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RSMATHS99.COM

CLASS VI MATHS              RS AGGARWAL

1.       Number system  ---------------------------------------------------------

2.       Factors multiples --------------------------------------------------------

3.       Whole Numbers ---------------------------------------------------------

4.       Integers                 --------------------------------------------------------

5.       Fractions              ---------------------------------------------------------

6.       Simplification     ---------------------------------------------------------

7.       Decimals              ---------------------------------------------------------

8.       Algebraic expressions -------------------------------------------------

9.       Linear Equations in One Variable -----------------------------------rsmaths99.com

10.   Unitary method, Ratio, and Proportion  ---------------------------

11.   Line Segment, Ray and Line-------------------------------------------

12.   Parallel Lines--------------------------------------------------------------

13.   Angle and their measurement----------------------------------------

14.   Constructions-------------------------------------------------------------

15.   Polygons-------------------------------------------------------------------

16.   Triangles-------------------------------------------------------------------

17.   Quadrilaterals------------------------------------------------------------

18.   Circles----------------------------------------------------------------------

19.   Three-Dimensional Shapes--------------------------------------------

20.   Two-Dimensional Reflection Symmetry- rsmaths99.com

21.   Concept of Perimeter and Area--------------------------------------

22.   Data Handling------------------------------------------------------------

23.   Pictograph-----------------------------------------------------------------

24.   Bar Graph------------------------------------------------------------------

 

EXERCISE – 1A                   rsmaths99.com

Q1.   Write the numerals for each of the following numbers:

                I]  Nine thousand eighteen   - 9018

                Ii]  Fifty-four thousand seventy –three - 54073

                Iii]  Three lakh two thousand five hundred six - 302506

                Iv]  Twenty lakh ten thousand eight -  2010008

                V]  six crore five lakh fifty – seven – 60500057  rsmaths99.com

                Vi]  two crore two lakh two thousand two hundred two - 20202202

                Vii]  twelve crore twelve lakh twelve thousand twelve - 121212012

                Viii]  Fifteen crore fifty lakh twenty thousand sixty-eight - 155020068

Q2.         Write each of the following numbers in words:

                I]             63,005 – sixty- three  rsmaths99.com

                Ii]            7,07,075 – Seven lakh seven thousand seventy-five

                Iii]           34,20,019  - Thirty-four  lakh twenty thousand nineteen

                Iv]            3,05,09, 012 – Three crore five lakh nine thousand twelve

                V]            5,10,03,604 – five crore ten lakhs three thousand six hundred four

                Vi] Six crore eighteen lakh five thousand eight

                Vii]   Nineteen  crore nine lakh nine thousand nine hundred

                Viii]  Six crore fifteen lakh thirty thousand eight hundred seven

                Ix]  Six crore sixty lakh sixty thousand sixty    rsmaths99.com

Q3.         I]  15768 = (1 x 10000) + (5 x 1000)+ (7 x 100) + (6 x 10) + (8 x 1)

                Ii]  308927 = (3 x 100000) + (8 x 1000) + (9 x 100) + (2 x 10) + (7 x 1)

                Iii]  2405609 = (2 x 1000000) + (4 x 100000) + (5 x 1000) + (6 x 100) +(9 x 1)

                Iv]  53618493 = (5 x 10000000) + (3 x 1000000) + (6 x 100000) + (1 x 10000)

                                                + (8 x 1000) + (4 x 100) + (9 x 10) + (3 x 1)  rsmaths99.com

                V]  60606006 = (6 x 10000000)+ (6 x 1000000)+ (6 x 1000)+ (6 x 1).

                Vi]  91010510 = (9 x 10000000)+ (1 x 1000000) + (1 x 10000)+ (5 x 100)+(1 x 10)

Q4.         I]  62584  ii]  581623   iii]   20507905   iv]  3406507

Q5.         79520986  rsmaths99.com

The place value of 9 at the 90 lakh place = 9000000.

                The place value of 9 at the hundred place = 900

                Hence, the required difference = (9000000 - 900)=  8999100.

Q6.         27650934

                The place value of 7 at the  70 lakh place = 7000000.

                The face value of 7 = 7  rsmaths99.com

                Hence, the required difference = 7000000 – 7 = 6999993.

Q7.         The largest 6-digit nos. = 999999

                The smallest 6-digit nos. = 100000

                Number of all 6-digit nos. = (999999 – 100000) + 1 = 899.999 + 1 = 900,000.

Q8.         The largest 7-digit nos. = 9999999    rsmaths99.com

                The smallest 7-digit nos. = 1000000

                Number of all 7-digit nos. = (9999999 – 1000000) + 1 = 8999999 + 1 = 9000000.

Q9.         100 thousands make a lakh.

Q10.       10000 thousands make a crore.

Q11.       837 - 738  = 99.  rsmaths99.com

Q12.       9547999 + 1 = 9548000.

Q13.       9900000 – 1 = 9899999.

Q13.       10000000 – 1 = 9999999.

Q15.       234, 243, 324, 342, 423, 432

Q16.       10357.    rsmaths99.com

Q17.       964320.

Q18.      

 

MILLION

THOUSANDS

HUNDREDS

 

HM

TM

MILLON

HTh

TTh

Th

H

TENS

ONES

I

 

 

 

7

3

5

8

2

1

Ii

 

 

6

0

5

7

8

9

4

Iii

 

5

6

9

4

3

8

2

1

Iv

 

3

7

5

0

2

0

9

3

V

 

8

9

3

5

0

0

6

4

Vi

 

9

0

7

0

3

0

0

6

 

 

C

TL

L

TTh

Th

H

T

O

 

I]  735.821 – seven hundred thirty-five thousand eight hundred twenty-one.

