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Multiplying 2 numbers starting with same digit

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Multiplying 2 numbers starting with same digit

  1. 1. Xtra Math: Methods, Tips And Tricks Series. By Puwork Utara May 2012
  2. 2. Multiplying 2 NumbersStarting WithSame Digit(s)
  3. 3. 1st Examination 16 X 13 = ___ if reference point is 10 Step 1 : Determine how much 16 from 10 and how much 13 from 10 -6 Means 16 is 6 more than 10 16 10 13 - 3 Means 13 is 3 more than 10 10 Step 2 : Either ( 16 - (-3) ) X 10 = 19 X 10 = 190 Or (-6) = ( 13 - ) X 10 19 X 10 = 190 Step 3 : ( -6 ) X ( -3 ) = 18 Step 4 : 190 + 18 = 208 # We just solved this using reference point method of the base 10
  4. 4. 2nd Examination 16 X 13 = ___ if reference point is 20 Step 1 : Determine how much 16 from 20 and how much 13 from 20 +4 Means 16 is 4 less than 20 16 20 13 +7 Means 13 is 7 less than 20 20 Step 2 : Either ( 16 - ( + 7) ) X 20 = 9 X 20 = 180 Or ( + 4) = ( 13 - ) X 20 9 X 20 = 190 Step 3 : (+4) X ( + 7 ) = 28 Step 4 : 180 + 28 = 208 # We just solved this using reference point method of the base 20
  5. 5. 3rd Examination 16 X 13 = ___ if reference point is 30 Step 1 : Determine how much 16 from 30 and how much 13 from 30 + 14 Means 16 is 14 less than 30 16 30 13 + 17 Means 13 is 17 less than 30 30 Step 2 : Either ( 16 - ) X 30 ( + 17) = -1 X 30 = - 30 Or ( 13 - ( + 14) ) X 30 = -1 X 30 = - 30 Step 3 : ( + 14 ) X ( +1 7 ) = 28 Step 4 : - 30 + 238 = 208 # We just solved this using reference point method of the base 30
  6. 6. 9th Examination 16 X 13 = ___ if reference point is 90 Step 1 : Determine how much 16 from 90 and how much 13 from 90 + 74 Means 16 is 74 less than 90 16 90 13 + 77 Means 13 is 77 less than 90 90 Step 2 : Either ( 16 - ) X 90 ( + 77) = - 61 X 90 = - 5490 Or ( 13 - ( + 74) ) X 90 = - 61 X 90 = - 5490 Step 3 : ( + 74 ) X ( +77 ) = 5698 Step 4 : - 5490 + 5698 = 208 # The higher the base number the more difficult to solve the problem, but we still get the same result.
  7. 7. So, here are the recommendation of reference point 11 to 19 use 10 as the Base Number 21 to 29 use 20 as the Base Number 31 to 39 use 30 as the Base Number 41 to 49 use 40 as the Base Number 51 to 59 use 50 as the Base Number 61 to 69 use 60 as the Base Number 71 to 79 use 70 as the Base Number 81 to 89 use 80 as the Base Number 91 to 99 use either 90 or 100 as the Base Number 101 – 109 use 100 as the Base Number
  8. 8. Now!Adjust your chair tosee the rest of thisslideshow….
  9. 9. ( Let’s us use 20 as the Base Number ) 23 X 21 = _____ -3 23 20 ( 23 is 3 more than 20 ) -1 21 20 ( 21 is 1 more than 20 ) Either ( 23 - ( - 1 )) X 20 = 24 X 20 = 480 Or ( 21 - ( - 3 )) X 20 = 24 X 20 = 480 And (-3 ) X (-1) = 3 Last 480 + 3 = 483 #Either [ (23+1)*20 ] + (-3)(-1) = 483 or [ (21+3)*20 ] + (-3)(-1) = 483
  10. 10. ( Let’s us use 30 as the Base Number ) 34 X 32 = _____ -4 34 30 ( 34 is 4 more than 30 ) -2 32 30 ( 32 is 2 more than 30 ) Either ( 34 - ( - 2 )) X 30 = 36 X 30 = 1080 Or ( 32 - ( - 4 )) X 30 = 36 X 30 = 1080 And (-4 ) X (-2) = 8 Last 1080 + 8 = 1088 #Either [ (34+2)*30 ] + (-4)(-2) = 1080 or [ (32+4)*30 ] + (-4)(-2) = 1080
