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13. The common subtraction algorithm described in the text is not the only correct subtraction algorithm. Some people use the following algorithm instead: Line up the numbers as in the standard algorithm, and subtract column by column, proceeding 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 d and cross out the digit at the bottom of the column, re- placing 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 follow- ing example shows the steps of this new algorithm: 13 12 132 132 8. 1,3 2 1 8 79 -> - 79 -079 3 53 a. Use the new algorithm to solve 524 198 and 1003 – 95. Verify that the new algorithm gives correct answers. 15. b. Explain why it makes sense that this new algorithm gives correct answers to subtraction problems. What is the reasoning behind this new algorithm? c. What are some advantages and disadvantages of this new algorithm compared with our common

13. The common subtraction algorithm described in the text is not the only correct subtraction algorithm. Some people use the following algorithm instead: Line up the numbers as in the standard algorithm, and subtract column by column, proceeding 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 d and cross out the digit at the bottom of the column, re- placing 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 follow- ing example shows the steps of this new algorithm: 13 12 132 132 8. 1,3 2 1 8 79 -> - 79 -079 3 53 a. Use the new algorithm to solve 524 198 and 1003 – 95. Verify that the new algorithm gives correct answers. 15. b. Explain why it makes sense that this new algorithm gives correct answers to subtraction problems. What is the reasoning behind this new algorithm? c. What are some advantages and disadvantages of this new algorithm compared with our common

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.8: Introduction To Cryptography (optional)
Problem 15E: a. Excluding the identity cipher, how many different translation ciphers are there using an alphabet...
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13. The common subtraction algorithm described in the text is not the only correct subtraction algorithm. Some people use the following algorithm instead: Line Therefore the numbers as in the standard algorithm, and algorithm. up subtract column by column, proceeding from right to on left. The only difference between this new algorithm and our standard one is in regrouping. To regroup a. Use th calcula you ge with the new algorithm, move one column to the left and cross out the digit at the bottom of the column, re- placing it with that digit plus 1. (So replace an 8 with da 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 follow- ing example shows the steps of this new algorithm: b. Explai: rithm g subtrac tween lem in are the Work o12 132 13 12 132 13 2 18 999 79 - 79 079 -> - c. What a 3 53 the ad a. Use the new algorithm to solve 524 198 and 1003 – 95. Verify that the new algorithm gives rithm algorit correct answers. 15. After you b. Explain why it makes sense that this new algorithm gives correct answers to subtraction problems. What is the reasoning behind this new algorithm? fully abou find that y a. What c. What are some advantages and disadvantages of this new algorithm compared with our common use to and per one?
Transcribed Image Text:13. The common subtraction algorithm described in the text is not the only correct subtraction algorithm. Some people use the following algorithm instead: Line Therefore the numbers as in the standard algorithm, and algorithm. up subtract column by column, proceeding from right to on left. The only difference between this new algorithm and our standard one is in regrouping. To regroup a. Use th calcula you ge with the new algorithm, move one column to the left and cross out the digit at the bottom of the column, re- placing it with that digit plus 1. (So replace an 8 with da 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 follow- ing example shows the steps of this new algorithm: b. Explai: rithm g subtrac tween lem in are the Work o12 132 13 12 132 13 2 18 999 79 - 79 079 -> - c. What a 3 53 the ad a. Use the new algorithm to solve 524 198 and 1003 – 95. Verify that the new algorithm gives rithm algorit correct answers. 15. After you b. Explain why it makes sense that this new algorithm gives correct answers to subtraction problems. What is the reasoning behind this new algorithm? fully abou find that y a. What c. What are some advantages and disadvantages of this new algorithm compared with our common use to and per one?
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