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Class 6 R S Aggarwal Maths Solutions

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5.  Fractions   5A, 5B, 5C, 5D, 5E, 5F

6.  Simplification 6

7.  Decimals 7A, 7B, 7C, 7D

8.  ALGEBRIC EXPRESSION 8A, 8B, 8C, 8D

9.  LINEAR EQUATIONS IN ONE VARIABLE 9A ,9B, 9C  

 

 

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EXERCISE – 5A     FRACTIONS

 

Q4.      Write a fraction for each of the following:

            [i]     three- fourths =      [ii]  four – sevenths =

            [iii]   two – fifths =          [ iv]  three-tenths=

            [v]    one-eights =            [vi]  five-sixths =

            [vii]  eight-ninths =       [ viii]  seven-twelfths =

 

 

Q5.      [i]       numerator = 4, denominator = 9

            [ii]        numerator =8 , denominator = 11.

            [ii]       numerator = 8, denominator = 15

 

Q7.      [i]     two-third    [ ii]  four-ninths  [iii]   = two-fifths.

 

 

Q8.      We know that, 1 hr = 60 minutes     www.rsmaths99.com

             Required fraction =     =   

 

Q9.     Natural number from 2 to 10 are 2, 3, 4, 5, 6, 7, 8, 9, 10.

          So, there are 9 natural numbers from 2 to 10.

          And Prime numbers from 2 to 10 are 2, 3, 5, 7

          So, there are 4 prime nos.

            Required fraction = 

Q10.    i] .  ii]   x 27 = 18 balls.  iii]     

           

Q11.    i]  cups  ii]   rackets  iii]  = 24.

 

Q10.   

               

 

 

               

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Exercise – 5B

 

Q8.

 

 

EXERCISE – 5C 

 

 

Q1.      Write five fractions equivalent to each of the following:

 

            i]     ;       

 

          ii]   =          

 

Q2.      Which of the following are the pairs of equivalent fractions?

 

            [i]        => 5 x 24= 120 and 6 x 20 = 120

 

            5 x 24 = 6 x 20.   Hence,     are equivalent.

 

          [v]        =>  1 x 24 = 24and 3 x 9 = 27

 

            1 x 24  3 x 9.   Hence,    are not equivalent.

         

[ii]   and   .  www.rsmaths99.com

 

Hence  and  are equivalent.

 

                [iv]   and              

           

Hence,  and    are equivalent.

 

Q3.      [i]  Let       Clearly, 30 = 5 x 6  

 

    =   . Hence, the equivalent fraction is

[ii]   Let      Clearly, 24 = 3 x 8

         

                        =      Hence, the equivalent fraction is  .

 

Q4.     [i]  Let        www.rsmaths99.com

 

    =        Hence, the equivalent fraction is   .

           

            [ii]   Let     Clearly, 35 = 5 x 7

             

                    =   =   Hence, the equivalent fraction is   .

                  

Q6.        =   =    Hence, the equivalent fraction is    .

 

Q7.      [i]   Let          Clearly, 9 = 36

 

            =      =      Hence, the equivalent fraction is   .   

 

            [ii]  Let           Clearly, 4 = 48 12

 

                   =      =      Hence, the equivalent fraction is    .   

 

Q8.      [i]  Let   =      Clearly 4 = 56    www.rsmaths99.com

 

                 =      =       Hence, the equivalent fraction is    .   

 

            [ii]    Let   =      Clearly 10 = 70

 

                 =      =       Hence, the equivalent fraction is  .   

 

 

Q9.      [i]       => factor of 9 = 1, 3, 9. Factor of 15 = 1, 3, 5, 15.

                               

            Common factor = 1, 3.  HCF(highest common factor) = 3.

 

               Hence, the simplest form of     is   .

 

            [ii]        => factor of 18 = 1, 2, 3, 6, 9, 18. Factor of 24 = 1, 2, 3, 4, 6, 8, 12, 24.

            Common factor = 1, 2, 3, 6     HCF(highest common factor) = 6.

             .     Hence, the simplest form of       is

 

 

Q10.       Show in the simplest form:   www.rsmaths99.com

                I]      => factor of 8 = 1, 2, 4, 8.   Factor of 11= 1, 11

               

                HCF of 8 & 11 = 1            is in simplest form.

                Ii]        => factor of 9 = 1, 3, 9. Factor of 14 = 1, 2, 7, 14.

               

HCF of 9 & 14 = 1              is in simplest form. 

[iii]       => factor of 25 = 1, 5, 25.   Factor of 36 = 1, 3, 4, 6, 9,36

                HCF of 25 & 36 is 1.        is in simplest form. 

 

Q11.       (i)              

           

            (ii)         

 

(iii)          

 

 (iv)         

 

(v)     

 

(vi)       

 

 

EXERCISE -5D

 

 

Q1.         Define:

                Like fractions:- fractions having same denominator are called like fractions.

