28 February 2012

Does 6/2x(1+2) = 1 or 9?

A popular journalist on consumer financial matters, Martin Lewis, tweeted this question today and for several hours my Twitter timeline was inundated with argument about whether 6/2x(1+2) equalled 1 or 9. There were professors, teachers, students and the whole range of responses. Some had done calculations on their phones, others on calculators, some had used Excel or programme scripts. Many just worked it out in their heads.

Everyone in the 1 camp was quite convinced they were correct. As, of course, were the 9 camp. I have to admit to being in the 9 camp too, on the basis of BODMAS. Bodmas is what I was taught at school as the order in which we should do calculations: first calculate whatever's in the Brackets, then any 'Of' calculation which, confusingly seems the same as multiplication but not the M of Multiplication which comes after Division, finishing up with Addition and Subtraction (unless of course they're in the brackets!!).

So, doing the (1+2) gives you 3 and it's re-written 6/2x3. Then you do 6/2 which is also 3. Finally 3x3 gives you the majority view of the 9 camp.

The point of this short article is really just to say that I think it is simply lazy to write such an expression in the first place. It is bound to cause confusion - it isn't clear what you're talking about and, witness very respectable programmes and top end calculator results, it will produce different results on different programmes or machines and so is not suitable as an expression in the first place.

In the real world, the expression 6/2x(1+2) will be based on some actual activity. It could be that I have six kids and need to know how many fruit in total the girls have. Half of my kids are girls and each has 1 orange and 2 apples. Clearly the answer to that is 9. I have three girls (6/2) and each has (2+1) items of fruit.

On the other hand I may have six peaches and want to share them with two groups of kids, each group having one girl and two boys? Answer 1 each. Obvious really.

In each case I would never have dreamed of leaving the calculation down to chance. In the first case I would have written (6/2)x(1+2) and in the second 6/(2x(1+2)).

Then I could have been confident that everyone understood the question and could achieve the same and desired result. And I wouldn't have a day filled with beeps from new tweets every few minutes.

By the way Martin Lewis is well worth following if you're interested in money saving matters. You'll find him at @MartinSLewis. I'm @Kirrisdad and a money spending expert.

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