Ii]  6,057,894 – six million fifty-seven thousand eight hundred ninety-four.  rsmaths99.com

Iii]  56,943,821 – fifty-six million nine hundred forty-three thousand eight hundred twenty-one.

Iv]  37,502,093 –  Thirty-seven million five hundred two thousand ninety-three.

V]  89,350,064 – eighty-nine million three hundred fifty thousand sixty-four.

Vi] 90,703,006 -  ninety million seven hundred three thousand and six. rsmaths99.com

Q19.  rsmaths99.com

 

MILLION

THOUSANDS

HUNDREDS

 

HM

TM

MILLON

HTh

TTh

Th

H

TENS

ONES

I

 

3

0

1

0

5

0

6

3

Ii

 

5

2

2

0

5

0

0

6

Iii

 

 

5

0

0

5

0

0

5

 

EXERCISE – 1B COMPARISON OF NUMBERS         rsmaths99.com

Q1.         Total no of person visited the shrine during last two years-

               

                                13 7 8 9 5 0 9

                +             12 9 7 6 4 9 8

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

                               2 6 7 6 6 0 0 7

                ------------------------------------    Ans.

 

Q2.         Sugar produced by all three factories during last yr :-

                                2 4 8 0 9 5 6 5

                +             1 8 7 3 8 5 7 6

                                    9 5 6 4 5 6 8

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

                                5 3 1 1 2 7 0 9  rsmaths99.com

                ------------------------------------------ Ans.

 

Q3.         The new number will be  :-

                                3 7 6 8 4 9 5 5

                +                3 6 1 5 0 4 5

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

                                4 1 3 0 0 0 0 0

                --------------------------------- Ans.

 

Q4.         Total no of votes registered =     6 8 7 9 0 5           

                                                                                4 9 5 0 8 6

                                                                                    9 3 7 5 6

                                                                                    1 3 8 4 9

                                                                   +              2 5 4 6 7

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

                                                                             1 3 1 6 0 6 3  rsmaths99.com

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

 

Q5.         People have primary education =             1 6 2 3 5 4 6

                                    Secondary   “                  =             9 7 6 8 6 7 8

                                     Higher              “              =             6 8 3 7 9 5 4

                                Illiterate               “              =             2 6 8 4 5 3 6

                                Children below age         =                6  9 8 7 8 1

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

                                                                                             2 1 6 1 3 4 9 5

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

                Hence, the total population of state =    2 1 6 1 3 4 9 5.

 

Q6.         Bicycle prod. In a year                      =           8 7 6 5 4 3 5

                Increased prod.                                =            1 3 7 8 6 9 8         

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

                No. of bicycle prod. In 2nd yr                       1 0 1 4 4 1 2 4

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

               

No. of bicycle produced in these two years =    8 7 6 5 4 3 5

                                                                                                 +      1 0 1  4 4 1 2 4

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

                                                                                                        1 8 9 0 9 5 5 9      Ans.

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

               

Q7.         Sale in a year                      Rs. 2 0 9 5 6 4 8 0

                Sale increased by             Rs.     6 7 0 9 5 7 0

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

                                                                     2 7 6 6 6 0 5 0 rsmaths99.com

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

                Hence, total sale of company during these two years =   Rs. 2 0 9 5 6 4 8 0

                                                                                                                                        2 7 6 6 6 0 5 0

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

                                                                                                                                      4 8 6 2 2 5 3 0   Ans.

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

Q8.         Total population of a city    =      2 8 7 5 6 3 0 4

                                                                (-)         1 6 9 8 7 0 5 9

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

                                                                             1 1 7 6 9 2 4 5  rsmaths99.com

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

                Hence, no, of females I city = 1 1 7 6 9 2 4 5.

 

Q9.                         1 3 2 4 6 5 1 0

                          (-)     4 6 5 8 6 4 2

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

                                8 5 8 7 8 6 8                          Hence, it is larger by  8 5 8 7 8 6 8

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

 

Q10.                       1 0 0 0 0 0 0 0

                          ( )                   5 6 4 3 8 7 9

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

                                4 3  5  6 1 2  1       rsmaths99.com

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

Q11.       Let the required no. be y. Then 1 1 0 1 0 1 0 1  y = 2 6 3 5 9 6 7 .

                   y = 1 1 0 1 0 1 0 1     2 6 3 5 9 6 7 = 8 3 7 4 1 3 4 .

 

Q12.       ATQ,  y + 89 6 7 5 1 9  = 1 0 7 5 0 3 0 8 .

                Hence, y = 1 0 7 5 0 3 0 8   89 6 7 5 1 9   = 1 7 8 2 7 8 9 .

 

Q13.       Total amount    Rs.   2 0 0 0 0 0 0 0

                Spent              ( )       1 3 6 0 7 0 8 5

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

                Money left         =         6 3 9 2 9 1 5   rsmaths99.com

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

 

Q14.       Cost of property = 1 8 5 3 6 0 0 0

                Total collection :      membership fee  =   7 2 5 3 8 4 0

                                                                Loan                =   5 6 7 5 4 5 0

                                                                Donation        =   2 9 3 7 6 8 0

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

                                                                                             1 5 8 6 6 9 7 0

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

                Amount short by    1 8 5 3 6 0 0 0   1 5 8 6 6 9 7 0 = 2 6 6 9 0 3 0 .

