Friday, 5 December 2014

2.Mallapragada's Mathematics (Fractions-1)




 (Fractions/Surd)


Sl. No.
Questions/Problems

1.
Express as vulgar fractions:  0.75

2.
Express as vulgar fractions: .0056

3.
Express as vulgar fractions: 0.37
 

4.
Express as vulgar fractions: 3.1234567
 

5.
If 1/3.718=.2689 then find the value of 1/.0003718

6.
What value will replace the question mark in the following eq.?
 (1) 1234.56 + 2345.67 + ? = 3456.78
7.
Average the fractions 5/8, 7/12, 13/16, 16/29 and ¾ is ascending
 order of magnitude 
8.
Find the Product 5.50 x 1.5=?
9
Evaluate: 2.5 ÷0.0005=?

10
X ÷.025=80
 

11
337.63 + 8.590 + 34.4 = ?
12
892.50 -579.00-95.005=?
13
X + 543 +5.43 = 603.26 FIND X
14
3.14 x 106 =?

15
6523 x 10-5 =?
16
3 x 0.3 x 0.03 x 0.003 x 30 = ?
17
10x1.6 -2 x 1.4/2.8   = ?
18
0.2 x 0.2 + 0.2 x 0.02 / 0.044 = ?
19
(35.123)2 – (25.123)2 = ?
20
(10.05)2 – (5.05)2 / 10.05 + 5.05.=?
21
4.2 x 4.2 – 1.9 x 1.9 / 2.3 x 6.1 =?

22
(0.4)4 – (0.3)4 / (0.4)2 – (0.3)2 = ?
23
(7.5 x 7.5 + 37.5 + 2.5 x 2.5 = ?
24
The value of ¼+ 1/4x3  + 1/4x5x6
correct to 4 decimal places is
25
The sum of the first 20 terms of the series 1/5x6 + 1/6x7 + 1/7x8 +..…is
26
(0.2 x 0.2 + 0.01) (0.1x0.1 + 0.02)-1
27
5x1.6 -2x 1.4 /1.3 = ?
28
Solution (3+ 31/2)  (3- 31/2)
29
Solution (3+ 31/2) + (3- 31/2)
30
10/251/2 =

31
51/2  +2=

32
Subtract  5 root 3 + 7 root 5 rom 3 root 5 – 7 root 3 =?
33
641/6 + 161/2 +6251/4 = ?
34
(81)1/4 – 8 (343)1/3 +15(32)1/5+(225)1/2 = ?
35
2 ½ = 1.414, 31/2 =1.732,51/2=2.236
Find the value of 101/2- 151/2/ 221/2
36
Simplify  2 2/3.2 1/3 = ?
37
Simplify {(5) 1/7}4 = ?

38
Simplify 3 1/5 / 3 1/3  = ?



























                                                                 


Om Sri ram
Answers of above problems
Sol.1. 0.75= 75/100 = ¾ 
2. .0056 = 56/10000 = 7/1250
 
3. 0.37 
4   3.1234567= 3
 
5. 1/3.718= 1/.0003718 =10,000 x 1/3.718=           
   10000x .2689=2689 
6. 1234.56 + 2345.67 + x = 3456.78
    X= 3456.78 –(1234.56+2345.67)
       = 3456.78-3580.23=-123.45
7. 5/8, 7/12, 13/16, 16/29 and ¾
    0.0.625,< 0.5833,<0.8125,< 0.5517,<0.75
    Now ascending order :  0.5517< 0.5833 <
    0.0.625, <0.75   <0.8125,
     Ans. 16/29<7/12<5/8<3/4<13/16

 8. 5.55 x 1.5=8.325(Sum of decimal places (2+1=3)

 9. 2.5 ÷0.0005=? 25/10 ÷ 5/10000 =25/10 x
   10000/5 = 25000/5=5000

 10. X ÷.025=80 x x 1000/25= 80, x= 80 x 25/1000=2

 11. 337.63 + 8.590 + 34.4 = 337.63
                                                       8.59
                                                                                                            34.40
                                                                -----------
                                                                 80.62

 12. 892.50 -579.00-95.005= 892.50 – (579.00+95.005) = 892.500 – 674.005=218.495


 13. Let X + 543 +5.43=603.26 x= 603.26 –(543+5.43)
       603.26-548.43=54.83

14. 3.14 x 106 = 314/100 x 1000000 = 3140000

15. 6523 x 10-5  = 6523 x 1/100000 = .06523

16.  3 x 0.3 x 0.03 x 0.003 x 30 = 3 x 3/10 x 3/100 x
       3/1000 x 30 =3x3x3x3x30/105 = 2430/1000000
       0.00243    
        
