Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    8
    ReputationRep:
    1. Think of a positive two digit number.
    2. Calculate the digit sum.
    3. Subtract the digit sum from the number that you thought of.
    4. What did you get?

    Example:
    I think of the number 68.
    The digit sum is therefore 6+8=14
    68-14=54

    Now:

    I. Think of a new two/three-digit number and do the same thing again.

    II. Re-do the calculation with new numbers from the one before until you find that they have something in common. What does the answer have in common?

    III. Show that your foundings is valid for all two-digit numbers, the value of the two digit number can be written as 10*a+b

    IV. Investigate whether your foundings also applies to positive three-digit numbers
    Posted on the TSR App. Download from Apple or Google Play
    • Thread Starter
    Offline

    8
    ReputationRep:
    What I did was this:

    84-12=72
    72-9=63
    63-9=54
    54-9=45
    45-9=36
    36-9=27
    27-9=18
    18-9=9
    9-9=0

    I see that all answers are multiples of 9. How do I explain in words?
    Posted on the TSR App. Download from Apple or Google Play
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    I. Do it again...
    II. Do it again multiple times... you should get a series of results you can see a pattern to.
    III. So you have 10a + b and you have to subtract a+b as per the question... (This will answer part II)
    IV. You've been given that 10a + b = a 2 digit number so perhaps come up with the equivalent for a 3 digit number?
    Offline

    10
    ReputationRep:
    (Original post by manny103)
    What I did was this:

    84-12=72
    72-9=63
    63-9=54
    54-9=45
    45-9=36
    36-9=27
    27-9=18
    18-9=9
    9-9=0

    I see that all answers are multiples of 9. How do I explain in words?
    Apart from 84-12 all your examples start with a multiple of 9.

    You should do more general examples.

    E.g. 77 - 14 = 63 = 7 x 9.

    Your observation is correct though.

    At that point you only need to say that the result is a multiple of 9.

    Can you now work with the suggestion of using 10a+b?
    Offline

    15
    ReputationRep:
    (Original post by BuryMathsTutor)
    Apart from 84-12 all your examples start with a multiple of 9.

    You should do more general examples.

    E.g. 77 - 14 = 63 = 7 x 9.

    Your observation is correct though.

    At that point you only need to say that the result is a multiple of 9.

    Can you now work with the suggestion of using 10a+b?
    Spoiler:
    Show

    When you do it repeatedly the answers will of course give you multiples of 9 since the digit sum of multiples of 9 is always 9. So OP wasn't choosing multiples of 9 on purpose.
    Offline

    10
    ReputationRep:
    (Original post by uponthyhorse)
    When you do it repeatedly the answers will of course give you multiples of 9 since the digit sum of multiples of 9 is always 9. So OP wasn't choosing multiples of 9 on purpose.
    The result is a multiple of 9 regardless of the initial value. The OP's initial values were all multiples of 9. If they only consider these initial values then they cannot say much about what happens in general.
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by BuryMathsTutor)
    Apart from 84-12 all your examples start with a multiple of 9.

    You should do more general examples.

    E.g. 77 - 14 = 63 = 7 x 9.

    Your observation is correct though.

    At that point you only need to say that the result is a multiple of 9.

    Can you now work with the suggestion of using 10a+b?
    Is there any other words that I can explain my findings with? Besides being a multiple of 9? Is there a certain formula we are following here that I can give a validity to by doing this experiment?

