your method. 12. The standard subtraction algorithm described in the text is not the only correct...

  

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your method. 12. The standard subtraction algorithm described in the text is not the only correct subtraction algo- rithm. Some people use the following algorithm instead: Line up the numbers as in the standard algorithm, and subtract column by column, pro- ceeding from right to left. The only difference between this new algorithm and our standard one is in regrouping. To regroup with the new algorithm, move one column to the left and cross out the digit at the bottom of the column, replac- ing it with that digit plus 1. (So replace an 8 with a 9, replace a 9 with a 10, etc.) Then, as in the standard algorithm, replace the digit at the top of the original column with the original number plus 10. The following example shows the steps of this new algorithm: 132 - 79 12 132 - 79 3 13 12 132 18 - 079 53 122 Chapter 3. Addition and Subtraction a. Use the new algorithm to solve 524 - 198 and 1003-95. Verify that the new algorithm gives correct answers. b. Explain why it makes sense that this new algo- rithm gives correct answers to subtraction prob- lems. What is the reasoning behind this new algorithm? c. What are some advantages and disadvantages of this new algorithm compared with our common one? your method. 12. The standard subtraction algorithm described in the text is not the only correct subtraction algo- rithm. Some people use the following algorithm instead: Line up the numbers as in the standard algorithm, and subtract column by column, pro- ceeding from right to left. The only difference between this new algorithm and our standard one is in regrouping. To regroup with the new algorithm, move one column to the left and cross out the digit at the bottom of the column, replac- ing it with that digit plus 1. (So replace an 8 with a 9, replace a 9 with a 10, etc.) Then, as in the standard algorithm, replace the digit at the top of the original column with the original number plus 10. The following example shows the steps of this new algorithm: 132 - 79 12 132 - 79 3 13 12 132 18 - 079 53 122 Chapter 3. Addition and Subtraction a. Use the new algorithm to solve 524 - 198 and 1003-95. Verify that the new algorithm gives correct answers. b. Explain why it makes sense that this new algo- rithm gives correct answers to subtraction prob- lems. What is the reasoning behind this new algorithm? c. What are some advantages and disadvantages of this new algorithm compared with our common one?

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Step 3 b This new algorithm gives correct answer to subtraction problem because it is easy to ... View the full answer