MATHEMATICS EXERCISE 1.3(CBSE CLASS-7TH)

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                                                  SUBHAM TUTORIAL 

 

1.Answer the following.
  • 3(-1)= -3
  • (-1)×225=-225
  • (-21)×(-30)=+630
  • (-316)×(-1)=316
  • (-15)×0×(-18)=0
  • (-12)×(-11)×10=132×10=1320
  • 9×(-3)×(-6)=9×18=162
  • (-18)×(-5)×(-4)=90×(-4)= -360
  • (-1)×(-2)×(-3)×4=2×(-12)= -24
  • (-3)×(-6)×(-2)×(-1)=18×2=36  
2. Verify the following.
  (a) 18×[7+(-3)]=[18×7]+[18×(-3)]
  (b) (-21)×[(-4)+(-6)]=[(-21)×(-4)]+[(-21)×(-6)]
Answre 2:-
   (a)
         L.H.S:
                    18×[7+(-3)]=18×[7-3]=18×4=72
          R.H.S:
                     [18×7]+[18×(-3)]=126+(-54)=126-54=72
        Therefore L.H.S=R.H.S verified
   (B)
        L.H.S:
                   (-21)×[(-4)+(-6)]=(-21)×[-4-6]=(-21)×(-10)=210
        R.H.S:
                   [(-21)×(-4)]+[(-21)×(-6)]=[84]+[126]=210
      Therefore L.H.S=R.H.S verified
3.
     (i) For any integer a, what is (-1) × a equal to ?
     (ii) Determine the integer whose product with (-1) is
           (a)-22 (b) 37 (c)0
      Answer3 :
​                       (i). (-1) × a= -a
                       (ii). (a) (-22)×(-1)=22
                              (b) 37×(-1)=-37
                              (c)0×(-1)=O
 4. Starting from (-1)*5, write various products showing some         pattern to show (-1)×(-1)=1

      Answer4 :
​                        -1×5= -5
                        -1*4=-4= -5+1,
                        -1*3=-3= -4+1,
                        -1*2= -2= -3+1,
                        -1*1= -1= -2+1,
                        -1*0=0=-1+1,
                  So, -1*(-1)=0+1=1
5. Find the product , using suitable properties:
      (a) 26*(-48)+(-48)*(-36)
      (b)8*53*(-125)
      (c) 15*(-25)*(-4)*(-10)
      (d)(-41)*102
      (e) 625*(-35)+(-625)*65
      (f) 7*(50-2)
      (g)(-17)*(-29)
      (h)(-57)*(-19)+57
Answer 5 ​:
      (a) 26*(-48)+(-48)*(-36)
        =(-48)*[26+(-36)].    ( Distributive property)
        =(-48)*[26-36]
        =(-48)*(-10)
        =480
      (b) 8× 53×(-125)
        =[8×(-125)]×53.        ( Commutative property)
        = -1000×53
        =-53000
      (C.) 15×(-25)×(-4)×(-10)
        =[15×(-4)]×[(-25)×(-10).        (Commutative property)
        =-60×250
        =-15000
       (d) (-41)×102

         =(-41)×(100+2).                    ( Distributive property)
         =(-41)×100+(-41)×2
         =-4100+(-82)
         =-4100-82
         =-4182
       (e) 625*(-35)+(-625)*65
           (-625)*65 can also be written as 625*(-65)
           Therefore, 625*(-35)+625*(-65)
            =625[(-35)+(-65)]. Distributivity
            =625[-35-65]
            =625*(-100)
            = -62500
       (F). 7*(50-2)
          =7*50-7*2. Distributivity
          =350-14
          =336
       (g) (-17)*(-29)
          =(-17)*[(-30)+1]. Distributivity
          =(-17)*(-30)+(-17)*1
          =510+(-17)
          =510-17
          =493
      (h) (-57)*(-19)+57
          =(-57)*(-19)+(-57)*(-1). Distributivity
          =(-57)*[(-19)+(-1)]
          =(-57)*[-19-1]
          =(-57)*(-20)
          =1140
  6. A certain freezing process requires that room temperature        be lowered from 40°c at the rate of 5°c every hour   what 
        willbe the temperature 10 hours after the process begins?
      Answer 6:
                       Given , present room temperature =40°c
                      Decrease the room temperature in every hour =5°c
                       Room temperature after 10 hour =40°c+10*(-5)
                                                                                    =40°c+(-50)
                                                                                    =40°c-50°c
                                                                                    = -10°c
                    Thus, the room temperature after 10 hour is -10°c.    Question 7.
                   In a class test containing 10 question, 5 marks are                         awarded for every correct answer and (-2) marks 
                   are awarded for every incorrect answer and 0 for                         questions not attempted.
        (i) Mohan gets four correct and six incorrect answers.what
            Is his score?
       (ii) Reshma gets five Correct answer and five incorrect
            Answer what is her score?
       (iii) Heena gets two correct and five incorrect answer 
           Out of seven question she attempts .what is her score
Answer 7:
​              (i) mohan gets marks for four correct questions=4*5=20
                 He gets marks for six incorrect questions= 6*(-2)= -12
                 Therefore , total score of mohan= (4*5)+[6*(-2)]
                                                                            =20+(-12)
                                                                            =20-12
                                                                            =8
              (ii)Reshma gets marks for 5 correct questions= 5*5=25
             Reshma gets marks for 5 incorrect questions=5*(-2)= -10
                Therefore, reshma gets total score=25+(-10)=25-10=15
            (iii) Heena gets mark for 2 correct questions=2*5=10
                  She gets marks for 5 incorrect questions= 5*(-2)=-10
                                                            Total score =10+(-10)=10-10=0
                              Therefore, heena gets o score.
Question 8:
                  A cement company earns a profit of Rs.8 per bag of                      white cement sold and a loss of Rs 5 per bag of grey                      cement sold.
                (a) The company sells 3,000 bags of white cement and                       5,000 bags of grey cement in a month .what is it's
                     profit or loss?
                (b)What is the number of white cement bags it must                        sell to have neither profit nor loss ,if the number of                      grey bags sold is 6, 400 bags.
 Answer8:
                  Given, profit of 1 bag of white cement=RS 8
                  and loss of 1 bag of grey cement=Rs 5
                   (a) Profit on selling 3,000 bags of white                                                   cement=3000*8=24000
                    Loss on selling 5,000 bags of grey                                v                           cement=5000*5=25000
                             Since profit < loss
               His total loss on selling the grey cement bag=loss-profit
                                                =25000-24000
                                                =1000
               Thus he has loss of Rs 1000 ,on selling the grey cement.
                   (b) Let the no. Of white cement bag be 'x’
                        According to question, loss =profit,Therefore
                      5* 6400= x * 8
                      X*8=3200
                      X=3200/8=4000
               Thus , he must sell 4000 white cement bag to have                          neither profit or loss.

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