*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* **(ii) Eight hundred rupees is withdrawn.*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 |
\(5^{\circ}C\) below \(0^{\circ}C\) |

Sikkim |
\(3^{\circ}C\) below \(0^{\circ}C\) |

Chennai |
\(30^{\circ}C\) above \(0^{\circ}C\) |

Bangalore |
\(23^{\circ}C\) above \(0^{\circ}C\) |

Agra |
\(1^{\circ}C\) below \(0^{\circ}C\) |

* **(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 \(0^{\circ}C\)*

Ans. (i) Ladakh = \(-5^{\circ}C\)

Sikkim = \(-3^{\circ}C\)

Chennai = \(+30^{\circ}C\)

Bangalore = \(+23^{\circ}C\)

Agra = \(-1^{\circ}C\)

(ii)

(iii) The hottest place of all is Chennai.

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

* *

*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 *

Ans.

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