Extended Multiplication and Division

 Standard Algorithm      65   X34    260    4 X 65 ( 4 groups of 65 )  1950    30 X 65 ( 30 groups of 65 )  2212 Partial Product Algorithm     197   (100 + 90 + 7))     X68   (60 + 8)        56    8 X 7    Multiply:      720    8 X 90       800    8 X 100      420    60 X 7    5400    60 X 90    6000    60  X 100    13396                Add:

Long Division Algorithm

316R1
7 ) 2213
21
11
7
43
42
1

 316R1 7 ) 2213                                                        Or Shorten:        700       100      ( 100 groups of  7 )      1513        700       100      ( 100 groups of  7 )        813        700       100      ( 100 groups of  7 )        or (3 X 100)        113         70         10      ( 10  groups of  7 )          43            7            1      ( 1 group of  7 )  From here to          36                                              the bottom            7            1      ( 1 group of  7 )   can be done          29                                               in one            7            1      ( 1 group of  7 )   subtraction          22                                               step if it            7            1      ( 1 group of  7 )   is a known          15                                               fact.            7            1      ( 1 group of  7 )              8            7      +    1      ( 1 group of  7 )           or (6 X 7)            1        316 Interim Estimate Algorithm The Interim Estimate Algorithm uses estimation to find how many sets of a number can be found in another number. The assumption is that students understand division as a splitting up into equal groups action, that they can do several-digit subtraction arithmetic, and that they can multiply by a 1-digit number by multiples of 10s. Start by removing the largest amount possible by multiplying the divisor (7) by a multiple of 10 (100 works in this case) and subtracting this (700) from the dividend (2213) which creates a new dividend (1513) and the process continues until the multiple of 100 (700) can no longer be subtracted. Then the next largest multiple of 10 is used ( in this case 10 ) is multiplied by the divisor giving us (70) to subtract and finally 1 times the divisor (7). When this is completed simply add up all the multiples of 10 to the side and place the answer in the quotient. Terms:                     quotient                     divisor ) dividend