 

Q15.       Total amount                     Rs.          1 0 6 7 2 5 4 0

                Amount gave to wife     Rs. ( )      4 8 3 6 9 8 0

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

                Money left                         Rs.             5 8 3 5 5 6  0

                Money gave to son         Rs. (-)        3 9 6 4 7 9 0

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

                Money left                         Rs.              1 8 7 0 7 7 0

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

                Hence,  Rs  1 8 7 0 7 7 0   was received by the daughter.

 

Q16.       Cost  of one chair =    Rs.   1 4 8  5

                Cost of  469 “          =         x      4 6 9

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

                                                                 1 3 3 6 5

                                                 8 9 1 0 x

                                                             5 9 4 0 x x

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

                                                            6 9 6 4 6 5    rsmaths99.com

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

Hence, the cost of chair = Rs. 6 9 6 4 6 5.

 

 

Q17.       Total no. of students          =         1 7 8 6

                Each students contribute  = Rs.    6 2 5

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

                                                                                8 9 3 0

                                                                           3 5 7 2 x    

                                                                     1 0 7 1 6 x x                                                                                                    

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

                                                                     1 1 1 6 2 5 0

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

Hence , total collection   = Rs.  1 1 1 6 2 5 0 .

 

 

Q18.       Screw produce in one day            =             6 9  8 5

                “              “              “   365 “                 =        x       3 5 8

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

                                                                                                5 5 8 8 0

                                                                                           3 4 9 2 5  x

                                                                                        2 0 9 5 5 x x                   

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

                                                                                        2 5 0 0 6 3 0

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

Q19.       Mr. Bhasker save saves Rs. 8756 in one month.

                Then in 12 month he saves =   8 7 5 6  x 12 = Rs. 105072.

                Hence, in 13 years he saves =  Rs. 105072 x 13 = Rs. 1365936.

 

Q20.       Cost of one scooter        =             Rs. 36725.  rsmaths99.com

                   Cost of 487 scooter   =  Rs. 36725  x  487  =  Rs.  17885075.

 

 

Q21.       In 1 hr aeroplane covers     1485 km.

                  In 72 hrs  “           “             1485 x 72 = 106920 km.

 

Q22.       Let the one no. be y. Then,     y x 364 = 13421408.

               

Y =   = 36872.

 

Q23.       Cost of 36 flat = Rs. 68251500. Then cost of each flat  =   =

                =       rsmaths99.com

 

Q24.       Gas contained in cylinder = (30250 – 14480)g = 15770g   = 15kg 770g.  [1kg = 1000g]

                rsmaths99.com

Q25.       Length of cloth = 5 m = 500 cm.  & piece of length = 2m 85 cm = 285 cm. [1m = 100cm]

                  length of the remaining piece = (500 – 285)cm = 215 cm = 2m 15 cm.  

                               

Q26.       For one shirt required length of cloth = 2m 75cm = 275 cm.

                 For  16    “         “              “              “              =  275 cm 44m.

 

                rsmaths99.com

Q27.       Required cloth for each trouser = 185 cm = 1m 85cm.

 

Q28.       Mass of a brick = 2kg750g = 2000g + 750g =2750g.

                Mass of 14 bricks = 2750 x 14 = 38500 g = 38kg 500g.

 

Q29.       Mass of 8 packets = 10kg 600g = 10600g.

                Mass of each packet =    = 1325 g = 1kg 325 g.

 

Q30.       Length of each piece of rope =

------------------------------------------------------------X-----------------------------------------------------------------

 

EXERCISE -1D  ESTIMATION         rsmaths99.com

 

Q1.         Estimate each sum to the nearest ten:

 

(57 + 34) 

                57 estimated to the nearest ten =  60

                34 estimated to the nearest ten =  30

                Hence, the required estimation = 60 + 30 = 90.

 

Q2.         (95 + 58)               rsmaths99.com

                95 estimated to the nearest ten =  100

                58 estimated to the nearest ten =  60

                Hence, the required estimation = 100 + 60 = 160.

 

Q7.         (356 + 275)

                356 estimated to the nearest ten =  360

                275 estimated to the nearest ten =  280

                Hence, the required estimation =360 + 280 = 640.

 

Q10.       Estimate each sum to the nearest hundred

 

(236 + 689)          rsmaths99.com

                236 estimated to the nearest hundred= 200

                689 estimated to the nearest hundred =  700

                Hence, the required estimation = 200 + 700 = 900.

 

Q13.       (3280 + 4395)

                3280 estimated to the nearest hundred= 3300

                4395estimated to the nearest hundred =  4400

                Hence, the required estimation =  3300 + 4400 = 7700.

Q15.       (10083 + 29380)

                10083 estimated to the nearest hundred= 10100

                29380 estimated to the nearest hundred =  29400

                Hence, the required estimation = 10000 + 29300 = 39500.

 

Q16.       Estimate each sum to the nearest thousand:

(32836 + 16466) rsmaths99.com

                32836 estimated to the nearest thousand  = 33000

                16466 estimated to the nearest thousand  =  16000

                Hence, the required estimation =33000

Q17.       (46703 + 11375)

                46703 estimated to the nearest thousand  = 47000

                11375 estimated to the nearest thousand  =  11000

                Hence, the required estimation = 47000 + 11000 = 58000.

 

Q18.       54 balls in box A = estimated  balls= 50.

                79 balls in box B = estimated balls = 80.

Total no of balls = 50 + 80 = 130.

                rsmaths99.com

Q19.       Estimate each difference to the nearest ten:

(53 - 18)

                53 estimated to the nearest ten =  50

                18 estimated to the nearest ten =  20

                Hence, the required estimation = 50 - 20 = 30

 

               

Q22.       Estimate each difference to the nearest hundred:


                (678 - 215)           rsmaths99.com

                678  estimated to the nearest hundred= 700

                215  estimated to the nearest hundred =  200

                Hence, the required estimation = 700 -  200 = 500.