  11. 11. ( Let’s us use 40 as the Base Number ) 43 X 45 = _____ -3 43 30 ( 43 is 3 more than 40 ) -5 45 30 ( 45 is 5 more than 40 ) Either ( 43 - ( - 5 )) X 40 = 48 X 40 = 1920 Or ( 45 - ( - 3 )) X 40 = 48 X 40 = 1920 And (- 3 ) X ( -5 ) = 15 Last 1920 + 15 = 1935 #Either [ (43+5)*40 ] + (-3)(-5) = 1935 or [ (45+3)*40 ] + (-3)(-5) = 1935
  12. 12. ( Let’s us use 50 as the Base Number ) 53 X 55 = _____ -3 53 50 ( 53 is 3 more than 50 ) -5 55 50 ( 55 is 5 more than 50 ) Either ( 53 - ( - 5 )) X 50 = 58 X 50 = 2900 Or ( 55 - ( - 3 )) X 50 = 58 X 50 = 2900 And (- 3 ) X ( -5 ) = 15 Last 2900 + 15 = 2915 #Either [ (53+5)*50 ] + (-3)(-5) = 2915 or [ (55+3)*50 ] + (-3)(-5) = 2915
  13. 13. ( Let’s us use 60 as the Base Number ) 62 X 67 = _____ -2 62 60 ( 62 is 2 more than 60 ) -7 67 60 ( 67 is 7 more than 60 ) Either ( 62 - ( - 7 )) X 60 = 69 X 60 = 4140 Or ( 67 - ( - 2 )) X 60 = 69 X 60 = 4140 And (- 2 ) X ( - 7 ) = 14 Last 4140 + 14 = 4154 #Either [ (62+7)*60 ] + (-2)(-7) = 4154 or [ (67+2)*60 ] + (-2)(-7) = 4154
  14. 14. ( Let’s us use 70 as the Base Number ) 73 X 76 = _____ -3 73 70 ( 73 is 3 more than 70 ) -6 76 70 ( 76 is 6 more than 70 ) Either ( 73 - ( - 6 )) X 70 = 79 X 70 = 5530 Or ( 76 - ( - 3 )) X 70 = 79 X 70 = 5530 And (- 3 ) X ( - 6 ) = 18 Last 5530 + 18 = 5548 #Either [ (73+6)*70 ] + (-3)(-6) = 5548 or [ (76 + 3)*70 ] + (-3)(-6) = 5548
  15. 15. ( Let’s us use 80 as the Base Number ) 83 X 84 = _____ -3 83 80 ( 83 is 3 more than 80 ) -4 84 80 ( 84 is 4 more than 80 ) Either ( 83 - ( - 4 )) X 80 = 87 X 80 = 6960 Or ( 84 - ( - 3 )) X 80 = 87 X 80 = 6960 And (- 3 ) X ( - 4 ) = 12 Last 6960 + 12 = 6972 #Either [ (98+5)*90 ] + (-8)(-5) = 9310 or [ (95+8)*90 ] + (-8)(-5) = 9310
  16. 16. ( Let’s us use 90 as the Base Number ) 98 X 95 = _____ -8 98 90 ( 98 is 8 more than 90 ) -5 95 90 ( 95 is 5 more than 90 ) Either ( 98 - ( - 5 )) X 90 = 103 X 90 = 9270 Or ( 95 - ( - 8 )) X 90 = 103 X 90 = 9270 And (- 8 ) X ( - 5 ) = 40 Last 9270 + 12 = 9310 #Either [ (98+5)*90 ] + (-8)(-5) = 9310 or [ (95+8)*90 ] + (-8)(-5) = 9310
  17. 17. ( Let’s us use 100 as the Base Number ) 98 X 95 = _____ +2 98 100 ( 98 is 2 less than 100 ) +5 95 100 ( 95 is 5 less than 100 ) Either ( 98 - ( + 5 ) X 100 = 93 X 100 = 9300 Or ( 95 - ( + 2 ) X 100 = 93 X 100 = 9300 And (- 2 ) X ( - 5 ) = 10 Last 9300 + 10 = 9310 #Either [ (98-5)*100 ] + (-5)(-2) = 9310 or [ (95-2)*100 ] + (-5)(-3) = 9310
  18. 18. ( Let’s us use 100 as the Base Number ) 103 X 105 = _____ -3 103 100 ( 103 is 3 more than 100 ) -5 105 100 ( 105 is 5 more than 100 ) Either ( 103 - ( - 5 )) X 100 = 108 X 100 = 10800 Or ( 105 - ( - 3 )) X 100 = 108 X 100 = 10800 And (- 3 ) X ( - 5 ) = 15 Last 10800 + 15 = 10815 #Either [ (103+5)*100 ] + (-5)(-3) = 10815 or [ (105+3)*100 ] + (-5)(-3) = 10815
  19. 19. How to deal with234 x 232 = ____
  20. 20. 234 x 232 = __________ The reference point is 230 -4 234 230 ( 234 is 4 more than 230 ) -2 232 230 ( 105 is 5 more than 230 )Either ( 234 - ( - 2 )) X 230 = 236 X 230 = 54280Or ( 232 - ( - 4 )) X 230 = 236 X 230 = 54280 And (- 4 ) X ( - 2 ) = 08 Last 54280 + 08 = 54288 #The method and concept is same but it’s very tough for the beginners.
  21. 21. End Show GOOD LUCK !

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