Learn the trick of multiplying by some specific numbers. Multiplying by 11 is especially easy. The product of multiplying a two digit number by 11 is a three digit number, where the first and last digits are the same and the middle digit is the sum of the first and last digit: 11 X 23 = 253 because 2 + 3 = 5, and 11 X 44 = 484 because 4 + 4 = 8. To multiply by 5, cut a number in half and annex a zero. 5 X 12 = 60, because half of 12 is 6. Similarly, to compute 25 times a number, cut the number in half twice and annex two zeros, so 25 X 28 = 700 because half of half of 28 is 7.
Practice the art of multiplying certain pairs of numbers. If two numbers are both slightly over 100, the product of the numbers is 1 followed by the sum of the differences then by the product of the differences. For example 102 X 103 = 10506 because 2 + 3 = 5 and 2 X 3 = 6. Similarly, 107 X 109 = 11663 because 7 + 9 = 16 and 7 X 9 = 63.
Rearrange problems so that they are easy to do. For example, 3 X 44 = 3 X (4 X 11) = (3 X 4) X 11 = 12 X 11 = 132. Some other examples include 104 X 13 = (100 X 13) + (4 X 13) = 1300 + 52 = 1352 and 26 X 28 = (25 X 28) + 28 = 700 + 28 = 728 and 102 X 208 = 2(102 X 104) = 2(10608) = 21216. Sometimes algebraic knowledge helps with this process, for example:14 X 16 = 15^2 - 1 = 224 because (Z - 1)(Z + 1) = Z^2 - 1.