Q25.       (5612 - 3095)

                5612  estimated to the nearest hundred= 5600

                3095  estimated to the nearest hundred =  3100

                Hence, the required estimation = 5600 – 3100 = 2500.

 

Q26.       Estimate each difference to the nearest thousand

(35863 - 27677)

35863 estimated to the nearest thousand  = 36000

                27677 estimated to the nearest thousand  =  28000

Hence, the required estimation = 36000 – 28000 = 8000.

 

Q27.       47000 – 39000 = 8000.     rsmaths99.com

----------------------------------------------------------------X--------------------------------------------------------------

EXERCISE -1E  ESTIMATING THE PRODUCTS          rsmaths99.com

 

                Estimate each of the products by rounding off each number to the nearest ten.

 

Q1.         38 x 63                                 

                38 estimated to the nearest ten =  40

                63 estimated to the nearest ten =  60

                Hence, the required estimation = 40 x 60 = 2400.

 

Q2.         54 x 47  rsmaths99.com

                54 estimated to the nearest ten =  50

                47 estimated to the nearest ten =  50

                Hence, the required estimation = 50 x 50 = 2500.

               

                Estimate each of the products by rounding off each number to the nearest hundred.

 

Q7.         376 x 123

                376 estimated to the nearest hundred= 400

                123  estimated to the nearest hundred =  100

                Hence, the required estimation                = 400 x 100 = 40000.

 

                Estimate each of the products by rounding off the first no. upwards and the second no. downwards :

               

Q13        183 x 154              rsmaths99.com

                183 estimated upwards = 200

                154  estimated downwards = 100

                Hence, the estimated product = 200 x 100 = 20000.

 

Q17.       680 x 164

                680 estimated upwards = 700

                164  estimated downwards = 100

                Hence, the estimated product = 700 x 100 = 70000.

               

Estimate each of the products by rounding off the first no. downwards and the second no. upwards :

 

Q19.       356 x 278              rsmaths99.com

                356 estimated downwards = 300

                278  estimated upwards  = 300

                Hence, the estimated product = 300 x 300 = 90000.

--------------------------------------------------------------X----------------------------------------------------------------------

EXERCISE -1G  ROMAN NUMBERS            rsmaths99.com

Roman numbers

I

V

X

L

C

D

M

Hindu-Arabic numerals

1

5

10

50

100

500

1000

 

Q1.         I] 2 = II    II] 8 = VIII           III] 14 = XIV         IV]  29 = XXIX     VIII] 61 = LXI  XI]  91 = XCI

XIV]  105 =  100 + 5 = CV   XV]  114 = 100 + 10 + 4 = CXIV.

Q2.         I] 164 = 100 + 60 + 4 = CLXIV.       III]  226 = 200 +20 + 6 = CCXXVI

                VI]  596 = 500 + 90 + 6 = DXCVI    VIII]  759 = 700 + 50 + 9 = DCCLIX

Q3.         I]   XXVII = 10 + 10+ 7 = 27.            II] XXXIV = 34     IV] LIV = 50 + 4 = 54.

                IX]  CLIV = 100 + 50 + 4 = 154        XII] CDXIV = (500 – 100)+10+4 = 414.

                XIII] CDLXIV = 500 – 100 + 50 + 10 + 4 = 464. XV]  DCCLXVI = 766.

1=I

2 = II

3 = III

4 = IV

5 = V

6 = VI

7 = VII 

8 = VIII

9 = IX

10 = X

11 = XI

12 = XII

13 =XIII

14= XIV

15= XV

16 = XVI

17 = XVII

18 = XVIII

19 = XIX

20 = XX

21 = XXI

22 = XXII

23 = XXIII

24 = XXIV

25 = XXV

26 = XXVI

27 = XXVII

28 = XXVIII

29 =XXIX

30 = XXX

31 =XXXI

32 = XXXII

33 = XXXIII

 34 = XXXIV

XXXV

XXXVI

XXXVII

XXXVIII

XXXIX

40 = XL

41 = XL

42 = XLII

43 = XLIII

44 = XLIV

45 = XLV

46 = XLVI

47 = XLVII

48 = XLVIII

49 = XLIX

50 = L

91= XCI

92 = XCII

93 = XCIII

94 = XCIV

95 = XCV

96 = XCVI

97 = XCVII

98 = XCVIII

99 = XCIX

100 = C

               

RSMATHS99.COM

EXERCISE – 2A  FACTORS AND MULTIPLES             rsmaths99.com

Even numbers : all multiples of 2 are called even numbers.

Ex. – 2, 4, 6, 8, 10,…..etc

  Odd numbers : numbers which are not multiple of 2 .

Ex.-  1, 3, 5, 7, 9, 11, 13, …etc.  rsmaths99.com

Prime numbers : A number which is divisible by 1 and itself.  (25 prime nos.1 -100).

Ex.- 2, 3 ,5, 7, 11, 13,17, 19, 23,29, 31,37,41,43,47,53,59,61,67,71,73,79,83,89,97 etc.

Composite number : number having more than two factors.

Ex.- 4, 6, 8, 9, 10, 12, 14,  etc.

Natural numbers : counting numbers are called natural numbers.

Ex.- 1, 2, 3, 4, 5, 6, 7, 8, ….etc.      rsmaths99.com

Whole numbers :  All natural numbers together with 0(zero) .

