**EXERCISE-6.1**

**Q.1. For the following, write the opposite of it.**

(i) Increment of weight.

Ans. Decrement of weight.

(ii) 40 Km west.

Ans. 40 Km east.

(iii) 456 AD

Ans. 456 BC

(iv) 900 Rs loss

Ans. 900 Rs gain

(v) 200 m below sea level.

Ans. 200 m above sea level.

**Q.2. Express the following in terms of integers with signs.**

(i) Five hundred rupees is deposited.

**Ans**. +500

(ii) Eight hundred rupees is withdrawn.

Ans. – 800

(iii) The altitude of a plane is three thousand meters above the sea level.

Ans. +3000

(iv) The depth of a submarine is three hundred meters below sea level.

Ans. – 300

**Q.3. Express the given on a number line.**

(i) +6

(ii) – 9

(iii) +4

(iv) – 2

(v) – 5

**Q.4. For the given scenarios, answer the following:**

**(i) If the point C is +5, then what is point G?**

**(ii) Check whether the point A is a positive or negative integer.**

**(iii) For the point H and C, write the integer for it.**

**(iv) Which point has the highest value in the number line?**

**(v) Arrange the points in the increasing order.**

**Ans.** (i) Point G is – 6.

(ii) It is a positive integer (+2).

(iii) – 2 represents point H and +5 represents point C.

(iv) The point D has the highest value and its value is +8.

(v) E < F < G < H < A < B < C < D

**Q.5. The temperature on a particular day is given below for various cities.**

Place |
Temperature |

Ladakh | 5^{0}C below 0^{0}C |

Sikkim | 3^{0}C below 0^{0}C |

Chennai | 30^{0}C above 0^{0}C |

Bangalore | 23^{0}C above 0^{0}C |

Agra | 1^{0}C below 0^{0}C |

(i) Convert the following temperature in the form of aninteger.

(ii) Represent the following places in number scale.

(iii) Which is the hottest place?

(iv) What are the places whose temperature is below 0∘C

**Ans.**

(i) Ladakh = −5^{0}C

Sikkim = −3^{0}C

Chennai = +30^{0}C

Bangalore = +23^{0}C

Agra = −1^{0}C

**(ii)**

**(iii)** The hottest place of all is Chennai.

**(iv)** Ladakh and Sikkim are the places which are below 0 ^{0}C.

**Q.6. In the given pair, which lies on the right side in the number line.**

**(i) 3,7 (ii) -4,-5 (iii) -1,0 (iv) 12,-15 (v) -1,1 (vi) -122,2**

**Ans.** (i) 7. As 7 is > than 3

(ii) -4. As – 4 is greater than – 5.

(iii) 0. As 0 is > than – 1.

(iv) 12. As 12 is > than – 15.

(v) 1. As 1 is > than – 1.

(vi) 2. As 2 is > than – 122.

**Q.7. For the given pair, write all the integers in-between them.**

(i) 1 and 8

Ans. 2, 3, 4, 5, 6, 7

(ii) 2 and -5

Ans. – 4, -3, -2, -1, 0, 1

(iii) -21 and -27

Ans. -26, -25, -24, -23, -22

(iv) -15 and -20

Ans. -19, -18, -17, -16

**Q.8. (i) Give 5 integers which are greater than – 15.**

**Ans.** – 14, -13, -12, -11, -10

**(ii) Give 5 integers which are less than -5**

**Ans**. -6, -7, -8, -9, -10

**Q.9. State whether the following are True or False:**

(i) – 5 is on the right to – 9 on the number line.

**Ans.** True ( -5 > -9)

(ii) – 50 is on the right to -25 on the number line.

Ans. False ( -25 > -50 )

(iii) – 1 is the smallest negative integer.

Ans. False, as – 1 is the largest negative integer.

(iv) -26 is bigger than -27.