    10a+b, so a = 3 and b = 4
    30+4 = 34

    34-7 = 27
    27-9 = 18
    18-9 = 9

    It seems that any number I put in, into the formula where we have two digit numbers, gives me a multiple of 9?
    Posted on the TSR App. Download from Apple or Google Play
    Offline

    15
    ReputationRep:
    (Original post by BuryMathsTutor)
    The result is a multiple of 9 regardless of the initial value. The OP's initial values were all multiples of 9. If they only consider these initial values then they cannot say much about what happens in general.
    yep but the "initial" values they were using were the results of the previous calculation, they weren't chosen by the OP as far as I can tell

    (am I getting confused here?)
    Posted on the TSR App. Download from Apple or Google Play
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by BuryMathsTutor)
    The result is a multiple of 9 regardless of the initial value. The OP's initial values were all multiples of 9. If they only consider these initial values then they cannot say much about what happens in general.
    By initial values do you mean the first result I get when giving a and b values?
    a=5 b=3
    10a+b
    50+3=53
    Digit sum is 8? Which initial values did you refer to?
    Posted on the TSR App. Download from Apple or Google Play
    Offline

    10
    ReputationRep:
    (Original post by uponthyhorse)
    yep but the "initial" values they were using were the results of the previous calculation, they weren't chosen by the OP as far as I can tell

    (am I getting confused here?)
    Their instructions said, "Re-do the calculation with new numbers."

    I didn't even notice that they were taking the last output as the new input.
    Offline

    10
    ReputationRep:
    (Original post by manny103)
    Is there any other words that I can explain my findings with? Besides being a multiple of 9?
    Yes, there is a little more that you can say. Which multiple of 9 do you get? How is it related to the number you start with?
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by BuryMathsTutor)
    Yes, there is a little more that you can say. Which multiple of 9 do you get? How is it related to the number you start with?
    18, 27 etc.. the multiple of the first digit sum.
    (Original post by BuryMathsTutor)
    Yes, there is a little more that you can say. Which multiple of 9 do you get?
    The digit sum minus the original number gives you a multiple of 9, correct? So how can I explain this with a formula? If we have 36 and I have the digit sum 9 from it I will get 27, which is a multiple of 9 and one multiple below 36. But does it generally apply to every original number?

    (Original post by BuryMathsTutor)
    How is it related to the number you start with?
    The digit sum
    Posted on the TSR App. Download from Apple or Google Play
    Offline

    10
    ReputationRep:
    (Original post by manny103)
    18, 27 etc.. the multiple of the first digit sum.

    The digit sum minus the original number gives you a multiple of 9, correct? So how can I explain this with a formula? If we have 36 and I have the digit sum 9 from it I will get 27, which is a multiple of 9 and one multiple below 36. But does it generally apply to every original number?



    The digit sum
    You really need to look at the general case.

    10a+b \rightarrow 10a+b-(a+b)=...

    This will show that the result is a multiple of 9 and also which multiple of 9 it is.
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by BuryMathsTutor)
    You really need to look at the general case.

    10a+b \rightarrow 10a+b-(a+b)=...

    This will show that the result is a multiple of 9 and also which multiple of 9 it is.
    30+3 = 33
    33 - (6) = 27

    Right?
    Posted on the TSR App. Download from Apple or Google Play
    Offline

    10
    ReputationRep:
    (Original post by manny103)
    30+3 = 33
    33 - (6) = 27

    Right?
    Yes, that is correct, but can you finish this 10a+b-(a+b)=... ?
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by BuryMathsTutor)
    Yes, that is correct, but can you finish this 10a+b-(a+b)=... ?
    A=3 b= 3

    30+3-(a+b) = 33-a-b = 27

    Same thing?
    Posted on the TSR App. Download from Apple or Google Play
    Offline

    10
    ReputationRep:
    (Original post by manny103)
    A=3 b= 3

    30+3-(a+b) = 33-a-b = 27

    Same thing?
    Try it again but don't replace a and b with specific values.
    • Thread Starter
    Offline

    8
    ReputationRep:
    (Original post by BuryMathsTutor)
    Try it again but don't replace a and b with specific values.
    10a+b-a-b=....
    10a-a=....
    10a=....+a
    Posted on the TSR App. Download from Apple or Google Play
    Offline

    10
    ReputationRep:
    (Original post by manny103)
    10a+b-a-b=....
    10a-a=....
    10a=....+a
    You're OK as far as 10a-a.

    Just simplify that a little more.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: February 20, 2018
Poll
Do you agree with the proposed ban on plastic straws and cotton buds?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.