Ex.- 0, 1, 2, 3, 4, 5, 6, 7, 8, ….etc.

 rsmaths99.com               

Q1.         Define :

                I]   Factor : -A factor of a number is an exact divisor of that number.

                Ex. 20 = 1, 2, 4, 5, 10, 20.

                Ii]   Multiple : A number is said to be a multiple of any of its factors.

                Ex.    20 is a multiple of  the numbers 1, 2, 4, 5, 10 and 20.

Q2.         Factors :-   rsmaths99.com

                I] 20 = 1, 2, 4, 5, 10, 20.                   Ii]  36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.

                Iii]  60 = 1, 2, 3, 4, 6, 10, 12, 15, 20, 30, 60.   Iv]  75 = 1, 3, 5, 15, 25, 75.

Q3.         Multiples:

                I] 17 =    17, 34, 51, 68, 85               ii]  23 =  23, 46, 69, 92, 115

                Iii]  65 = 65, 130, 195, 260, 325   iii]  70 =  70, 140, 210, 280, 350.

Q4.         Even  numbers – i]32      iii]50        iv] 58                   vi]  144

                Odd numbers -    ii] 37    v]69        vii] 321                viii] 253.

Q5.         Prime numbers : A number which is divisible by 1 and itself is called Prime numbers.

Ex.- 2, 3 ,5, 7, 11, 13,17, 19, 23,29.

Q7.         I]   Smallest prime number is 2.  Ii] even prime no. is 2.

                Iii]  smallest odd prime no. is 3.

Q8.         Ii]  89     rsmaths99.com

Q9.         90, 91, 92, 93, 94, 95, 96,

Q10.       I] no,     ii] 1         iii]  4, 9, 25, 49.

Q11.       Composite number : number having more than two factors are called Composite number.

Ex.- 4, 6, 8, 9, 10, 12, 14,  etc.   yes, 9.       rsmaths99.com

Q12.       Twin primes : two consecutive odd prime numbers are known as twin primes.

                Twin primes between 50 and 100.  (59, 61),  (71, 73). rsmaths99.com

Q13.       Two numbers are said to be co-primes if they do not have a common factor other than 1.

                Ex.- i] 2, 3             ii] 3, 4    iii] 4,5    iv] 4, 9   v] 8, 15.

                Two co-prime need not be prime no. ex. 6, 7 are co-primes, while 6 is not a prime no.

Q14.       I] 36 = 7 + 29       ii] 42 = 5 = 37      iii] 84 = 17 = 67 iv] 98 = 79 + 19.

Q15.       I] 31 = 5 + 7 + 19 ii] 35 = 5 + 7 + 23   iii] 49 = 3+ 5+ 41  iv]   63 = 7 + 13 + 43

Q16.       I] 36 =17 + 19  ii] 84 = 41 + 43        iii] 120 =  59 + 61                iv ] 144 = 71 + 73

Q17.       I]  F         ii] F         iii] F        iv] F        rsmaths99.com

----------------------------------------------------------------X-----------------------------------------------------------               

EXERCISE – 2B                    rsmaths99.com

Q1.         We know that a no. is divisible by 2 if its unit digit is 0, 2, 4, 6, 8. Then,

I] 2650       iii] 59628           v]  357986            vi]  367314  are divisible by 2.

Q2.         We know that a no. is divisible by 3 if the sum of its digits is divisible by 3. Then,

                ii] 1 + 0 +0 + 3 + 8 = 12     iv] 5 + 2 + 4 + 7 + 8 + 1 = 27.are divisible by 3.

Q3.         We know that a no. is divisible by 6 if it is divisible by both 2 and 3.

                I] 2070 = 2 + 7 = 9 and unit digit is 0. rsmaths99.com

III]  71232 = 7+1+2+3+2 =15 and unit digit is 2.  

V]  251730 = 2+5+1+7+3+0 = 18 and unit digit is 0.

Q4.         We know that a no. is divisible by 4 if the no. formed by its digits in the tens and unit places is divisible by 4.

                Iii] 63712 ΰ 12 is divisible by 4. Hence it is divisible by 4.

                iv] 35056 ΰ 56 is divisible by 4. Hence it is divisible by 4.

                vi] 810524 ΰ 24 is divisible by 4. Hence it is divisible by 4.

                rsmaths99.com                 rsmaths99.com

Q5.         We know that a no. is divisible by 8 if the no. formed by its digits in the hundreds, tens and unit places is divisible by 8.

                Iii]   36792 ->  792 is divisible by 8. Hence it is divisible by 8.           

v]    136976 -> 976   is divisible by 8. Hence it is divisible by 8.

vi]   1790184 -> 184 is divisible by 8. Hence it is divisible by 8.

Q6.         We know that  a no. is divisible by 10 if its unit digit is zero and a no. is divisible by 5 if its unit digit is 0 and 5.

                No. divisible by 5 are :-    i] 4965   ii] 23590  iv]  723405 v] 438750

                No. divisible by 10 are:-   ii]  23590   v]  438750

Q7.         We know that a no.  is divisible by 11 if the difference the difference of the sum of its digits in odd places and the sum of its digits in even places (starting from the units place) is either 0 or a multiple of 11.          rsmaths99.com

                I] 4334        ii] 83721           iv] 137269            v] 901351.

Q8.         I]    2 + 7 + x + 4 = 13 + x => 13 + 2 = 15.  Which is divisible by 3.

                Ii]   5 + 3 = x = 4 = 6 = 18 + x => 18 + 0 = 18. Which is divisible by 3.

