Problem solved...can someone please confirm and xplain with mathematical terms?

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cruz33

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Determine the check digit for an Avis rental car withidentification number 540047

The check digit for the number 540047 is 4 because:
540047 = 7 x 77149 + 4

I found the check digit, but my problem is explaining thisproblem in words (step by step). Can someone please attempt to explain it? Thank you!

 
cruz33 said:
The check digit for the number 540047 is 4 because:

540047 = 7 x 77149 + 4

I found the check digit, but my problem is explaining

Click to expand...

4 is the remainder, after dividing 540047 by 7

Is your class studying modular arithmetic?
 
thanks for replying

mmm4444bot said:
4is the remainder, after dividing 540047 by 7

Is your class studying modular arithmetic?
Click to expand...

No, I'm taking contemporary math. This is what I have so far...(Ineed to do a step by step explanation) :)

Step 1
540047 divided by 7 = 77149
Step 2
77149 …. (not sure by what I am dividing or multiplying thisnumber with)

Can you please add to my step by step explanation.

Thank you!


 
Last edited:
cruz33 said:


No, I'm taking contemporary math. This is what I have so far...(Ineed to do a step by step explanation) :)

Step 1
540047 divided by 7 = 77149
Step 2
77149 …. (not sure by what I am dividing or multiplying thisnumber with)

Can you please add to my step by step explanation.

Thank you!
Click to expand...
Contemporary math!!!!! How incredibly stupid a phrase. Euclid's proof of the infinitude of primes is just as valid today as it was 2400 years ago.

I presume this means some math course that uses modern notation and a few recently discovered mathematical ideas without getting at anything substantial.

Divide 54007 by 7. The answer is NOT 77149. It is, going back to basic arithmetic, 77149 with a remainder of 4. So if the check digit is 4, the number was probably coded correctly.

There is nothing more complicated involved.
 
JeffM said:
Contemporarymath!!!!! How incredibly stupid a phrase. Euclid'sproof of the infinitude of primes is just as valid today as it was 2400 yearsago.

Divide 54007 by 7. The answer is NOT 77149. It is, going back to basicarithmetic, 77149 with a remainder of 4. So if the check digit is 4, the numberwas probably coded correctly.

There is nothing more complicated involved.
Click to expand...

Hi JeffM

Believe me, I am terrible at math! I spend hours trying to solveone mathematical problem! This is why Idare to ask this question: Why 4? Where does that 4 comes from?

I get the beginning, 540047 divided by 7 = 77149
So, what now? How do I get the answer which is 4?


Thank you for trying to explain this problem for me.


 
cruz33 said:


Hi JeffM

Believe me, I am terrible at math! I spend hours trying to solveone mathematical problem! This is why Idare to ask this question: Why 4? Where does that 4 comes from?

I get the beginning, 540047 divided by 7 = 77149
So, what now? How do I get the answer which is 4?


Thank you for trying to explain this problem for me.
Click to expand...
Anyone can learn math if they have basic concepts explained to them clearly and then do enough practice.

Check digits were invented to help identify numbers that were incorrectly written down or coded and thereby correct them. That is the purpose of the check digit.

Now suppose I arbitrarily say that my process for verifying a check digit is that I divide the main number by 7, and the remainder, which can be 0 through 6, is the check digit. It is just a freely chosen rule.

So I write down the number 540047-4. The meaningful part is the 540047; let's say it means bananas. Someone wants to buy oranges, which have the identifying number 540074, but write down 540047 by mistake. So I'll send them bananas when they want oranges, and I'll have an unhappy customer. If I have a check digit that is the remainder when the meaningful part of the number is divided by 7, then the number for bananas will by 540047-4 because 540047 divided by 7 is 77149 with a remainder of 4 and the number for oranges will be 540074-3 because 540074 divided by 7 is 77153 with a remainder of 3. So if I get a number 540074-4, I know the number is wrong, and I call my customer to find out whether the order is for oranges or bananas. With 540074-4, either the check digit is wrong or the main number is wrong, but something is messed up. Got the idea?

This is very simple if you are doing the math by hand, but calculators actually make this harder.

When I divide 540047 by 7 on a calculator, I get 77149.571428..... So to find the check digit I ignore everything after the decimal point. I multiply 77149 by 7 (which is my ARBITRARY number for check digit computations) and get 540043, which 4 less than the number I want. So the check digit is 4.

You good now?
 
You understand, do you not, that people, or companies, can define "check digits" in many different ways. It would appear, here, that the "check digit" is the remainder when you divide by 7. But it would be impossible to know that you were to divide by 7 without being told that! Was there somewhere in your book that it said that, for Avis, the check digit was generated by dividing by 7?
 
Thank you!!!

JeffM said:
Anyone can learn math if they have basic concepts explained to them clearly and then do enough practice.

Check digits were invented to help identify numbers that were incorrectly written down or coded and thereby correct them. That is the purpose of the check digit.

Now suppose I arbitrarily say that my process for verifying a check digit is that I divide the main number by 7, and the remainder, which can be 0 through 6, is the check digit. It is just a freely chosen rule.

So I write down the number 540047-4. The meaningful part is the 540047; let's say it means bananas. Someone wants to buy oranges, which have the identifying number 540074, but write down 540047 by mistake. So I'll send them bananas when they want oranges, and I'll have an unhappy customer. If I have a check digit that is the remainder when the meaningful part of the number is divided by 7, then the number for bananas will by 540047-4 because 540047 divided by 7 is 77149 with a remainder of 4 and the number for oranges will be 540074-3 because 540074 divided by 7 is 77153 with a remainder of 3. So if I get a number 540074-4, I know the number is wrong, and I call my customer to find out whether the order is for oranges or bananas. With 540074-4, either the check digit is wrong or the main number is wrong, but something is messed up. Got the idea?

This is very simple if you are doing the math by hand, but calculators actually make this harder.

When I divide 540047 by 7 on a calculator, I get 77149.571428..... So to find the check digit I ignore everything after the decimal point. I multiply 77149 by 7 (which is my ARBITRARY number for check digit computations) and get 540043, which 4 less than the number I want. So the check digit is 4.

You good now?
Click to expand...


WOWgreat explanation…I wish I had half your mathematical brain! J

Andyou are right, practice makes perfection so I will practice and practice these concepts many times until I completely get it.

Thanks a lot!!!
 
cruz33 said:
WOWgreat explanation…I wish I had half your mathematical brain! J

Andyou are right, practice makes perfection so I will practice and practice these concepts many times until I completely get it.

Thanks a lot!!!
Click to expand...
You're welcome. And thank you for the compliment, but there is nothing special about my brain. Learning math is primarily about learning concepts, not mechanical rules. Why am I supposed to use this rule is the main question that takes thinking: how to use the rule is what the practice is for,

By the way, Halls of Ivy mentioned something very important. To validate a check digit, you have to have been told in advance how the check digit is created.
 
division by 7 scheme

HallsofIvy said:
You understand, do you not, that people, or companies, can define "check digits" in many different ways. It would appear, here, that the "check digit" is the remainder when you divide by 7. But it would be impossible to know that you were to divide by 7 without being told that! Was there somewhere in your book that it said that, for Avis, the check digit was generated by dividing by 7?
Click to expand...

HallsofIvy, yes, you are right, I forgot to add that details; for this problem, I needed to use the division by 7 scheme. Thank you!
 
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