Multiplication Patterns

5Squared Products of 11 Products of 5 11x12 9x8 X = 1x2=2 Pattern recognition Product Factor 1. All products (25, 225, 625, 1225 etc.)end with 25 because, the factors have 5 in the units place. 25 in the product is the dominant pattern. 0x0=0 1x1=2 3x3=12 2x2=6 4x4=20 2. Ignoring the factors and the dominant pattern from the product, we get the following pattern: 3. The mathematical pattern will be correct if we use this logic. 2x3=6 3x4=12 4x5=20 That is to say, in squaring numbers ending with 5, we get 25 as the dominant pattern; at the product's Right Hand Side The Left Hand Side is the product is Factor times (Factor + 1) Hence, 995x995=990025. 99x100=9900 LHS is 99x(99+1) RHS is 25 Compute: 995x995 99995x99995=9999000025 9995x9995=99900025 999995x999995=999990000025 Factor 2 Factor 1 The middle digit is the digit sum of Factor 2 First Digit Last Digit 1+1=2 1+2=3 1+3=4 Middle Digit In all Products, the first digits of Factor 2 and Product are same In all Products, the last digits of Factor 2 and Product are same x Challenge: Why is 11x73=803? 9 is 1 less than 10 8 is 2 less than 10 Hence 8x9=72 -1 times -2 is 2. This is the value for the RHS Cross adding, either (9 & -2) or (8 & -1) we get 7. This is the value for LHS +1 +2 Cross adding, either (11 & +2) or (12 & +1) we get 13. This is the value for LHS Hence 11x12=132 Since we have units of 10x10, we cut the 1x10 piece in green from fig 1 and place it at the bottom of fig 2 to get the figure 3 Figure 1 10x10 Piece 10 Rows x 11 Colums Piece 12 Rows x 10 Column Piece 12 Rows x 11 Columns Piece We write this way as 11 is 1 more than 10 We write this way as 12 is 2 more than 10 We find the product of 1 x 2: 1 times 2 is 2. This is the value for the RHS As the base is 10, we cut the green colored 2x7 piece from Fig 1 and fix it at the bottom of Fig 2. The result is Fig 3 Fig 1 Fig 2 Fig 3 Multiplier Times Multiplicand Half of 888 is 444 Half of 2 is 1 10x10 piece 8 rows x 9 columns As the base is 10, we cut the green colored 1x9 piece from Fig 1 and fix it to the right of Fig 2. The result is Fig 3. Either way we get 72 0.00 0.00 00.00 00.00 00.00 000.00 00.00 00.00 000.00 00.00 00.00 0000.00 00.00 00.00 0000.00 00.00 00.00 0000.00 00.00 00.00 0000.00 00.00 00.00 0000.00 00.00 00.00 0000.00 00.00 00.00 0000.00 000.00 000.00 00000.00 000.00 000.00 00000.00 000.00 000.00 00000.00 000.00 000.00 00000.00 000.00 000.00 00000.00 000.00 000.00 00000.00 000.00 000.00 00000.00 00.00 00.00 000.00 0.00 0.00 000.00 00.00 00.00 000.00 0.00 0.00 000.00 00.00 00.00 000.00 0.00 0.00 000.00 00.00 00.00 000.00 00.00 00.00 000.00 00.00 00.00 000.00 00.00 00.00 000.00 00.00 00.00 000.00 00.00 00.00 000.00 00.00 00.00 000.00 00.00 00.00 000.00 00.00 00.00 000.00 00.00 00.00 000.00 00.00 00.00 000.00 00.00 00.00 000.00 00.00 00.00 000.00 00.00 00.00 000.00 00.00 00.00 000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 0.00 00.00 0.00 00.00 0.00 00.00 0.00 00.00 0.00 00.00 0.00 00.00 0.00 00.00 0.00 000.00 0.00 000.00 0.00 000.00 0.00 000.00 0.00 000.00 0.00 000.00 0.00 000.00 000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 00.00 00.00 00.00 00.00 00.00 00.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 00.00 00.00 00.00 0.00 0.00 00.00 0.00 0.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 0.00 0.00 00.00 0.00 0.00 00.00 0.00 0.00 0.00 0.00 00.00 00.00 00.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 00.00 00.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00 -0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 00.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 00.00 00.00 00.00