                Iii]   8 + x + 7 + 1 + 1 = 17 + x => 17 + 1 = 18. Which is divisible by 3.

                Iv]    6 + 2 + x + 3 + 5 = 16 + x = 16 + 2 = 18. Which is divisible by 3.

                V]     2 + 3 + 4 + x + 1 + 7 = 17 + x => 17 + 1 = 18. Which is divisible by 3.

                Vi]   6 + x + 1 + 0 + 5 + 4 = 16 + x => 16 + 2 = 18. Which is divisible by 3.

                rsmaths99.com rsmaths99.com

Q9.         We know that a no. Is divisible by 9 if the sum of its digits is divisible by 9.

                I]     6 + 5 + x + 5 = 16 + x => 16 + 2 = 18. Which is divisible by 9.

                ii]     2 + x + 1 + 3 + 5 = 11 + x => 11 + 7 = 18. Which is divisible by 9.

                Iii]    6 + 7 + 0 + 2 + x = 15 + x => 15 + 3 = 18. Which is divisible by 9.

                Iv]    9 + 1 + x + 6 + 7 = 23 + x => 23 + 4 = 27. Which is divisible by 9.

                V]      6 + 6 + 7 + 8 + x + 1 = 25 + x => 28 + 8 = 36. Which is divisible by 9.

                Vi]      9 + x + 8 + 0 + 7 + 1 = 25 + x => 25 + 2 = 27. Which is divisible by 9.

Q10.         i] x + 2 => 9 + 2 = 11  , 5 + 6 = 11. Diff = 11- 11 = 0 which is divisible by 11.

                ii] 3 +x + 3 = 6 + x, => 6 + 7, 4 + 9 = 13 diff 13 – 13 = 0.   –Do-

                iii] 2 + x + 8  => 10 + 3 = 13,  7 + 6 = 13 diff = 13 – 13 = 0.   –DO-                     

iv]   9 + 7 + 4 = 20 & 1 + x + 6 = 7 + x  => 7 + 2 = 9  diff 20 – 9 = 11.  –Do-

v]  4 + 3 + 7 = 14 & x + 2 + 1 = x + 3 => 0 + 3 = 3 diff 14 – 3 = 11.   –Do-

vi]  1 + 0 + x = 1 + x => 1+ 1 = 2 & 7 + 8 + 9 = 24 Diff 24 – 2 = 22.   –Do-

Q12.       I] 612 is divisible by 4 but not by 8.            rsmaths99.com

                ii] 154 is divisible by 2 but not by 4.

                iii] 104 is divisible by 2 and 8 but not by 16.

                iv] 176  is divisible by 4 and 8 but not by 32.

                v] 1177 is divisible by 11 and ends with 7.

Q13.       i]    1 + 0 + 0 + 0 + 1 & 0 + 0 + 0 + 1 = 1 diff 1 – 1 = 0. It is divisible by 11.

                ii]   5 + 6 + 8 + 9 = 28 & 2 + 3 + 0 + 1 = 6 diff 28 – 6 = 22.  It is divisible by 11.

                iii]  Total = 24 which is not divisible by 9. rsmaths99.com

                Iv]  Divisible        v] not divisible   vi] divisible

                rsmaths99.com rsmaths99.com

Q14.       These are not a prime nos.:-

161    7 = 23

                203   7 = 29

                217   7 = 31

                291   3 = 97       rsmaths99.com

                381  3 = 127 and the other nos. are prime nos.  

-----------------------------------------------------------X-----------------------------------------------------------------

EXERCISE-2C       rsmaths99.com

Find the prime  factorization:

Q             1]            12 = 2 x 2 x 3 = 22 x 3.

                2]            18 = 2 x 3 x 3 = 32 x 2

                3]            48 = 2 x 2 x2 x 2 x 3 = 24 x 3.

                4]            56 = 2 x 2 x 2 x 7 = 23 x 7.  rsmaths99.com

                11]          1224 = 2 x 2 x 3 x 2 x 3 x 17 = 23 x 32 x 17.

                13]          8712 = 2 x 2 x 2 x 3 x 3 x 11 x 11 = 23 x 32 x 112.

                14]          9317 = 7 x 11 x 11 x 11 = 7 x 113.

                15]          1035 = 5 x 3 x 3 x 23 = 32 x 5 x 23.

                        16]       1197 = 3 x 3 x 7 x 19 = 32 x 7 x 19.

                17]          4641 = 3 x 7 x 13 x 17 . rsmaths99.com

                18 ]         4335 = 3 x 5 x 17 x 17.

                19]          2907 = 3 x 3 x 17 x 19 = 32 x 17 x 19.

                20]          13915 = 5 x 11 x 11 x 23 = 5 x 112 x 23.

                rsmaths99.com  rsmaths99.com

-----------------------------------------------------------X-----------------------------------------------------------------

EXERCISE-2D      rsmaths99.com

Find the HCF by using the prime factorization: 

Q1.         84  = 2 x 2 x 3 x 7

                98 = 2 x 7 x 7

                   HCF = 2 x 7 = 14   rsmaths99.com

Q2.         170 = 2 x 5 x 17                  238 = 2 x 7 x 17     HCF = 2 x 17 = 34.

Q3.         504 = 2 x 2 x 2 x 7 x 3 x 3.   

                980 = 5 x 2 x 2 x 7 x7         HCF = 2 x 2 x 7 = 28.

Q4.         70 = 2 x 2 x 2 x 3 x 3    108 = 2 x 2 x 3 x 3 x 3. 

