(1.) The trick when it comes to multiply by 11 has already been given on the Mathematics Trivia page. You can Click Here to read it. (2.) To square any number of 9's immediately without multiplying: set down as many 9's less one (beginning on the left) as there are 9's in the given number, an 8, as many 0's as you do 9's, and a 1. Example: 999 * 999: Put down two 9's [i.e., 99]. Then an 8 [i.e., 998]. Then two o's [because there are two 9's, hence, 99800]. Then append a 1 [i.e., 998001]. That's it.! (3.) To square any number ending in 5: Omit the 5, and multiply the number as it will then stand, by the next higher number, and finally append 25 to the product. Example: 35 * 35: Omit the 5 [i.e., 3 is left]. Next multiply 3 by the next higher number [i.e., 3 * 4 = 12]. Finally, append 25 [i.e., 1225]. That's the answer..! (4.) To square any compound fraction containing 1/2: For instance 5 1/2 [Five and one half], Multiply the whole number by the next higher whole number and append 1/4 to the product. Thus, 5 1/2 * 5 1/2 = 30 1/4 [5 * (5 + 1) = 30 and append 1/4 to get 30 1/4]. (5.) To multiply any two like numbers with fractions that sum to 1: For instance 4 3/4 * 4 1/4, Multiply the whole number by the next highest number [4 * 5 = 20], and append the product of the fractions [1/4 * 3/4 = 3/16]. In this case, the answer is 20 3/16. (6.) To multiply any two numbers whose ones digits sum to 10 and with like remaining numbers: For instance, 106 * 104, Multiply the upper tens numbers by the next higher number [Here, 10 * 11 = 110], and multiply the ones digits that sum to 10 [Here, 6 * 4 = 24] and then set the products next to one another successively [i.e., 11024]. Another example, 57 * 53 = 3021.! Check it out...!!! (7.) To multiply any number by any number of 9's: For instance, 28 * 99, Append as many 0's to the multiplicand (28 is called the multiplicand) as there 9's in the multiplier [It becomes 2800], and from this number subtract the multiplicand [2800 - 28]. The remainder is the answer [i.e., 2772]. If you know more about similar tricks, I shall appreciate if you will let know. My E-Mail is given below. Cheers..!