                Ex.-      ,and     

           

            Unlike fraction :- fractions having different  denominator are called unlike fractions.

                Ex. -   , 

 

Q2.         Convert into like fractions:   , 

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

                So, we convert each fractions into an equivalent fraction with 30 as the denominator.

                Thus, we have,

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Q4.      i]           [ii] >  [iii]         [iv] > [v] <   [vi] >

 [If denominator is same then compare the numerator only]

 

Q5.      i]   [ By cross multiplication 5 x 3 = 15 and 4 x 3 = 12. ]

           

            ii]      [By cross multiplication 10 x 7 = 70 and 8 x 7 = 56]

               

[OR If numerator is same then smaller denominator is greater of the two]

 

Q6.          By cross multiplication = 7 x 4 = 28 and 5 x 5 = 25

           

                 

 

Q16.         By cross multiplication = 7 x 10 = 70 and 8 x 9 = 72

           

             

 

Arrange in the ascending order:   www.rsmaths99.com

 

Q18.           LCM of 2, 4, 6, 8 =(2x2x3x2)= 24.

           

            So, we convert each fractions into an equivalent fraction with 24 as the denominator.

                Thus, we have,

                 

 

            Clearly,                

          Hence, the given fractions in the ascending order are   ,    

 

Q19.     

 

            LCM of 3, 6, 9, 18 = (3 x 3 x 2) = 18.  www.rsmaths99.com

 

                So, we convert each fractions into an equivalent fraction with 18 as the denominator.

                Thus, we have,

                  =     = ;       

 

            Clearly,    <             <   <   .

Hence, the given fractions in the ascending order are    ,   ,  .

 

Q20.     ,  

 

            LCM of 5 , 10, 15, 30 = 30    www.rsmaths99.com

          So, we convert each fractions into an equivalent fraction with 30 as the denominator.

            Thus, we have,

            ;   ;        

 

          Clearly,  <   <  <            <    .

          Hence, the given fractions in the ascending order are   ,    

 

Q21.   ,     LCM of 4, 8, 16, 32 = (2 x 2 x 2 x 2x 2)=32.

          So, we convert each fractions into an equivalent fraction with 32 as the denominator.

            Thus, we have,

           

             =           

 

          Clearly,    <        <   <      

          Hence, the given fractions in the ascending order are   ,  ,   .

 

                Arrange the following fractions in the descending order:

Q22.        ,      LCM of 4, 8, 12, 24= (4 x 3 x 2)= 24    www.rsmaths99.com

               

                So, we convert each fractions into an equivalent fraction with 24 as the denominator.

                Thus, we have,

               

                       

 

            Clearly,   >        

            Hence, the given fractions in the descending order are    .

 

Q23.       LCM of 9, 12, 18, 36 = (3 x 3 x 2 x 2)= 36.

 

            So, we convert each fractions into an equivalent fraction with 36 as the denominator.

                Thus, we have,

                      

               

            Clearly,   >         > 

                Hence, the given fractions in the descending order are     ,  .

Q28.       Lalita read 30 pages of a book containing 100 pages

                Sarita read   of 100 =   = 40 pages

                Hence, Sarita read more pages than Lalita.   www.rsmaths99.com

 

Q29.       We will compare the exercise time of both i.e.   hr with  hr

                By cross multiplying, we get:

                4 x 2 = 8 and 3 x 3 = 9

                Clearly, 8  < 9

Hence,   hr <   hr

Therefore, Rohit exercised for a longer time.

 

Q30.       Passed students in VI A =   =  

                Passed students in VI B =    =

 

                 Now,      =  

                 So, both sections have the same result.

              

EXERCISE -5E  

 

Find the sum:

 

Q1.     

 

Q3.      1 +   =     www.rsmaths99.com

 

 Q7.       =

 

Q11.    3 +   =

 

Q14.    = 10.

 

Q15.    2 + =             

 

Q16.    Cost of pencil = Rs

            Cost of eraser = Rs

            Total cost of both the articles =        +  

 

Q17.      Total cloth purchased by Sohini =

 

Q18.    Distance of Kishan’s house from school = dist. covered by rickshaw + on foot

             Total distance =      www.rsmaths99.com

 

Q19.    Weight of cylinder filled with  gas = wt. of an empty gas cylinder + wt. of gas

              Total weight =  

 

EXERCISE-5F 

 

 

Find the difference:

 

Q1.       

 

Q4.       =     [ LCM of 6 and 9 = 18 ]

 

Q10.  

Simplify:

 

Q13.    =

 

Q16.  

 

Q19.    

 

Q22.   19 -

 

Q23.      www.rsmaths99.com

 

Q24.    =

           =  . now subtract;   =3

 

Q25.   Let us compare   

          7x 3 = 21 and 5 x 4 = 20,  and 21>20

   >

          Required difference = -   =

          Hence,    by   

 

Q26.     -    == 1

 

Q27.   Actual duration of the film =