1.Integers are marked on the number line. which is the biggest and which is the smallest. 

The numbers marked are -3 and 2.

2 is on the right side of -3.

Therefore  biggest  number = 2

Smallest number = -3

2. Write the integers between the pairs of integers given below. Also, choose the biggest and smallest integer  from them. 

a) -5, -10         b) 3,-2

a) Integers between -5 and -10 are -6,-7,-8,-9.

    Smallest integer = -9

    Biggest integer = -6

b) Integers between 3 and -2 are -1,0,1,2

   Therefore smallest integer = -1

   Biggest  integer =2

3. Represent 6,-4, 0 and  4 on a number line.

4.  Represent the following additions on a number line.

    a) 5+7        b) 5+ -2

5. Compute the following.

a)  14+(-6)      b) 4+ (-4)    c)  11+3       d) 14+ (-10)

   a) 14+(-6)  = 14-6 = 8

   b) 4+(-4) = 4-4 = 0

   c) 11+3 = 14

   d) 14+ (1-0) = 14-10 = 4

6. Solve the following.

   a) 17- (-14)    b) 25-33         c) 80-(-50) 

  a) 17-(-14) = 17+14

                    = 31

   b) 25-33    = - (33-25)

                    = -8

   c) 80-(-50)  =  80+50

                      = 130

7. A certain freezing process requires that room temperature be lowered from 40^oC at the rate of 5^oC every hour. What will be the  room temperature 10 hours after the process begins? 

      At present, the room temperature = 40^oC

     The total  decrease in temperature after 10 hours at the rate of 5^oC a hour = 10 x 5 = 50^o

Therefore temperature after 10 hours = 40^o-50^o= -10^oC. 

8. In a  class test containing 10 questions, '3' marks are awarded for every correct answer and (-1) mark is for every incorrect answer and '0' for questions not attempted. 

   (i)  Gopi gets 5 correct and 5 incorrect answers.  What is his score?

   (ii)  Reshma gets 7 correct answers and 3 incorrect answers. What is her score?

    (i)  Gopi's score= 5 x 3 +5(-1) = 15+(-5)

                                                  = 15-5=10

     (ii) Reshma's score = 7 x 3 +3 x (-1)

                                     = 21+(-3) = 21-3=18

9.Verify 18 x  [7+ (-3) = [18 x 7] + [18 x (-3)]. 

   LHS = 18 x [7+ (-3)]

           = 18 x 4

           = 72

   RHS = [18 x 7]+ [18 x (-3)]

           = 126 +(-54)= 72

RHS = LHS

10. Find the product using suitable properties.

   i) 26 x (-48)+(-48) x (-36)

  ii) 8 x 53 x (-125)

  iii) 625 x (-35)+ (-625) x 65

 i) 26 x (-48)+(-48) x (-36)= -48(26-36)

                                    =-48 x -10

                                    =480

 ii) 8 x 53 x (-125) = 53 x [8 x (-125)]

                        = 53 x -1000

                        =-53000

 iii)625 x (-35)+ (-625) x 65 = 625(-35-65)

                                       = 625 x (-100)

                                       = -62500

11. In a class test containing 15 questions, 4 marks are given for every correct answer and (-2) marks are given for every incorrect answer.

  i) Bharathi attempts all questions but only 9 answers are correct.  What is her total score? 

 ii) One of her friends Hema answers only 5 questions correct.  What will be her total score?

 i) Bharathi's score = 4 x Number of correct answers+ (-2) x number of wrong answers

               = 4 x 9 + (-2) x 6

               = 36-12=24

 ii) Hema's score = 4 x 5+ (-2) x 10

                          = 20+(-20)=0

12. The temperature at  12 noon was 10^o C above zero. If it decreases at the rate of 2^oC per hour until mid-night, at what time would the  temperature be 8^oC below zero.  What  would be the temperature at midnight. 

    The temperature at 12 noon = 10^oC

   Given  temperature = 8^oC below zero = -8^oC

   Difference between the temperature = 10^o- (-8^o) = 18^oC

 Therefore time lasted= 18÷2=9 hours

 ie, at 9 o' clock the temperature would be -8^oC.

 At midnight  the temperature = 10+12(-2)

                                             = 10+(-24) =-14^oC

13. An elevator descends into a mine shaft  at the rate of 6 meters per minute. If the descent  starts from 10 m above the ground level, how  long will it take to reach - 350 m.

  Total length to be descend = -350-10= -360 m

    Rate of the  speed of the elevator = 6 m per minute

   Total time to descend = 360/6= 60 minute

                                       =1  hour

14. Is the commutative law holds for  integers w. r.t subtraction?

  Consider two integers 10 and -12.

   10 - (-12) = 10+12=22

          (-12) -10 = -22

  Therefore 10-(-12) ≠(-12) -10

   Therefore integers are not commutative w.r.t subtraction.

15. Simplify 13-12-15+16+8.

    13-12-15+16+8= (-13-12-15) +(16+8)

                             = -40+24

                             = -16