1

This is my fist post on Mathematics, so I hope my question isn't too trivial - you won't need a degree to answer this one! - but it's messing with my head....

Allow me to explain.....

I'm helping my daughter prepare for her Eleven Plus exam in the UK and as a maths lover myself, I've been enjoying setting her written questions that require some thought in order to write them in an algebraic form and find the solution.

Years ago, I demonstrated negative numbers to her, using pocket money as an example. Every Friday she gets £5 and if she's been good and wants something before Friday, then I will advance her the £5, or however much.

She understood the concept of negative numbers in this way - if she was advanced £10, it would take her two pocket money payments to repay the amount she owed:

-£10 + £5 + £5 = 0. Simple hey!?

So, I've told her that if she does a chore around the house, such as washing the car, I will take an amount off her debt (£3), but if she's naughty, she will get 50 pence (-£0.50) added to the amount she owes me.

When I decided to be clever (clearly not) and set an example question about this, I got into a pickle.

She currently owes me £10 and from her previous lessons from me, knows that her pocket money could be said to stand at -£10.

When calculating how much pocket money she'd owe if she was naughty 5 times (a minus £2.50 charge!), she has baffled me with the following:

(-£10.00) + (-£2.50) = -£7.50

~ she has a charge of -£2.50 added (+) to her debt ~

She has deduced that because -£2.50 will be added to her pocket money debt, she will actually be better off = being naughty is profitable!

Conversely, washing the car will take away from her debt by £3.00. Therefore:

(-£10.00) - (+£3.00) = -£13.00

Therefore: Being helpful is not profitable!

~ I'm going to give her £3 (+) to take off her debt (-) ~

Doh!

Now, humour me please, as I know my error is extremely basic and as soon as someone answers I will face-palm, but regardless, I cannot find a way to verbally explain how taking amounts away and adding amounts to her pocket money debt, can literally be applied in this way; especially as she's now being pedantic!

  • @MorganRodgers - I'd really love to claim that as a deliberate mistake. Her net worth is -10. I can't agree that it's +10 unless you are verbally explaining it as such. –  Feb 12 '16 at 21:33
  • 3
    @brandall Debt is the opposite of worth. If she has net worth $-10$ pounds, she's in debt by $10$ pounds. The very fact that we have words like "debt" is because people in general were never as comfortable with negative numbers as with positive numbers, so we say things like "I will debit your account $10$ pounds" when we mean "I will credit your account $-10$ pounds." – David K Feb 12 '16 at 21:37
  • 1
    @MorganRodgers Just to be pedantic: That is not euros, but pound :) – Bobson Dugnutt Feb 12 '16 at 21:42
  • @Lovsovs ha! She pointed that out! I understand your comments David, but the point is to start from a negative 10, as suggested with the number line below. If I change her 'debt' to +10, she's simply going to ask me to hand it over now! –  Feb 12 '16 at 21:45
  • Thanks @MorganRodgers If I start with +10 then it does make the maths work. I will sleep and see clearly tomorrow no doubt... –  Feb 12 '16 at 22:02

1 Answers1

2

$(-£10.00) + (-£2.50)$ is not equal to $-£7.50$ (it's equal to $-£12.50)$.

And although $$(-£10.00) - (+£3.00) = -£13.00$$ is technically correct, you shouldn't subtract the $£3$, but add it, giving a money balance of $(-£10.00) + (+£3.00) = -£7.00$, which is what you'd expect if she was being rewarded.

If it helps, draw the number line (for instance from $-15$ to $15$) and go right when you add and left when you subtract.

Bobson Dugnutt
  • 10,672
  • Thanks for your answer and spotting the painful mistake. If I apply your logic for the second part, to the first then I would have to subtract +£2.50. and she would be worse off, which is right. However, telling her I'm going to add money to her debt doesn't sound verbally correct or suggest she will be rewarded. –  Feb 12 '16 at 21:36
  • Adding to her debt when she misbehaves is (mathematically) correct, i.e. her debt increases... if she doesn't understand that this is negative, tell her what debt is (the amount you owe) - it's a good lesson to learn! – Bobson Dugnutt Feb 12 '16 at 21:39
  • Your second part says to add to her debt when she washes the car = behaves? 'you shouldn't subtract the £3, but add it' ? –  Feb 12 '16 at 21:41
  • @brandall I'm not adding to ther debt, but to her money. Debt is the negative of money (think about having £10 in debt vs. having £10). – Bobson Dugnutt Feb 12 '16 at 21:43
  • "Debt is the negative of money" <-- It sounds profound! I'm going to sleep on this. I'll return in the morning, face-palm and mark your answer as correct. Thanks. –  Feb 12 '16 at 21:47
  • @brandall Sleeping is always the solution! Glad I could help! – Bobson Dugnutt Feb 12 '16 at 21:48