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cClass 7 Maths R S Aggarwal Solutions

Contents

1.        Integers 1A, 1B, 1C

2.        Fractions 2A, 2B

3.        Decimals 3A, 3B, 3C, 3D

4.        Rational Numbers 4A, 4B, 4C, 4D, 4E, 4F

EXERCISE – 1A  INTEGERS

Q1.         [i]   15 + (-8) = 15 – 8 = 7.   [ii]    (-16 ) + 9 = 16 +  9 = -7.

 [iii]   (-7)+(-23) = -7 -23 = -30.     [iv]  -32 + 47 = 15    

  [v] 53 + (-26) = 53 -26 = 27.    [vi]  (-48) + (-36)= -48 – 36 = -84.

 

Q2.         Find the sum :     [i]  153 + -302 = 153 -302 = -149.   www.rsmaths99.com

 [ii]   1005 – 277 = 728.    [iii]   -2035 + 297 = -1738. 

[iv]  -489 +(-324) = -489 -324 = -813. [ V] -562    vi] 262.

 

Q3.         Additive inverse of:

                [i]   -83  = 83  [ii] 256 = - 256.  [iii]  0 = 0  iv]  -2001 = 2001.

 

Q4.         Subtract:    [i]  -42 – 28 = -70. [ii] 42 – 36 = 78.

 [iii]  -53 –(-37) = -53 +37 = -16.

 

Q5.         -1032 + 878 = -154.   -34 –(-154)= -34 + 154 = 120.

 

Q6.         38 + -87 = 38 -87 = -49.   -49 –(-134)= -49 + 134 = 85.

www.rsmaths99.com

Q8.         {-13 – (-27)}+ {-25 –(-40)} = (-13 + 27)+ (-25 + 40) = 14 + 15 = 29.

 

Q9.         36 –(-64) and (-64)-36    =  36 +64 and -64 -36 =>  100  100.

Q10.       (a + b)+ c = a + (b + c)  => -8 + (-7) + 6 = -8 + (-7 + 6)  =>  -8 -7 +6 = -8 -7 + 6 .

                -15 + 6 = -15 + 6  => -9 = -9.

Q11.       Show that: (a - b) (b - a) = [-9 –(-6)]  & [(-6 )- (-9)]  =   -9 + 6 &    -6 +9   = -3   3.    

Q12.       X + y = -16.  => x + 53 = -16  => x = -16 – 53 = -69.

Q13.       X + y = 65 x – 31 = 65 => x = 65 + 31 = 96.  www.rsmaths99.com

Q14.       a – (-6) = 4 => a + 6 = 4 =>a = 4 -6 = -2.

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EXERCISE – 1B  INTEGER   

RULES:         1)   (-1) X (-1) X (-1)X …..n = 1   where n is even.

1)      (-1) X (-1) X (-1)X …..n = -1   where n is odd .

Q1.         Multiply:   [i]   -53 x 18 = -954.       [x]  -36 x -50 = 1800.

Q2.         [i]   3x 4 x (-5) =  12 x -5 = -60.       [iii]  -5 x -8 x -3 = -120.  [rule 2]

                [iv]  - 6 x 6 x -10 = - 36 x -10 = 360.   [rule 1]    www.rsmaths99.com

Q4.         90 –ve integers. Here 90 is even no. so, sign will be +ve. [rule 1] & 9 integers is +ve. 

                Thus the sign of product will be +ve.

Q5.         Here, 103 –ve  integers which is odd no. [Rule 2] & 65 +ve integers is +ve sign.

                Thus the sign of product will be –ve. Because 103 > 65.

Q6.         Simplify:   www.rsmaths99.com

                [v]   (-11 x -15) + (-11 x -25)   =  165 + 275 =  440.

                [viii]    (-26 x 72) + (-728)  = -1872 – 728 = -2600.

Q8.               5 marks(correct)         -2 marks(incorrect)         0 marks(no attempted)

                [i]       4 x 5 = 20                  6 x – 2 = -12        score = 20 – 12 = 8.

                [ii]      5 x 5 = 25                  5 x – 2 = - 10         score = 25 – 10 = 15.

                [iii]    2 x 5 = 10                  5 x – 2 = 20          score = 10 -10 = 0.

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EXERCISE – 1C INTEGER: DIVISION 

 

Q1.         Div ide:      www.rsmaths99.com

                [i]            65 by -13  =    [ii]      [iii] 

 

                [iv]                     [v]             [vi]            

 

[vii]                    [Viii]                  [ix]

 

[x]                     [xi]  = 1.        [Xii]    

 

Q2.         [I]           72    =>

 

                [iii]         x

 

Q3.         [i]           0   True     [ii]  (-6 )    [iii]  F

 

                [iv]         T              [v]  F      [vi]  T.     www.rsmaths99.com

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EXERCISE-2A FRACTIONS                                  

                               

                Fraction s:    are whole numbers and b

                In     a is call as numerator and b as denominator     [trick to remember D = down]

Q1.         Compare the fractions:   www.rsmaths99.com

                [i]             . hence, .