17. 10x1.6 -2 x 1.4/2.8 = 10 x 16/10 – 2 x 14/10 / 28/10  == 16- 2x14/28 == 16-2x1/2 = 15

18. 0.2 x 0.2 + 0.2 x 0.02 / 0.044 =
       0.2(0.2+0.02)/0.044 = (0.2 x 0.022)/ 0.044
        0.044/0.044 = 1  

19. (35.123)2 – (25.123)2 = a2-b2=(a+b)(a-b)
        (35.123  +  25.123)  (35.123  -  25.123)
         60.246 x 10 = 60246/1000  x 10 = 602.46

20. (10.05)2 – (5.05)2 / 10.05 + 5.05.=
        (10.05 + 5.05).(10.05 - 5.05)./  10.05 + 5.05.
         5

 21. 4.2 x 4.2 – 1.9 x 1.9 / 2.3 x 6.1 =
       (4.2)2 – (1.9)2 / 2.3 x 6.1 == 6.1 x 2.3/ 6.1 x 2.3
        Ans. 1

  22. (0.4)4 – (0.3)4 / (0.4)2 – (0.3)2 = {(0.4)2}2 –
        {(0.3)2}2 / (0.4)2 – (0.3)2
       (0.4)2 + (0.3)2 (0.4)2 – (0.3)2 / (0.4)2 – (0.3)2
         0.16 + 0.09 = 0.25

23. (7.5 x 7.5 + 37.5 + 2.5 x 2.5 = a2+2ab+b2=(a+b)2
          (7.5 + 2.5)2 = 100






24. The value of  +  +    
       correct to 4 decimal places is
              37/120 =0.3083
      Ans. 0.3083

25. The sum of the first 20 terms  
       Of the series  +  +  
       +…is
       {(1/5-1/6) + (1/6-1/7) + …+
         (1/24-1/25)} = 1/5 -1/25 =
         4/25=0.16



26 0.2 x 0.2 + 0.01) (0.1x0.1 + 
      0.02)-1
       0.04 + 0.01 / 0.01 + 0.02 = 
       0.05/0.03 = 5/3 is Ans.

27. 5x1.6 -2x 1.4 /1.3 =8.0-2.8/1.3 
       =5.2/1.3
     52/13 = 4

28. Solution (3+ 31/2)  (3- 31/2)
                     32 – (31/2)2 = 9-3=6

29. Solution (3+ 31/2) + (3- 31/2)
                   (3+ 31/2 + 3- 31/2) = 6
      Which is a rational number

30. 10/2   = 10 x 51/2/2x5-1/2 5-1/2 
      Multiply in both
       sides root five  10 x51/2 2   =  
       10/2 10÷2 /2 = 5/ = =

31 2=(51/2) 2 + 2 x 2 51/2  + 22
        = 9+451/2 

32 5 root 3 + 7 root 5 = (5x 31/2 + 
     7x51/2)from  (3x51/2- 7x31/2)=                                (3x51/2 - 7x31/2) 
     - (5x 31/2 + 7x51/2)= 3x51/2 
     -7x31/2- -5x 31/2 - 7x51/2 =    -{4 
     51/2 +12 31/2}

33. 641/6 + 161/2 +6251/4
           (26)1/6 + (42)1/2 + (54)1/4 = 11

34. (81)1/4 – 8 (343)1/3 + 
       15(32)1/5+225)1/2 = ?
       (34)1/4 – 8 (73)1/3 + 15(25)1/5+
       (152)1/2 =                         
     Ans.  3-56+30+15=-8= -23

35. 2 ½ = 1.414, 31/2 
      =1.732,51/2=2.236
      Find the value of 101/2- 151/2/   
      221/2(2x5)1/2- (3x5)1/2/ 2 21/2 = 
      51/2(2 ½ - 31/2)/ 2 21/2
       2.236(1.414-1.732)/2 x 1.414   
        == -- .318x2.236/2x1.414 =

36. 2 2/3.2 1/3 = ?
       2 2/3 + 1/3 = 2 3/3 =2

37. {(5) 1/7}4 = 5 4/7
38. 3 1/5 / 3 1/3  = 31/5 - 1/3 = 3 3-5/15 
      = 3 -2/15  1/   3 2/15

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