Archive for the ‘Mathematics’ Category

1 8 * 1 8 = ?

Number = 20

Actual Base = 10

Convenient Base = 20

Deficiency = 18 – 20 = -2

Second Part = -2 * -2 = 4

Intermediate First Part = 18 + -2 = 16

c.b/a.b = 20/10= 2

First part = 16 * 2 =32

Ans 324

For the numbers near 100

a b * c d

a b a b-100

c d c d-100

(a b+c d-100) ((a b-100)(c d-100))

Example:

8 8 * 9 8 =

8 8 -1 2
9 8 -2

=(8 8 – 2)(1 2 * 2)

=8624

FORMULA N5 * N5=(N+1)*N25

Example:

25*25=((2+1)*2)(25)=625

55*55=((5+1)*5)(25)=3025

Explanation:

The last two numbers will be 25. Just increment the first digit and multiply it with the value before incremented.

8 * 8 = ?

Number = 8

Base = 10

Deficiency = 8 – 10 = -2

First part = 8 + -2 = 6

Second part = (-2) * (-2) = 4

ans 64

Now let us try a bigger number

92 * 92

Number = 92

base = 100

Deficiency = -8

First part = 92 – 8 = 84

Second part =(-8) * (-8) = 64

Answer = 8464

Anurpyena means propotionality. This method is helpful to find the product of two numbers when both of them near to common base 10. We can follow 3 approaches to solve a problem..

Approach 1 :

46 X 43

Take the base as the higher multiple of ten.. In above example, lets take 50..

Write the numbers and their differences to 50 as shown below

46          -04

43          -07

——————

now we have to follow the cross addiition

46          -04

43          -07

——————

(46-07) or (43-04)

multiply the differences and write the product on the left side

46          -04

43          -07

——————

39/(04*07)

39/28

Since base is 50 which is 100/2, we have to divide 39 by 2.

39/2 = 19 1/2.. which we can write as 19 and the half will be added to the right side answer .. (50 + 28)

Hence the answer is 1978..

Approach 2: If you find division process as difficult one you can go for this..

The steps are same as above.. But while taking the base we are going to take 50 which is 5 X 10(remember, in the last approach we took as 100/2).

46          -04

43          -07

——————

(46-07) or (43-04)

46          -04

43          -07

——————

39 / 28

Since, we took base 50 as 5 X 10 we have to multiply left part by 5 and add the first digit of right answer to it!

46          -04

43          -07

——————

39 X 5        8

+2

46          -04

43          -07

——————

(195 + 2) / 8 = 1978

Formula:

Na * Nb = (N+1) * N(a *b) where a + b = 10

Example:

54 * 56 = (5 +1) * 5(4 * 6)=(6 * 5)(4 * 6)= 3024

62 * 68 =(6+1) * 6(2 * 8)=(7 * 6 )(2 * 8)= 4216

Explanation:

If the tens digit of the two numbers is same and the unit digits add up to 10 then increment the number and multiply it with the value before incremented and multiply the unit digits .

Formula

ab * cd = (ac)(ad+bc)(bd)

Example:

51 * 32 = ?

(5*3)(5*2 + 3*1)(2*1)

1
1 5 3 2

answer is 1632