 

            [ii]       =  

 

            [iii]      .     

 

Q2.      Arrange in ascending order:

            [i]         LCM of 4,6,9,12 = 3 x 2 x 2 x 3 = 36.

 

 

 

                     www.rsmaths99.com

                [ii]     LCM of 5, 10 , 15, 20 = 5 x 2 x 3 x 2 = 60.

 

                       

 

                                = 

 

Q3.         Arrange in desending order:

            [i] 

 

             =,    www.rsmaths99.com

 

          < 

 

          [ii] 

         

Q4.     Reenu got-   . Sonal got larger.

               www.rsmaths99.com

Q5.     Find the sum:  [i]           [ii]  

          [iii]        [LCM 4 x 3 x 2 x 2 = 48]

Q6.      Find the difference: 

          [iii]      [iv]  7 -

Q7.       Simplify:

            [i] 

Q8.       Total wt. of fruit =

Q9.       Perimeter =     +

Q10.    

Q11.    

Q12.    

Q13.       www.rsmaths99.com

Q14.        .

Q15.            =    diff.  Hence,

Q16.       Cost of pen = Now,

                 Hence, Pen cost is more by

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EXERCISE -2B FRACTIONS;  MULTIPLICATION.

Q1.         [i]                    [vi]   = 625.

Q2.         [i]           = [v] 

Q3.         [i]                 [vii]         [ix]

                [x]              [xi]    [xii]

Q4.         Cost of apple =     www.rsmaths99.com

Q5.         Cost of cloth = .

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EXERCISE -2B FRACTIONS; Division

Q1 .        Reciprocal :

                [i]       [ii]   7 =    

  [iii]          [iv]  

Q2.     Simplify:                www.rsmaths99.com

            [i]  

            [ix]  

Q3.     Divide:

            [i]            

[vi]  63  63 x .

Q4.     Length of each piece =

Q5.     Hence each box weight = 

Q6.     He sell oranges =  =     www.rsmaths99.com

Q7.     Mangoes wt. =

Q8.     He walks 

Q9.     Price of sugar per kg =

Q10.   No. of notebooks purchased =

Q11.   No. of ticket sold =

Q12.   No. of students =

Q13.   No. of students =

Q14.   No. of times =

Q15.   Other no. =    www.rsmaths99.com

Q16.  

Q17.    

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EXERCISE – 3A  DECIMALS

Decimals:  The no. expressed in decimal forms are called decimals.

Q1.         Convert into a fraction:   www.rsmaths99.com

                [i]  .8 =           [iv]   .285 =

Q2.         Convert as a mixed fraction:

                [i]  5.6 =  .       [iii]  

Q3.                             [v] 

Q8.         Express 45 mm in cm, m , km

                  

                 

Q9.         8 paise =       www.rsmaths99.com

 [ii]  9rupees 75 paise  =  Rs.9.75   [iii] Rs. 8.05.

Q10.       [i]     65m =      [ii]   2.84m = 0.284km.

 [iii]  3 x

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EXERCISE – 3B  ADDITION AND SUBTRACTION

ADD:

Q1.         16.00

                   8.70

                   0.94

                   6.80

                   7.77

-----------------

40.21

 

                Subtract:             

Q9.         14.79 from  72.43    www.rsmaths99.com

                                 7 2 .  4 3

-          1 4 . 7 9

------------

5 7 . 6 4

Q16.         6.732 from 9.001

                                   9.001

-  6.732

----------

  2.269

 

Q17.                       9.100

-          5.746   

----------

3.354

 

Q18.                       63.58 + y = 92.     => y = 92.00 – 63.58 = 28.42.

 

Q19.                       8.1 –y = 0.813.   => y = 8.1- 0.813 = 7.287.   www.rsmaths99.com

 

Q20.                       32.67 + y = 60.1 => y = 60.1 – 32.67 = 27.43.

 

Q21.                       74.3 – y = 26.87.  => y = 74.3 – 26.87 = > y = 47.43.

 

Q22.                       23.75

                                  2.85

                                15.90

                                -------

                                42.50                                    

 

  50.00

                                -42.50   

                                ---------

                                Rs.7.50.

               

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EXERCISE -3C  MULTIPLICATION OF DECIMALS

 

Q1.         Find the product:   www.rsmaths99.com

                [i]           73.92 x 10 = 739.2             [vi] 0.032 x 10 = 0.32

Q2.         [i]           2.397 x 100 = 239.7.

Q7.         [i]           1.2 x 1.2 = 1.44                   [ii]  0.7 x 0.7 = 0.49.

Q8.         0.3 x 0.3 x 0.3 = 0.27.

Q9.         62.5 x 18 = 1125 km.

Q10.       16.8 x 45 = 756 kg.

Q11.       97.8 x 500 = 58900kg.

