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Does mental arithmetic add up in a world of calculators?


I doubt many people share my sustained enthusiasm for mathematics, and a new survey from BAE Systems confirms this. It seems many people can’t live without a calculator – can you?

I’m probably in the minority when I say I loved maths at school. I liked nothing more than hunkering down to do quadratic equations, and at one point I had Pi memorised to 24 decimal places.I also adored my maths teacher, Miss Edmunds, to whom I used to sing the Neighbours theme tune, swapping in her surname for the name of the show.

BAE’s poll of 2,016 adults found that one in four people said maths was their least favourite lesson, while 30% said they found the subject ‘uninspiring’. Clearly, they didn’t have a Miss Edmunds guiding them through the hazy world of simultaneous equations and trigonometry.

Sum of us need calculators

Is this lack of love for figures creating a world in which people are non-plussed by numbers without the aid of a calculator? The BAE poll found that, despite one in four needing to do some form of maths every day in their jobs, when it comes to multiplying big numbers together, we just can’t seem to manage it with a piece of paper and a pen.

The people that BAE polled were asked to carry out a series of multiplication tests, with the 11 times table proving the trickiest to master, with one in five making basic errors. This is particularly worrying given that, visually, the 11 times table is one of the easiest to remember.

And it doesn’t take much to get people clambering for the calculator if confronted by big numbers. Some 2% said they needed to use a calculator to work out all sums involving numbers bigger than 10, 3% for numbers over 20 and 13% for numbers higher than 100.

The cushion of the calculator

Are we a nation of numeric nitwits? Or does the cushion of the calculator, or the formula in a spreadsheet, make mental arithmetic a redundant exercise altogether? Given that we have technology constantly at our finger-tips, you could argue that it doesn’t really matter. But what if you’re put on the spot to make a big purchasing decision, or you’re buying a financial product? The ability to work out the big numbers could well see you bagging a better deal.

Hopefully this is something that the introduction of financial education will aim to address. By putting mathematics into a context that relates to the real world, pupils may well be able to see the benefit and ‘inspiration’ behind the subject. Here’s hoping that there’s an army of teachers like mine to help push maths into being a lesson to look forward to. All together now: ‘Edmunds, everybody needs Miss Edmunds…’

Without using a calculator, what does 27 x 32 equal?

864 (79%, 1,951 Votes)

764 (10%, 243 Votes)

867 (5%, 121 Votes)

648 (4%, 88 Votes)

I don't know (2%, 61 Votes)

Total Voters: 2,464

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You don’t even need a piece of paper and a pencil for that one! I often do the 13x and 14x tables upto nineteen [above that number I would probably split the multiplication and add the results], and sometimes I see how far I can get adding up three columns simultaneously and doing long division in my head. I usually add up the cost of purchases in a shop so that I can give the right money and I have a rather un-amusing tendency to say “Correct!” when the assistant tells me the total. I enjoy arithmetic but I am no mathemetician.Trigonometry defeated me and I never mastered the slide rule.


Without the ability to use your own grey matter, know can anyone be confident that they even typed in the numbers right ?

And as John described above I split the numbers multiply x 2 store, start again by multipling by 3 , multiply that by another 10 look at the answers, select one.


For me the simplest way of calculating 27 x 32 is to add together the products of 27 x 30 and 27 x 2.

I used to add up the price of my shopping, like John, when Tesco used to give vouchers if you spent more than a certain amount, though there was the cost of loose fruit & veg to be added when these were weighed at the till.

Using a slide rule was what gave me more confidence with numbers than anything else because it is necessary to do an approximate calculation to decide where to put the decimal point.

My first calculator was a Sinclair Cambridge, bought as a kit for £24.95 plus VAT. I used this a great deal when I was doing my PhD. The components had to be soldered to a circuit board. I still have the calculator and the stabilised power supply that I made to avoid the high cost of batteries. The calculator did not have a Pi key but the instructions said that Pi could be calculated by dividing 35500001 by 11300001. Useful but definitely not up to Gareth’s standard.

While working in university I tried to encourage undergraduate and postgraduate science students to handle numbers without using calculators but soon gave up and focused on helping them gain confidence with numbers with the aid of their calculator. At one time, many Greek students could do mental arithmetic and I was told that they were not allowed to use calculators at school.

I can’t say I enjoyed maths, though it is very handy to be able to do basic mental arithmetic.


You mean you can’t quote pi to a silly no. of dp from memory ? 3.1415926535 I used to be able to include 8979 on the end

And I can still roughly remember the square roots of 2 (1.41) and 3 (1.7) although not to the same number of dp I could do and 5 was just not even close. Why 30+ years on I can still remember them I’ll never know.

I used to write silly programs to run on things like ARPANET (if anyone can remember that) and was impressed when 1000! (I’d like to put 1000000! but I’m having a hard time believing that now) was computed in under 2 secs on one machine I found ( with all the digits). Don’t think I could manage to write that one know though.

I don’t use calculators anymore, I’ve moved onto spreadsheets, although I’m aware that some well known versions have got their sums wrong in the past.


Calculators were not allowed in school exams in my days.

I did and enjoyed maths up to A level and use quick maths
calculations all the time at supermarkets.

Try multiply 55 by 55 or 65 by 65 or indeed 95 by 95 that can
all be done instantly at one go w/out splitting anything.

Got it?


On that basis, Pi rounds to 3.1415926536 🙂

Like William, I can remember all sorts of numbers, including those that I used to use when I was at school and university. Log to the base 10 of 2 is 0.3010, log of 273 and 760 (STP temperature and pressure) are 2.4362 and 2.8808, and so on. Perhaps if my brain was not clogged with numbers and how to do calculations I might remember people’s names for more than five minutes. 🙁


I worked with someone who used his calculator all the time – even when dividing by 2 (that sticks in my mind). Mental arithmetic is a habit, and one well worth practising. Out shopping to decide the cheapest option, calculating quantities for decorating, measuring for carpets to get an idea of cost, estimating mpg (litres/100km if you’d rather) and lots of other examples where you wouldn’t have a calculator.
There are lots of short cuts we learned at school; I bet they don’t teach them now.


Those who don’t do mental arithmetic are likely to have a phone with a calculator – wherever they go. To start with, phone calculators were pathetic things that did not recognise algebraic priority but modern offerings are more sophisticated.