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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.

Rosie O'Hara says:
14 March 2013

Without the basics of mental maths we are stuck, I was stuck for many years, I had some incredibly good strategies to get round what I couldn’t do.
I’m currently researching how people do mental maths to produce an NLP Model to teach children effectively. I now know the basics and I used those to do the sum above correctly 12 years agao i could not have done that (I possess a free bus pass now by the way)

If you have any good tips, please share. I think the Trachtenberg system is interesting. Anyone else use it? http://en.wikipedia.org/wiki/Trachtenberg_system

Ian Addison says:
19 March 2013

There used to be a thing called arithmetic which was seen as separate from mathematics but everyone knew it was a required basic grounding. Its focus was the use of “arithmetic ” in every day uses. Adding up bills, calculating how much paint, distance , miles per hour , sailing times, bank interest compound and simple, stocks and shares, currency exchange. It even had its own higher (yes I am Scottish). This concept seems to have disappeared. I think it is a great pity as folks seem to only talk about mathematics and that puts folk off (oh I like mathematics ) and I can understand why.

Ian Addison says:
19 March 2013

oops i meant “o” level

Rosie O'Hara says:
19 March 2013

It’s called Maths or Mathematics at school at all levels in Scotland, which is the area in which are located and working predominantly.
(It was arithmetic in my day – I still couldn’t do it.)

Clint Kirk says:
21 March 2013

How many of you answered by first working out the exact answer and then looking for it among the choices? I just looked at the numbers, realised they are both approximately 30, so the answer must be around 900, then looked at the choices. There were two possibilities. Since 2×7=14, I chose the one that ended with a 4. Is that cheating?

Without any, even basic mental arithmetic skills, many people would even struggle to do that. And yes 2 x 7 ends in 4 so that leaves just 2 possible answers. Nothing wrong with that, its still mental arithmetic 🙂

The easiest way is to look for the ones ending in a 4. I think that’s why 764 is in second place.

This shows the dubious value of multiple-choice answers. It isn’t mental arithmetic to decide it ends in 4, and therefore you can choose between two answers – that is more logic. Mental arithmetic is working the answer out without any clues.

I agree, Malcolm. It would be better if the we could type in our answer and be told whether it is right or wrong, plus the percentage of correct answers submitted. Even if the website was capable of doing this, some people would cheat and use a calculator.

Maybe even enter your answer, then enter your method of calculating it, mental, calculator, spreadsheet, smart phone etc, to see how many people who use gadgets still get the answer wrong.

I’m afraid that’s beyond the capabilities of our poll… but how about a new question.

Without using a calculator, what is 1782 / 321? (Round answers to the nearest integer and explain your method of calculating)


Oh sorry, 321 + 321 = 642 double that 1284 add 321 = 1605 ; So that’s 5 times and still a bit more to go

1782 – 1605 = 177, which is more than half 321 hence 6

6 rounding up. 5 x 321=1605. 1782-1605=177 – more than 1/2 of 321 so nearer 6.

I calculated 5 x 321 and 6 x 321 and wrote down the answers: 1605 and 1926, respectively. The latter is closer to 1782, so the answer is 6.

Well done all. Interesting to see the slightly difference methods.

Next question: (256 x 16)/4

1024. It’s just 256 x 4. Double 256 twice gives 1024.

Sorry, too easy. Why don’t you give a sum Wavechange?

Next time I go shopping I will look for a real example of the need to do mental arithmetic to compare unit price of individual items and multi-buys.

franjam says:
29 March 2013


6 is closest to 1782 Qed.

franjam, it hasn’t taken you 8 days to do this, has it? (Just teasing!)

The ability to do mental arithmetic decreased soon after calculators became popular but we all had to be able to check our change until tills that showed the amount due became universal. I expect every dart player can subtract numbers from 301 without thinking about it. Working with numbers frequently certainly helps to learn mental arithmetic, become confident and use short cuts such as the one Clint suggested. (Yes, I did this too.)

Though I’m glad that I learned mental arithmetic, the world has moved on and young people have different skills.

Having watched many people playing Tetris, Angry Birds and the like on their phones, I wonder if there is an opportunity to develop game apps that could help people learn and improve their abilities at mental arithmetic. It would have to be compulsive, with enough opportunity for development to ensure that it would remain popular for years.

I think there are quite a few mental arithmetic games on phones.

I am not surprised, but what’s needed is a game that becomes compulsive and that this type of game remains popular over a long period. Until then, phones have calculators. 🙁

1024. 16/4 = 4 x 256.

At Junior School during the war we had regular mental arithmetic tests, often several times a day. The discipline stays with one and I would feel somehow incomplete without the ability to make mental calculations. As mentioned by another correspondent, when using slide rules it was essential to be able to make a simple estimate of the result and I now do the same thing when using a calculator to make sure that I haven’t fed in the wrong number at some point. My mental arithmetic capabilities, though, were greatly exceeded by my mother’s. She could just run her finger down a list of prices in £sd and write down the total, and get it right every time!

Rosie O'Hara says:
22 March 2013

We are currently modelling mental arithmetic skills and games apps etc. won’t in our experience help, we are pretty sure we know how it works, are however looking for some more people to model – if you live in Scotland, near Inverness or in Moray or Aberdeen or Dundee, please contact me, I need to ask you twelve simple arithmetic questions face to face and to video you (for research purposes only). Please help we are a Social Enterprise working on learning skills.