There is more than one way to multiply two numbers.
You can learn a few tricks to simplify the process of multiplying two numbers together. The secret is not working faster, but doing less work. Learn enough of these tricks and chances are you can solve many math problems without looking for your calculator.
The Multiplication Table
Learning the multiplication table is the first difficult mathematical problem most people encounter. It is easier to look for patterns. For example, you can reduce the 9s table to a simple formula: when you multiply a digit N by 9 you will get a two digit number AB. The formulas are A = N -1 and B = 9 - A. For example 7 X 9 = 63 because 6 = 7 - 1 and 3 = 9 - 6. There are smaller patterns, such as 7 X 3 = 21, 7 X 6 = 42 and 7 X 9 = 63 -- this pattern is not so obvious, but once you see it the multiplication table is a little easier --when you multiply 7 by something that can be describes as 3N, the product is AB where B = N and A = 2N.
Special Numbers
Multiply 11 by the two digit number AB, to get the three digit number A (A + B)B. For example 11 X 23 = 253 and 11 X 11 = 121. Multiplying by 5 can be done by annexing a zero; sticking a zero on the end of the number, and cutting the number in half: 5 X 22 = 110 because 22 with an annexed zero is 220 and half of 220 is 110. Similarly 5 X 84 = 420. Multiplying by 25 requires annexing two zeros and cutting in half twice, so 25 X 44 = 1100 and 25 X 56 = 1,400.
Special Pairs of Numbers
You will find it easy to multiply two, three-digit numbers when both are close to 100. These two, three-digit numbers will have a product with five digits. The first digit will always be one. The next two digits will be the sum of how much the two factors exceed 100; the rightmost two digits will be the product of how much the two factors exceeded a hundred. For example, 103 X 104 = 10712, because 3 + 4 = 7 and 3 X 4 = 12.(see references 3)
Squaring
Squaring a number means multiplying the number by itself. Numbers that end in 5 are simple to square. A two-digit number N5, when squared, will be a three-digit number N(N+1)25. For example, 25 squared is 325 and 7 squared is 5,625. A closely related trick is multiplying a number by a number that is two larger: (N-1)(N+1) = NXN -1. This means that 14 X 16 = 224 because 14 X 16 = 15X15 - 1 = 225 - 1 = 224.
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