                180 = 2 x 2 x 5 x 3 x 3.         HCF = 2 x 2 x 3 x 3 = 36.

                rsmaths99.com                 rsmaths99.com

Q5.         84 = 2 x 2 x 3 x 7.    120 = 2 x 2 x 2 x 3 x 5

                138 = 2 x 3 x 23.                    HCF = 2 x 3 = 6.

Q6.         106 = 2 x 53.        159 = 3 x 53.       

                371 = 7 x 53.           HCF = 53.

Q7.         272 = 2 x 2 x 2 x 2 x 17     425 = 5 x 5 x 17.    HCF = 17.

Q8 .        144 = 2 x 2 x 2 x 2 x 3 x 3  and       252 = 2 x 2 x 7 x 3 x 3

                630 = 5 x 2 x 7 x 3 x 3.                         HCF =   2 x 3 x 3= 18.

Q9.         1197 = 3 x 3 x 133  and    5320 = 5 x 2 x 2 x 2 x 133

                4389 = 33 x 133                     HCF = 133.

Find the HCF by division method: rsmaths99.com

Q10.       58)70 ( 1

                      58

                ------------

                12)58( 4

                      48

                ------------

                        10)12 (1

                              10

                --------------------

                                2)10(5

                                    10

                                --------

                                    X

                                ---------    HCF = 2.

rsmaths99.com

Q11.       399)437 ( 1

                        399

                ---------------

                          38 )399( 10

                                   380

                                ---------

                                     19)38 ( 2

                                           38

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

                                           X

                                ---------------      HCF = 19.

 

Q13.       1965 )2096 ( 1 rsmaths99.com

                            1965

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

                                131)1965 ( 15

                                         1965

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

                                                X

                                -----------------         HCF = 131.

 

Q14.       2241) 2324 ( 1

                           2241          rsmaths99.com

                -----------------

                                83)2241( 27

                                        2241

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

                                         X

                                -----------------       HCF = 83.

 

 

 

Q16.       754)1508 (2  rsmaths99.com

                         1508

                ----------------

                          X

                ---------------      

                754) 1972 ( 2

                          1508

                -----------------

                                464)754 ( 1

                                        464

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

                                        290)464 ( 1

                                                 290      rsmaths99.com

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

                                                174)290 (1

                                                        174

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

                                                        116)174 (1

                                                                  116

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

                                                                   58)116 ( 2

                                                                         116

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

                                                                                X  rsmaths99.com

                                                                --------------------       HCF = 58.

                rsmaths99.com

Q17.       391)425 ( 1

                         391

                --------------

                          34)391( 11

                                  374

                                -----------

                                  17)34(2

                                         34

                                -----------

                                       X    rsmaths99.com

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

                17)527 ( 31

                      527

                -----------

                       X     rsmaths99.com

                ------------               HCF = 17.

 

 

 

Q18.       1794)2346 ( 1

                          1794

                -----------------

                             552)1794(3

                                       1659

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

                                       138)552 (4

                                                552

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

                                                X

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

                152)4761 (34

                        4692               rsmaths99.com

                --------------

                           69)138 (2

                                   138

                                --------

                                     X

                                -----------                 HCF = 69.

 

 

Q34.       I]   HCF of two prime nos. = 1

                Ii]   HCF  of two consecutive nos. = 1

                Iii]   HCF  of two co-prime nos. = 1

                Iv]   HCF of 2 and on even no = 2.

 

-------------------------------------------------------------X-----------------------------------------------------------------

 

 

EXERCISE – 2E                    rsmaths99.com

 

Find the LCM:

 

Q1.        

7

42, 63

3

6,   9

 

2,   3

               

LCM = 7 x 3 x 2 x 3 = 126.

Q5.

                rsmaths99.com

                                                                                               

6

36, 40, 120

2

6, 40, 20

2

3, 20, 10

5

3, 10, 15

 

3,  2,    1

               

 

 

 

 

               

              LCM = 6 x 2 x 2 x 5 x 3 x 2 = 60 x 6 = 360.

 

Q6.        

2

16, 28, 40, 120

2

8, 14, 20, 77

2

4, 7, 10, 77

7

2, 7, 5, 77

 

2, 1, 5, 11

               

LCM = 2 x 2 x 2 x 7 x 2 x 5 x 11 = 56 x 110 – 6160.

 

Q7.         rsmaths99.com

2

48, 64, 72, 96, 108

2

24, 32, 36, 48, 54

2

12, 16, 18, 24, 27

2

6,    8,    9,  12, 27

3

3,   4,    9,   6,   27

3

1,   4,    3,   2,    9

2

1,   4,    1,   2,    3

 

1,   2,    1,   1,   3

               

                LCM = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3= 1728.

 

                Find the HCF and LCM:

Q10.       117, 221

 

                117)221( 1

                        117   rsmaths99.com

                --------------

                         104)117 (1

                                   104

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

                                    13)104 ( 8

                                          104

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

                                                X  rsmaths99.com

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

HCF = 13

And LCM =  

 

Q11.       234)572 ( 2

                        468   rsmaths99.com

                -------------------

                         104)234 ( 2

                                   208

                                -----------

                                    26)104 ( 4

                                          104

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

                                          X

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

                HCF = 26  and    LCM =     9 x 572 = 5148.

 

Q12.       693) 1078 (1

                            693   rsmaths99.com

                -------------------

                             385) 693 (1

                                        385

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

                                        308) 385 ( 1

                                                   308

                                                --------

                                                   77) 308 (4

                                                           308

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

                                                            X   rsmaths99.com

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

                HCF = 77 and  LCM =    693 x 14 = 9702.

