Subtraction

[Kassee]

How do kids learn to subtract nowadays. Say take 600 - 426 = ?
When I was at school you added 10 to the top and one to the bottom (I still do today) but my granddaughter is having none of it. But cant remember how she was taught to do it. Just started senior school. Thanks.

[Old_Geezer]

Obviously it's the same thing Chris, but in my view a more complicated rule.

Borrowing doesn't really make anything bigger. One used a ×10 digit and later found a way to compensate. No rearranging needed.

That said in real life I'd tend to work right to left in my head simply checking as I go whether I need to subtract a further 1 because it'd be needed by less significant columns.

[jim360]

I think you're kidding yourself Murdo if you believe that everyone (or even most people) could do simple arithmetic back then. I wouldn't care to say if it's better or worse now, but we do have a very selective memory about these things and about education standards (which are, anyway, far more variable than people make out even for themselves).

Since there is only ever one right *answer* to subtraction, the method you use to get there can be whatever you like. The modern teaching method embraces this perhaps a little too freely -- I'd prefer that one method be taught, and others used only if it's seen that some kids are struggling with the first one.

[Jackdaw33]

@divebuddy

In the days before electronic tills that's how shop assistants worked. They calculated the change by counting up from the price to the amount you had given them. If you bought something for 1/11 and handed over 2/6 they would say,"1/11, a penny's 2/- and sixpence is half a crown".

[woofgang]

well but there are different ways of tying a tie and tying shoe laces......method isn’t irrelevant. My dh and I were at primary school 50 years ago and he was taught the pay it back method and I was taught the borrowing method...if you are trying to help a child, you need to know what method they were taught to use.

[jim360]

Well yes, up to the fact that you should be able to explain your method. I don't think it's necessarily a problem that children are taught different methods from their parents, but communication between parent and school (and between teacher and pupils) could be clearer.

[Buenchico]

>>> I think you're kidding yourself Murdo if you believe that everyone (or even most people) could do simple arithmetic back then

Murdo's probably also kidding himself if he believes that most people nowadays can use Google. Based upon the number of questions here which I can answer in seconds by using Google properly (when the questioner says "I've been googling for hours"), I suspect that most people haven't got a clue about how to use Google!

[jim360]

Yeah... that's called selective memory.

I would suggest that mental arithmetic these days is probably a little more noticeable if it's poor, rather than poorer absolutely. In the days when using a calculator itself was a highly non-trivial skill, those people who couldn't cope with mental maths wouldn't last long in any job that demanded it of them. Now you can "get away with it" a lot more, for sure, because mental arithmetic is increasingly a redundant skill. I do actually think that's sad, and I pride myself on my own, but on balance a world in which I don't have to waste so much time on trivial calculations I can hand to a computer is a world in which I can get a lot more useful work done (in theory, at least...)

[weecalf]

600 is the big number so if 426 is the wee number the the difference is the big number less the wee number or what would I have to add to the wee number to make the big number simple

[Marshwarble]

It's not symptomatic of the modern age that we have a new form of subtraction per se. Maths changes all the time, Fermat's Last Theory has only just been solved. Was that completed because it's "the modern age"?

[Buenchico]

^^^ Pierre de Fermat's own proof of his last theorem is yet to be found; it remains the Holy Grail of mathematics.

While 'proof by exhaustion' is a valid mathematical technique, it lacks 'elegance' (which mathematicians should always seek after) when it involves thousands of hours of computer time.

[wolf63]

I have no idea how I was taught this at school in the 70s but I calculated benefit payments of different types using my fingers and/or my trusty calculator.

[Jackdaw33]

Subtraction never really bothered me. What I hated was long division, not that I couldn't do it but found it so tedious. Pre-calculator days, my book of log tables &c was a boon.

[Buenchico]

^^^ Life got even better, JD33, when we advanced to using (mega-expensive) slide rules ;-)

[Jackdaw33]

Slide rules were strictly forbidden at my school unless one was in 6th form science. As I was arts I was never taught how to use one and wouldn't have a clue today. Fortunately they are now redundant.

[jim360]

Yeah, it [as in Fermat's proof] probably doesn't exist. His margin comment sounds too much like an excited graduate student!

It's not really a "new form of subtraction". Every form of subtraction, ever, works with the principle of trying to take single digits away from single digits when it gives a non-negative number, and adding and subtracting ten if it does not. The only difference between the methods is where you put the ten, and how many intermediate scribblings you allow along the way.

In that sense, it's frustrating to hear that so many parents are left flummoxed by modern methods. I suspect that this means such parents didn't really understand the one they were taught either, although they may have been able to use it all the same. But the point is that once you know one method, you can in principle deduce how any other method of subtraction works.

[Buenchico]

>>> Yeah, it [as in Fermat's proof] probably doesn't exist.

Oh, please, don't say that, Jim. I'd like to think that one day all my thousands pages of scribblings on the subject might yet yield something of value!

[tonyav]

What I hated was long division, not that I couldn't do it but found it so tedious.

Ahhhggg, same here, jd.

[jim360]

Well, you certainly could get a few fires going.