + (– 52) – (– 36) = 36 -52 + 36 = – 16 + 36 = 20

0 < 20

L H S < R H S

Ans: 39 + (– 24) – (15) < 36 + (– 52) – (– 36)

(e) – 231 + 79 + 51 –399 + 159 + 81

L H S = – 231 + 79 + 51= -152 + 51 = -101

R H S = –399 + 159 + 81 = -240 + 81= -159

-101 > -159

L H S > R H S

Ans: – 231 + 79 + 51 > –399 + 159 + 81

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