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Division Algorithms
An algorithm is a process or series of steps used to solve a problem. There are different algorithms for addition, subtraction, multiplication and division. Depending on the problem, students would choose the algorithm that best “fits” their problem. Students need to master at least one algorithm that they are successful, efficient, and accurate with. There are two division algorithms taught in the Everyday Math program, Partial Quotients and Column Division.
One way to think about division is creating equal “groups of” something. How many weeks is 57 days? You are starting with 57 days and breaking the days into groups of 7 (one week). |
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| Example Partial Quotients Estimate the number of 8s in 142. Begin with groups of ten because they are easier to think about. You start with what you know (this could change with each person). I know they are at least 10 groups of 8 in 142. 8 groups of 10 are 80 so I subtract 80 from 142, which leaves 62. I know that there are at least 7 more groups of 8 in 62. 7 groups of 8 are 56. Subtract 56 from 62, which leaves 6. 6 is too small to make another group of 8. I now add the number of groups I made when dividing. 10 + 7 added together to get 17 with a remainder of 6. 142/ 7 = 17 r 6 |
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| 10 + 7 = 17 R 6 |
| 142 / 8 = 17 R6 |
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Column Division Column division is similar to the algorithm you probably used as a student, but is easier to use. It separates the dividend (the whole you are starting with) by each digit’s place value and then divides that place value number by the number you are dividing by, the divisor. |
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There are at least 100 4's in 576, so place a 1 above the 500 and subtract the 4 hundreds from the 5 hundreds that were there. |
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Trade the 100 that was left for 10 tens and add 10 tens to the 7 that were there. There are 4 4's in 17 so place a 4 about the 17 tens. 17 tens minus 16 tens leaves 1 ten.
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There was 1 ten left so trade it for 10 ones. Add the 10 ones to the 6 ones that were there and divide. There are 4 4's in 16 with nothing left over. Put a 4 above the 16 ones. The answer is 144. |
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