Mental Calculation of Multiplication by Two-Digit Numbers

n x r = a x c x 100 + (a x d + b x c) x 10 + b x d

let
n = a x 10 + b ; First Two-Digit Number
r = c x 10 + d ; Second Two-Digit Number

example

44 x 51 = (4 x 5 x 100 = 2000) + ((4 x 1 + 4 x 5) x 10 = 240) + (4 x 1 = 4) = 2244

52 x 34 = (5 x 3 x 100 = 1500) + ((5 x 4 + 2 x 3) x 10 = 260) + (2 x 4 = 8) = 1768

61 x 72 = (6 x 7 x 100 = 4200) + ((6 x 2 + 1 x 7) x 10 = 190) + (1 x 2 = 2) = 4392

91 x 24 = (9 x 2 x 100 = 1800) + ((9 x 4 + 1 x 2) x 10 = 380) + (1 x 4 = 4) = 2184

Mental Calculation of n^2 Base 100

n^2 = (n+(n-100))x100+(n-100)^2

From

n^2 = (n-100)^2 + 200n - 100^2 <<< (n^2 - 200n + 100^2) + 200n - 100^2

example

105^2 = ((105 + 5) x 100 = 11000) + ( 5 x 5 = 25) = 11025

107^2 = ((107 + 7) x 100 = 11400) + ( 7 x 7 = 49) = 11449

111^2 = ((111 + 11) x 100 = 12200) + (11 x 11 = 121) = 12321

97^2 = (( 97 - 3) x 100 = 9400) + (-3 x -3 = 9) = 9409

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