Ans. True (-26 > -27)

**Q.10. With the help of number line, answer the following.**

**(i) What is the number when we move from -3 to four places right to it?**

**(ii) What is the number when we move from 3 to five places left to it?**

**(iii) What is the direction if we move from -6 to -11?**

**(iv) What is the direction if we move from -2 to 3?**

**Ans.**

(i)

We will move to 1.

(ii)

We will reach – 2.

(iii)

We move in the left direction

(iv)

We should move in the right direction.

**EXERCISE-6.2**

**Q.1. Using number line, answer the following.**

**(i) 3 greater than 2**

Ans.

Therefore, 5.

**(ii) 5 greater than –2.**

Ans.

Therefore, 3.

**(iii) 6 less than 3**

Ans.

Therefore, -3.

**(iv) 3 less than -4**

Therefore, -7.

**Q.2. Add the following integers in the number line.**

**(i) 10 + (-6)**

Ans.

Therefore, 4.

**(ii) 6 + ( -11)**

Ans.

Therefore, -5.

**(iii) (-4) + 10**

Ans.

Therefore, 6.

**(iv) (1) + (-7)**

Ans.

Therefore, -6.

**(v) (7) + (-2) + (-3)**

**Ans.**

Therefore, 2.

**(vi) (3) + (8) + (-4)**

**Ans.**

Therefore, 7.

**Q.3. Find the integer without using number line.**

(i). 12 + (-5) = 7.

(ii). (-14) + (+19) =5.

(iii). (-11) + (+15) = 4.

(iv). (-350) + (+250) = -100.

(v). (-225) + (-150) = -375.

(vi). (-120) + (-100) = -220.

**Q.4. Find the sum of:**

**(i) 140 and -240**

**Ans.** 140 + (-240) = -100

**(ii) -67 and 67**

**Ans.** -67 + 67 = 0

**(iii) – 122, 23 and 231**

**Ans.** – 122 + 23 +231 = 132

**(iv) -60, -250 and 300**

**Ans.** – 60 – 250 + 300 = -10

**Q.5. Find the sum of the following:**

**(i) (12) + (-21) + (34) + (-6).**

**(ii) (-32) + (43) + (-54) + (23).**

Ans. (i) 12 + (-21) + 34 + (-6) = 19.

(ii) (-32) + 43 + (-54) + 23 = -20.

**EXERCISE-6.3**

**Q.1. Find the answers for the following.**

(i) 12 – (15) = -3

(ii) 23 – (12) = 11

(iii) -12 – (-25) = 13

(iv) 34 + (13) = 47

(v) 23 – (-20) = 43

(vi) -43 – (-23) = -20

**Q.2. Check whether the following are >, < or = sign.**

**(a) (– 4) + (– 7) _______ (– 4) – (– 7)**

**Ans**. -11 < 3

**(b) – 22 – (– 11) ________ (– 32) + (– 12) **

**Ans.** -11 > -44

**(c) 46 – (– 12) __________ 58 + (– 5)**

**Ans.** 58 > 53

**(d) (– 26) – (– 43) __________ (– 43) – (– 26)**

**Ans.** 17 > –17

**Q.3. Complete the following:**

**(a) (-7) + ____ = 0**

**Ans.** 7

**(b) 14 + _____ = 0**

**Ans.** –14

**(c) 14 + (-14) = _____**

**Ans.** 0

**(d) (-5) + _____ = –13**

**Ans.** -8

**(e) _____ – 16 = –10**

**Ans.** 6

**Q.4. Answer the following:**

**(a) (–8) – 9 – (–26)**

**Ans.** – 8 – 9 + 26 = 9

**(b) (–14) + 33 – 9 – 2**

**Ans.** – 14 + 33 – 9 – 2 = 8

**(c) (– 8) + (– 9) + (– 91)**

**Ans**. – 8 – 9 – 91 = –108

**(d) 51 – (–41) – (–3)**

**Ans.** 51 + 41 + 3 = 95