Multiplying 2 Numbers Starting With Same Tens Digits CoffeeMath Methods, Tips & Tricks Series

16 13 10 10 - 6 - 3 1st Examination Means 13 is 3 more than 10 Means 16 is 6 more than 10 16 - ( - 3 ) ( ) 10 X = 19 X 10 = 190 13 - ( - 6 ) ( ) 10 X = 19 X 10 = 190 ( -6 ) ( -3 ) X = 18 + = 18 190 208 # Step 1 : Determine how much 16 from 10 and how much 13 from 10 Step 2 : Or Either Step 3 : Step 4 : We just solved this using reference point method of the base 10 16 X 13 = ___ if reference point is 10

16 13 20 20 + 4 + 7 Means 13 is 7 less than 20 Means 16 is 4 less than 20 16 - ( + 7) ( ) 20 X = 9 X 20 = 180 13 - ( + 4) ( ) 20 X = 9 X 20 = 190 ( + 4 ) ( + 7 ) X = 28 + = 28 180 208 # Step 1 : Determine how much 16 from 20 and how much 13 from 20 Step 2 : Or Either Step 3 : Step 4 : 2nd Examination We just solved this using reference point method of the base 20 16 X 13 = ___ if reference point is 20

16 13 30 30 + 14 + 17 Means 13 is 17 less than 30 Means 16 is 14 less than 30 16 - ( + 17) ( ) 30 X = -1 X 30 = - 30 13 - ( + 14) ( ) 30 X = -1 X 30 = - 30 ( + 14 ) ( +1 7 ) X = 28 + = 238 - 30 208 # Step 1 : Determine how much 16 from 30 and how much 13 from 30 Step 2 : Or Either Step 3 : Step 4 : We just solved this using reference point method of the base 30 3rd Examination 16 X 13 = ___ if reference point is 30

16 13 90 90 + 74 + 77 Means 13 is 77 less than 90 Means 16 is 74 less than 90 16 - ( + 77) ( ) 90 X = - 61 X 90 = - 5490 13 - ( + 74) ( ) 90 X = - 61 X 90 = - 5490 ( + 74 ) ( +77 ) X = 5698 + = 5698 - 5490 208 # Step 1 : Determine how much 16 from 90 and how much 13 from 90 Step 2 : Or Either Step 3 : Step 4 : The higher the base number the more difficult to solve the problem, but we still get the same result. 9th Examination 16 X 13 = ___ if reference point is 90

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23 X 21 = _____ 23 21 20 20 - 3 - 1 ( 21 is 1 more than 20 ) ( 23 is 3 more than 20 ) 23 - ( - 1 ) ( ) 20 X = 24 X 20 = 480 Either 21 - ( - 3 ) ( ) 20 X = 24 X 20 = 480 Or (-3 ) (-1) X = 3 And + = 3 Last 480 483 # ( Let’s us use 20 as the Base Number ) Either [ (23+1)*20 ] + (-3)(-1) = 483 or [ (21+3)*20 ] + (-3)(-1) = 483

34 X 32 = _____ 34 32 30 30 - 4 - 2 ( 32 is 2 more than 30 ) ( 34 is 4 more than 30 ) 34 - ( - 2 ) ( ) 30 X = 36 X 30 = 1080 Either 32 - ( - 4 ) ( ) 30 X = 36 X 30 = 1080 Or (-4 ) (-2) X = 8 And + = 8 Last 1080 1088 # ( Let’s us use 30 as the Base Number ) Either [ (34+2)*30 ] + (-4)(-2) = 1080 or [ (32+4)*30 ] + (-4)(-2) = 1080

43 X 45 = _____ 43 45 30 30 - 3 - 5 ( 45 is 5 more than 40 ) ( 43 is 3 more than 40 ) 43 - ( - 5 ) ( ) 40 X = 48 X 40 = 1920 Either 45 - ( - 3 ) ( ) 40 X = 48 X 40 = 1920 Or (- 3 ) ( -5 ) X = 15 And + = 15 Last 1920 1935 # ( Let’s us use 40 as the Base Number ) Either [ (43+5)*40 ] + (-3)(-5) = 1935 or [ (45+3)*40 ] + (-3)(-5) = 1935

53 X 55 = _____ 53 55 50 50 - 3 - 5 ( 55 is 5 more than 50 ) ( 53 is 3 more than 50 ) 53 - ( - 5 ) ( ) 50 X = 58 X 50 = 2900 Either 55 - ( - 3 ) ( ) 50 X = 58 X 50 = 2900 Or (- 3 ) ( -5 ) X = 15 And + = 15 Last 2900 2915 # ( Let’s us use 50 as the Base Number ) Either [ (53+5)*50 ] + (-3)(-5) = 2915 or [ (55+3)*50 ] + (-3)(-5) = 2915

