MAGIC MATHS

(**) Squaring A Number Ending In 8:    A.   This method  comes from algebra: (10 a – 2) 2 = 100 (a)(a – 1) + 10(6    B.   Using numbers instead of variables we get the following: 1.   Write down 4. 2.   Add 1 to the ten’s digit and multiply by 6. Write this number down, carry if necessary. 3.   Multiply the number in the ten’s digit by that number plus 1.   Write this result. Ex [1 ]   68 2 =_________. a)       Write down 4. b)       6 x (6 + 1) = 42 .   Write 2, carry *4. c)       6 x (6 + 1) = 42 + *4 = 46 d)       The answer is 4624 . Ex [2 ]   118 2 =_________. a)       Write down 4. b)       6 x (11 + 1) = 72 .   Write 2, carry *7. c)       11 x (11 + 1) = 132 + *7 = 139 See Multiplying by 11 . d)       The answer is 13924







(**) Squaring A Number Ending In 9: A.   This method comes from algebra: (10 a – 1) 2 = 100 (a)(a – 1) + 10(8 a) + 1 B.   Using numbers instead of variables we get the following: 1.   Write down 1. 2.   Add 1 to the ten’s digit and multiply by 8. Write this number down, carry if necessary. 3.   Multiply the number in the ten’s digit by that number plus 1.   Write this result. Ex [1 ]   79 2 =_________. a)       Write down 1. b)       8 x (7 + 1) = 64 .   Write 4, carry *6. c)       7 x (7 + 1) = 56 + *6 = 62 d)       The answer is 6241 . Ex [2 ]   249 2 =_________. a)       Write down 1. b)       8 x (24 + 1) = 200 .   Write 0, carry *20 c)       24 x (24 + 1) = 600 + *20 See Multiplying by 25 . d)       The answer is 62001 .