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.
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.
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 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.