62 X 67 = _____ 62 67 60 60 - 2 - 7 ( 67 is 7 more than 60 ) ( 62 is 2 more than 60 ) 62 - ( - 7 ) ( ) 60 X = 69 X 60 = 4140 Either 67 - ( - 2 ) ( ) 60 X = 69 X 60 = 4140 Or (- 2 ) ( - 7 ) X = 14 And + = 14 Last 4140 4154 # ( Let’s us use 60 as the Base Number ) Either [ (62+7)*60 ] + (-2)(-7) = 4154 or [ (67+2)*60 ] + (-2)(-7) = 4154

73 X 76 = _____ 73 76 70 70 - 3 - 6 ( 76 is 6 more than 70 ) ( 73 is 3 more than 70 ) 73 - ( - 6 ) ( ) 70 X = 79 X 70 = 5530 Either 76 - ( - 3 ) ( ) 70 X = 79 X 70 = 5530 Or (- 3 ) ( - 6 ) X = 18 And + = 18 Last 5530 5548 # ( Let’s us use 70 as the Base Number ) Either [ (73+6)*70 ] + (-3)(-6) = 5548 or [ (76 + 3)*70 ] + (-3)(-6) = 5548

83 X 84 = _____ 83 84 80 80 - 3 - 4 ( 84 is 4 more than 80 ) ( 83 is 3 more than 80 ) 83 - ( - 4 ) ( ) 80 X = 87 X 80 = 6960 Either 84 - ( - 3 ) ( ) 80 X = 87 X 80 = 6960 Or (- 3 ) ( - 4 ) X = 12 And + = 12 Last 6960 6972 # ( Let’s us use 80 as the Base Number ) Either [ (98+5)*90 ] + (-8)(-5) = 9310 or [ (95+8)*90 ] + (-8)(-5) = 9310

98 X 95 = _____ 98 95 90 90 - 8 - 5 ( 95 is 5 more than 90 ) ( 98 is 8 more than 90 ) 98 - ( - 5 ) ( ) 90 X = 103 X 90 = 9270 Either 95 - ( - 8 ) ( ) 90 X = 103 X 90 = 9270 Or (- 8 ) ( - 5 ) X = 40 And + = 12 Last 9270 9310 # ( Let’s us use 90 as the Base Number ) Either [ (98+5)*90 ] + (-8)(-5) = 9310 or [ (95+8)*90 ] + (-8)(-5) = 9310

98 X 95 = _____ 98 95 100 100 + 2 + 5 ( 95 is 5 less than 100 ) ( 98 is 2 less than 100 ) 98 - ( + 5 ) ( ) 100 X = 93 X 100 = 9300 Either 95 - ( + 2 ) ( ) 100 X = 93 X 100 = 9300 Or (- 2 ) ( - 5 ) X = 10 And + = 10 Last 9300 9310 # ( Let’s us use 100 as the Base Number ) Either [ (98-5)*100 ] + (-5)(-2) = 9310 or [ (95-2)*100 ] + (-5)(-3) = 9310

103 X 105 = _____ 103 105 100 100 - 3 - 5 ( 105 is 5 more than 100 ) ( 103 is 3 more than 100 ) 103 - ( - 5 ) ( ) 100 X = 108 X 100 = 10800 Either 105 - ( - 3 ) ( ) 100 X = 108 X 100 = 10800 Or (- 3 ) ( - 5 ) X = 15 And + = 15 Last 10800 10815 # Either [ (103+5)*100 ] + (-5)(-3) = 10815 or [ (105+3)*100 ] + (-5)(-3) = 10815 ( Let’s us use 100 as the Base Number )

11 to 19 use 10 as the Base Number So, here are the recommendation of reference point 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 101 – 109 use 100 as the Base Number 91 to 99 use either 90 or 100 as the Base Number

Multiplying 2 Numbers Starting With Same Hundreds Digits And Same Tens Digits CoffeeMath Methods, Tips & Tricks Series Example: 234 x 232 = ____ ?

The reference point is 230 234 232 230 230 - 4 - 2 ( 105 is 5 more than 230 ) ( 234 is 4 more than 230 ) 234 - ( - 2 ) ( ) 230 X = 236 X 230 = 54280 Either 232 - ( - 4 ) ( ) 230 X = 236 X 230 = 54280 Or (- 4 ) ( - 2 ) X = 08 And + = 08 Last 54280 54288 # 234 x 232 = __________ The method and concept is same but it’s very tough for the beginners.

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