Remedial maths for TheFrogger

Discussion in 'About the Members' started by TheFrogger, Oct 10, 2019 at 1:21 AM.

  1. TheFrogger Valued Senior Member

    Messages:
    1,911
    I had a similar conundrum, SpeakPigeon.

    Is the following correct to solve 24n?

    24n=24n
    n=24n÷24
    n=n÷24
    n÷n=24
    1=24

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  3. James R Just this guy, you know? Staff Member

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    33,248
    Last step doesn't follow from the previous one, unless n=0. Do you know how to do algebra?
     
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  5. TheFrogger Valued Senior Member

    Messages:
    1,911
    JamesR...

    n=24n÷24
    n=(24÷24)(n÷24)
    n=1(n÷24)
    n=n÷24
    n÷n=24
    1=24

    ???
     
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  7. James R Just this guy, you know? Staff Member

    Messages:
    33,248
    Second step doesn't follow from the first, unless n=0, again. How did you get through maths at school? Or are you, perhaps, still at school and just learning this stuff now?
     
  8. TheFrogger Valued Senior Member

    Messages:
    1,911
    I thought you do the same to each number (divide by twenty-four?) Therefore...

    n=(24÷24)(n÷24)

    Help please.

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  9. James R Just this guy, you know? Staff Member

    Messages:
    33,248
    That's the problem. You didn't do the same thing to the left-hand side of your equation that you did to the right.

    Hope this helps you!

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  10. TheFrogger Valued Senior Member

    Messages:
    1,911
    Thanks JamesR. But I thought you could simply MOVE a number to the other side, and switch the operator?
     
  11. billvon Valued Senior Member

    Messages:
    16,331
    Heck no. You can add or subtract the same number from both sides, and you can divide or multiply the entire equation by some number, but you can't just "simply move a number and switch the operator."

    Here's how to do it right:

    24n=24n
    n=24n/24
    n=n
     
  12. James R Just this guy, you know? Staff Member

    Messages:
    33,248
    Suppose you have

    $24n = x$

    Then, you can move the 24 to the other side and switch the operator, if you want to think of it that way. The 24 multiplies n, so move it to the other side and it now divides x, like so:

    $n=x/24$
    As a rule of thumb, it's okay to think of it that way, but when you're first starting with this stuff, it's better to think about doing the same operation on both sides of the "=" sign:

    $24n=x$

    Divide both sides by 24:

    $\frac{24n}{24}=\frac{x}{24}$

    Then notice on the left-hand side that 24/24=1:

    $n=\frac{x}{24}$

    This kind of thing applies to any operation. For example, add 3 to both sides:

    $n+3=\frac{x}{24}+3$

    Take the natural logarithm of both sides:

    $\ln (n+3)=\ln \left(\frac{x}{24}+3\right)$

    etc. etc.

    Didn't they teach this properly at your school?
     
    Last edited: Oct 11, 2019 at 2:29 AM
  13. James R Just this guy, you know? Staff Member

    Messages:
    33,248
    TheFrogger:

    So, with all that in mind, you should now understand what you did wrong here:

    So, start with

    $n=n$

    Multiply both sides by 1:

    $1n=1n$

    Recognise that $1=24/24$ and use that to replace that 1 on the right-hand side:

    $1n=\frac{24}{24}n$ ... (*)

    This is the same as your $n=24n \div 24$. But then look at your next step:

    $n=(24 \div 24)(n \div 24)$

    which is the same as

    $n = \frac{24}{24}\frac{n}{24}$

    But what operation did you use on the equation (*), above to get to this? For instance, if we take (*) and divide both sides by 24 we get:

    $\frac{n}{24}=\frac{24}{24}\frac{n}{24}$

    which has $n/24$ on the left-hand side, whereas you had just $n$.

    Once you made that error, the rest of the working was worthless, because you no longer have equality between the left and right sides of the equation.

    Hope this helps!
     
    Last edited: Oct 11, 2019 at 2:35 AM

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