Q12.       16 x 48.450 = 775.2kg.

Q13.       0.845 x 72 = 60.84 kg.

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EXERCISE -3D  DIVISION OF DECIMALS

 

Q1.         Divide:

                [i]  131.6 by 10  =

 

Q4.         [i]   12 by 8                          8) 12  (1.5

                                                                       8

                                                                -----------

                                                                     40      www.rsmaths99.com

                                                                     40

                                                                ---------

                                                                      xx    

 

Q8.         Cost of each chair =

 

 

Q9.         No. of shirts can be made =     

 

 

Q10.       2.4 ltr ------------------22.8km

                In 1ltr  ---------------

Q11.       Required tin =

Q12.       Wt. of each bags =

Q13.       Capacity of each bucket =

Q14.       No. of pieces Monica gets =

Q15.       No. of bags he buys =   www.rsmaths99.com

Q16.       1.89 x 100 = 189cm.  no. of plywood require=

Q17.       Y x 17.6 = 261.36 x 10.     => y =

[Note: start dividing with smallest no. 2, then 3 and others.]

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EXERCISE – 4A RATIONAL NUMBERS

Q1.         Rational number: The numbers of the form

   eg.- +ve rational no. =  

-ve rational no. =   Yes, zero is a rational no. which is neither +ve nor –ve.

Q2          we know rational no. is in the form of  where q  0, then except ix] & x]

                All are rational no.   www.rsmaths99.com

Q3.         [ trick : to remember Denominator, remember D for down.]

Q7.         Find four rational nos.

                [i]                 

Q8          [i]               [ii]   

Q9.         [i]  .          [ii]  

Q16.         [ ii]  

Q15.       [i]   .   [ii]    =     www.rsmaths99.com

Q17.       Write in standard form :   [i]       

 [ v]  

[Vi]    .   [notes:  take HCF of 68, & 119 it will be 17

 and then divide both the no. by 17.  17 x 4 = 68, 17 x 7 = 119.]

                [Vii]          .    [HCF of 87 & 116 = 29].

                [Viii]        .   [HCF of 299 & 161 = 23]

Q18.       [i]            

Q19.       [i]                        

It is equivalent rational no. 

 [ii]             =  

Hence,   &   are equivalent.

                [iv]         7 x 60 = -28 x 15 => 420  -420.   www.rsmaths99.com

=> Hence,

Q20.       [i]          

                [ii]         

                [V]         

Q21.       [i]            .        [ii]    

                [iii]           =>    www.rsmaths99.com

Q22.       [i]    F     II]   T      III]  F      IV]  T      V]  F.

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EXERCISE-4B

 

Q1.                                                                                                        

                                                |              |              |              O             |              |              |1

               

Q2.      [i]       or  0.   Since, every +ve rational no. is greater than 0, Hence,  > 0.

            [Vi]      Since -17 < -15.     .   www.rsmaths99.com

 

Q3.      Which one is greater:

            [i]          LCM of 9 & 8=72.      . 

Hence,

            [Vi]       <  

Hence,

 

Q4.                   www.rsmaths99.com 

=>  or,  

            Hence,

 

Q5.         Arrange the rational no. in ascending order:      

[i]               [LCM of 5,10,15,30 = 30]    

 

                                  <      Hence,

 

                [ii]              [LCM of 4,12,16,-24 = 48]

 

                                =  

 

                               www.rsmaths99.com

 

Q6.         Arrange the rational no. in decreasing order:    

                I]    LCM of 5,10,15,30 = 30.     = 

                   [since -12>-19>-21>-22]

 

                     =   

 

Q.           To find rational nos. between any two given rational nos. say 2 & 3, the following methods could be followed.   www.rsmaths99.com

                I]   Equivalent fraction method-

                Change the given rational no. into equivalent fractions, hence find the required no. of rational nos.

 

                Q1.          find 5 rational nos. between 2 and 3.

                2 = 2 x           3 = 3 x  . Any 5 rational nos. are

 

                2]   Average method:

                Q 2.         find 3 rational nos. between 2 and 3.   www.rsmaths99.com

                                1st rational no. =  

   2nd  rational no. =   =   

                                3rd rational no =     =  .

                                Decimal method:

                Q3.         find 100 rational nos. between 2 and 3.

                                100 rational nos. are (2.001 + .100= 2.101)  2.001, 2.002, 2.003,…..2.101.

 

Q8.         Find 5 rational nos. between -3 and -2.   www.rsmaths99.com

                -3 = -3 x       -2 = -2 x  .

 

  5 rational nos.  .

 

Q9.         Find 5 rational nos. between -1 and 1.

                -1 = -1 x .       1 x  

  5 rational nos. are

 

Q10.       Find 5 rational nos. between .

                LCM of 5 and 2 = 10

                    www.rsmaths99.com

                 .

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EXERCISE- 4C,   ADDITION OF RATIONAL NUMBERS

 

Q1.        Add :

[i]           .    

 [viii]