 

Q15.       2923) 3239 ( 1

                            2923

                ------------------

                               316) 2923 ( 9

                                          2844

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

                                              79) 316 ( 4

                                                       316

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

                                                         X   rsmaths99.com

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

                                                                                                               

                HCF = 79 and  LCM =   119843.

 

                rsmaths99.com    rsmaths99.com                                                                                                                                                                                             

 

Q26.       LCM of 36 cm, 48cm, 54cm = 36 x 12 = 432 cm.    

3

36, 48, 54

3

12, 16, 18

4

4,   16, 6

2

1,   4,   6

 

1,   2,   3

 

                 They will step together simultaneously after 432 cm.

 

Q27.       LCM of 48sec, 72 and 108 sec = 432 sec = 7 min 12 sec.

12

48, 72, 108

2

4, 6, 9

3

2, 3, 9

 

2, 1, 3

                                                                               

 

 

rsmaths99.com

 

Q29.       LCM of 15 min and 20 minute = 60 min = 1hr.

5

15, 20

 

3,  4

                                                                                               

rsmaths99.com                

 

   Time at where the devices will beep together = 6 + 1 = 7 am.

 

Q30.       Least distance required = LCM of 50 cm, 60 cm, 75cm, and 100cm.

 

                = 300 cm.                                                            

               

5

50, 60, 75, 100

5

10, 12, 15, 20

2

2, 12, 3, 4

3

1, 6, 3, 2

2

1, 2, 1, 2

 

1, 1, 1, 1

 

----------------------------------------------------------X------------------------------------------------------------------------

RSMATHS99.COM

EXERCISE – 9C APPLICATIONS OF EQUATIONS            rsmaths99.com

 

Q1.         L et the no. be x . Then ATQ, x + 9 = 36.   => x = 36 – 9 = 27.

Q2.         4 x – 11 = 89.   => 4x = 89 + 11 = 100.   x =

Q3.         X x 5 = x + 80.    => 5x – x = 80  => 4x = 80.  => x =

Q4.         (x) + (x + 1) + (x + 2) = 114.  rsmaths99.com

                3x + 3 = 114  => 3x = 114 – 3 = 111   => x =

                 x = 37,  x + 1 = 38,   x + 2 = 39.

Q5.         (X x 17) + 4 = 225.   => 17x  = 221.   => x =

Q6.         3x + 5 = 50.   => x =  15.  rsmaths99.com

Q7.         X + (x + 18) = 92.   =>  2x = 92 – 18 = 74.    x =

                Other no. is x + 18 = 37 + 18 = 55.

Q8.         X + 3x = 124.   => 4x = 124   => x =  

Hence no. = x = 31 & 3x = 93.

Q9.         5x – x = 132   => 4x = 132.   x =  =33. 

                Other no. = 5x = 5 x 33 = 165. rsmaths99.com

Q10.      L = 3x, B = x,   perimeter of park = 2(L + B) = 2 (3x + x)

                 168 = 2(4x).   => 4x =      x =   L = 21 x 3 = 63m.

                rsmaths99.com                 rsmaths99.com

-------------------------------------------------------X--------------------------------------------------------------

RSMATHS99.COM

EXERCISE – 10A UNITARY METHOD          rsmaths99.com

 

Q1.         cost of 24 oranges = Rs. 33.60

                “              1              “     = Rs.       [less orange less cost]

                “              30           “      = Rs. 

Q2.         Cost of 5 bar = Rs. 31  rsmaths99.com

Cost of 1 bar = Rs.
 “     “  24 “    = 

                rsmaths99.com

Q3.         Cost of 25 m cloth            = Rs. 912.50

                    “         1m           “              = Rs.

                 “          8m          “              =  Rs. .

                rsmaths99.com

Q4.         Cost of 9kg rice = Rs. 120.60

                Cost of 1 kg rice = Rs. 

                 cost of 50 kg rice= Rs. 

rsmaths99.com rsmaths99.com

 

Q5.         Weight of 22.5 m rod = 85.5kg.

                Wt. of       1m rod              =

                 wt. of 5m  rod                = 

                rsmaths99.com

Q6.         In a day, 18 horses needed to feed = 135 kg.

                In a day, 1 horses needed to feed    =

                 In a day, 45 horses needed to feed  =   

                rsmaths99.com

Q7.         Oils contain in 15 tins  = 234 kg

                Oils contain in 1 tins    =  

                Oils contain in 10 tins =     

Q8.         To contains 6000 pens needed 48 boxes.

                To contains 6000 pens needed  

                 To contain 1875 “          “             

                rsmaths99.com

Q9.         Distance covered in 6 hrs   =  399km

                Dist.    covered   in    1 hr   =

                  Dist. covered in   16 hrs  =

                Since, 399 km covered in 6 hrs.

                             1km       “             

                             1330 km  “  

                rsmaths99.com

Q10.       Charge to carry 25 tons = Rs. 180.

                Charge to carry 1 ton  =  Rs. 

                  “       “       “   35  ton  =

                rsmaths99.com

Q11.       Dist. covered on 12 ltrs of petrol = 222km

                “              “              1ltr         “              =

                   “        “              22ltrs     “              =

                rsmaths99.com rsmaths99.com

Q12.       Copper contain in 4.5 g of alloy = 3.5g

                “              “              1g           “              =

                  “         “              18.9 g  “                =

                rsmaths99.com rsmaths99.com

Q13.       No. of table can be purchased in Rs. 23520 = 32

                No. of table can be purchased in Rs. 1 =  

                No. of table can be purchased in Rs.51450 =    70.

 

RSMATHS99.COM

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