Multiplication Made Easy (Part III)

Case III : Multiplication with Mixed Bases

Example 1:

108 x 94

Step 1 (I Part). Base is 100 for both numbers.

94      –    6
108    +   8
—————————–
(94 + 8) or (108 – 6) = 102
—————————–

Step 2 (II Part)

(-6) (+8) = (-48)

Step 3

102 / -48

II part cannot be negative. To remove the negative, Subtract 1 from the First part and write the complement of Second Part.

101 / 52

The Answer is 10152.

Example 2:

89 x 114

Step 1 (I Part)

89 – 11
114 + 14
—————————–
(89 + 14) or (114 – 11) = 103
—————————–

Step 2 (II Part)

(-11) (+14) = (-154)

Step 3

104 / -154

II part cannot be negative. Before making the Second part Positive, we must make sure that the number of digits on the Second part is equal to the number of Zeroes in the base. The base is 100.

104 / -154 becomes 103 / -54. (Carry over -1 to the First part)

To make it positive,

102 / 46 (Subtract 1 from the First part and writing complement of the Second part)

The Answer is 10246

Example 3

9996 x 10011

Step 1 (I Part)

9996 – 4
10011 + 11
—————————————-
(9996 + 11) or (10011 – 4) = 10007
—————————————-

Step 2 (II Part)

(-4) (+11) = (-44)

Step 3

10007 / -44

II part cannot be negative. Before making the Second part Positive, we must make sure that the number of digits on the Second part is equal to the number of Zeroes in the base. The base is 10000.

10007 / -44 becomes 10007 / -0044. (Adding Zeroes to the second part)

To make it positive,

10006 / 9956 (Subtract 1 from the First part and writing complement of the Second part)

The Answer is 100069956