﻿ Write the following numbers in generalized form. (i) 25 (ii) 73 (iii) 129 (iv) 302   from Mathematics Playing with Numbers Class 8 Manipur Board

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Write the following in the usual form.
(i) 10 x 5 + 6             (ii)  100 x 7 + 10 x 1 + 8        (iii) 100 x a + 10 x c + b

(i) 10 x 5 + 6 = 50 + 6 = 56
(ii) 100 x 7 + 10 x 1 + 8 = 700 + 10 + 8 = 718
(iii) 100 x a + 10 x c + b = 100 a + 10c + b =

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Check what result would have been if Sundaram had chosen the numbers shown. 1.17 2.21 3.96 4.37.

1.                           Chosen number  = 17
Number with reversed digits  =  71
Difference  = 71 - 17 = 54
= 9 x [6]

2.                                    Chosen number = 21
Number with reversed digits = 12
Difference  = 21 - 12 = 9
= 9 x [1]
= 9 x [Difference between the digits of the chosen number (2 - 1 = 1)]

3.                      Chosen number = 96
Number with reversed digits = 69
Difference  = 96 - 69 = 27
= 9 x [3]
= 9 x [Difference between the digits of the chosen number (9 - 6)]

4.                                  Chosen number = 37
Number with reversed digits  = 73
Difference = 73 - 37 = 36
= 9 x [4]

= 9 x [Difference between the digits of the chosen number (7 - 3 = 4)]

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Check what the result would have been if Minakshi had chosen the numbers shown below. In each case keep a record of the quotient obtained at the end.

1. 132                      Chosen number = 132
Reversed number = 231
Difference  = 231 - 132
= 99
We have                          99 + 99 = 1, remainder = 0

2. 469                       Chosen  number = 469
Reversed number = 964
Difference = 964 - 469 = 495
We have                           495 + 99 = 5, remainder = 0

3.                             Chosen  number = 737
Reversed number  = 737
We have dirrerence = 737 - 737 = 0
0 + 99 = 0, remainder = 0

4.                              Chosen number   = 901
Reversed number  = 109
Differende  = 901 - 109
=  792
We have               792 + 99 = 8, remainder = 0
Forming three digit number with given three dgits.

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Write the following numbers in generalized form. (i) 25 (ii) 73 (iii) 129 (iv) 302

(i)       25 = 20 + 5
= 10 x 2 + 5 x 1 = 10 x 2 + 5

(ii)       73 = 70 + 3
= 10 x 7 + 3 x 1 = 10 x 7 + 3

(iii)      129 = 100 + 20 + 9
= 100 x 1 + 20 x 2 + 1 x 9 = 100 x 1 + 10 x 2 + 9

(iv)       302 = 100 x 3 + 10 x 0 + 1 x 2 = 300 + 0 + 2

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Check what the result would have been if sundaram had chosen the numbers shown below. 1. 27 2. 39 3. 64 4. 17

1.                      Chosen number = 27
Number with reversed digits = 72
Sum of the two numbers  = 27 + 72 = 99
Now,                                   99  = 11[9]
= 11[2 + 7]
= 11(Sum of the digits of the chosen number)

2.                         Chosen number = 39
Number with reversed digits = 93
Sum of the two numbers = 39 + 93 = 132
Now,                              132 + 11 = 12

i,e,                                 132 = 11[12]
= 11 [ 3 + 9]
= 11 [ Sum of the digits of the chosen number]

3.                                     Chosen number = 64
Number with reversed digits  = 46
Sum   = 64 + 46 = 110
Now,                                                110 = 11[10]
= 11[6 + 4]
= 11[ Sum of the digits of the chosen number

4.                                      Chosen number    =  17
Number with reversed digits     = 71
Sum   =  17 + 71 = 88
Now,                                                    88    = 11[8]
= 11[1+7]
= 11[Sum of the digits of the chosen number]

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