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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![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 and cross out the digit at the *bottom* of the column, replacing 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:
\[132 \quad \overset{12}{\phantom{1}} \quad \overset{13}{\phantom{8}} \]
\[- 79 \quad \rightarrow \; - 79 \quad \rightarrow \; - 8\overset{\small{12}}{0}\]
\[ \phantom{1} \, 3 \quad \phantom{1} \quad \phantom{1} \, 5 \, 3\]
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 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 one?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e8e4384-845d-4e77-8936-233e84dfd8a4%2F29226dde-e18f-4cf3-a0b9-3c6bf0e76374%2F21ac49c_processed.jpeg&w=3840&q=75)
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 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 and cross out the digit at the *bottom* of the column, replacing 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:
\[132 \quad \overset{12}{\phantom{1}} \quad \overset{13}{\phantom{8}} \]
\[- 79 \quad \rightarrow \; - 79 \quad \rightarrow \; - 8\overset{\small{12}}{0}\]
\[ \phantom{1} \, 3 \quad \phantom{1} \quad \phantom{1} \, 5 \, 3\]
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 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 one?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
