Extended Division
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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
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