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[Guest]

It was a long time ago Dave but I think that we were always taught to bracket the first calculation.

Laurie

[colin m]

Sorry Colin. Misread your reply so didn't answer.There are two ways of doing this calculation. Either do the addition first to get two plus two (equals four) then divide by two to get the answer two.

Or you could do the division first to get two divided by two (equals one) plus two to get three.

The guys have mentioned BODMAS. This is/was a mathematical convention used to define the order in which multiple calculations should be carried out. This ensured that, at least in theory, when you wrote a multiple calculation, the rule made you write it in a specific order to ensure that it gave the result you wanted. It also made sure that anyone else would use the same rule to work it out.

Nowadays though, ALL simple calculators, and the calculators on SOME mobile phones - but not all - use sequential calculations; ie they do the calculation in the order it is written. But ALL scientific calculators and SOME mobile phones - but not all - use the old BODMAS rule. All this makes life very confusing for kids trying to learn maths today.

A couple of examples I use with my students:

Example 1

You want to buy an identity bracelet. The jeweller has quoted £50 for the bracelet and £2 per letter for the engraving. If you want the name DAVID engraved, how much will the bracelet cost?

Scientific calculator (BODMAS)

Cost of brace let = £50 + £2 × 5 = £60 Correct!

Normal cheap calculator

Cost of bracelet = £50 + £2 × 5 = £260 Wrong!

Example 2

You play for a local darts team which has just come third in the league. Your team receives £200 in prize money from the league and during the year you have collected £300 from selling raffle tickets. If there are 10 members on the team, how much should each receive?

Scientific calculator (BODMAS)

Amount received = £200 + £300 ÷ 10 = £230 Wrong!

Normal cheap calculator

Amount received = £200 + £300 ÷ 10 = £50 Correct!

It doesn't matter what rule you pick - BODMAS or Sequential - as long as you follow it and use it correctly. Where everything breaks down of course is when different people use different rules.

And here was you thinking how much easier it is for kids to do maths today than it was for you! You didn't have all these new-fangled gadgets like calculators and computers to do all the work for you!

Gern

Brilliant Dave.

I asked my wife and two daughters if they have heard of BODMAS, and they have. I wonder if I was off on BODMAS day ? Anyway, thanks for the detailed explanation. Whilst I might have missed BODMAS, I do remember a lecturer drumming into us that we should always estimate the answer before calculating it, I can see he had a good point !

Colin M..

[Gern]

There's all sorts of ways to sort this type of problem Laurie. Alas, simply adding brackets doesn't always work. (Adding brackets to the calculations above as you suggest would give the wrong answer to example 1 and the correct answer to example 2 - whichever type of calculator you used!).

At the levels I have to teach maths, I reckon the simplest answer for my students is to do the calculations separately. That way no-one has to worry about which way round to do the calculations or which way round their calculating machine does them.

Anyway, interesting as this is to me an' thee, I can see everybody else's eyes glazing over as they fall asleep! That's a symptom I recognise quite easily as I see it in my classrooms every day!

Gern

[Guest]

Adding brackets will ALWAYS work- so long as you put the brackets in the right place. For the first example you put them round the lsat 2 terms ie

£50 + (£2 × 5)

for the second you put them round the first two terms

(£200 + £300) ÷ 10

its BODMAS that isn't perfect, not the brackets rule. You still need to understand the logic of the problem or question to formulate the solution and that is why you create the equation BEFORE putting it into the calculator.

I spent 10 years helping scientists write software and they were crap at it for this type of reason I've got a scientific background too (Degree in Astrophysics) but spent more time programming so learned how to convert scientific formula into code that produces the right answers and it all comes down to analysing the problem rather than applying rules.

[Guest]

Think Dave that my era was different from the era I was quoting from.

We that far back only had primitive adding machines. They actually added up as they went along. This type still do.

They are reasonably reliable. They are a hands off version (ie no hands needed to use) very forward in their thinking. High memory & able to reverse & redo calculations at the drop of a hat. They come with a high imagination value but some times can be slow & reluctant.

At that time we were all given a brand new working one at a very early age. In fact it was some time before I realised I actually had one. I have made fair use of it & even though now old warn & battered my Cranium Mk1 still serves me pretty well !

Present day students seemed to have virtually binned it opting for the glossy smart looking inhuman types. But they can also it seems give the wrong answer.

Matter of interest I now think that our maths teacher must have bracketed the first calculation to get us to understand the maths logic. The problem with brackets is they do work as Andrew has said. But if you rely on brackets you are going to be in a real mess if someone presents you with a mathematical problem without the brackets.

Anecdote at the time of adding machines joining the market. Client receives from us building costs. He wishes to multiply a figure by 100. Grabs this new machine. Dibbs in 1, then crashes his finger on the nought, extended hesitation, then I realised he was looking for the second nought on the pad.

Moral. He was a grocer, once, at the above time he was a multimillionaire owner a chain of supermarkets. Used the old Cranium Mk1 efficiently.

Laurie

PS hope the spelling is OK !

[Gern]

Apologies folks! Andrew is correct. Brackets will always work if they're in the right place. I should have made my post a little clearer by saying that automatically bracketing the first two terms won't always work.

Getting the students to understand the logic behind the mathematics can be VERY hard with the calibre of students I have. That's why I get them to split the calculations up.

Gern

[Ian M]

So if I have understood all this maths 'mumbo jumbo' correctly, when I work out my wages and other income I am to use a Scientific calculator. When I do my taxes and other expenses I use the normal one.

Brilliant.

Unfortunately it would seem that the tax office have got it the other way around!

Ian M