Where or how can I practice quick mental arithmetic?

Question

My maths is of an good standard, A at GCSE (uk exams at 16) but I find I still need to write down simple aritmetic on paper, before being able to work it out.

For example, questions I encounter day to day I cannot work out "on the spot mentally" or as quick as I would like, such as

Work out 8% of 17000.
The meal cost 0.97 for the drink and 1.85. I paid with £5, how much do I get back?
Quickly tell me what 15 multiplied by 12 is.


I can easily work these out given pen and paper quite quickly, but it's hopeless if Im not. However I notice a lot of people that didn't do that well at maths in exams, can work these sums out on the spot. What is their secret?

Is my brain wired differently?

Books or sites advice would be best.

Just to mention, I can also work out e.g. 12 mulitiplied by 15 if I just look at the numbers physically written like on this screen, since I can "see" the numbers written down, as if Im doing the calculation.

My problem is I cannot mentally work these sums out, if somebody asks me them without showing me a piece of paper etc.

Answer 1

Try and work in a decimal system, round up/down, or use bigger blocks of numbers you know, and then add/subtract as needed. (I hate math, so have had to hack out things on my own so I can function.)

For example "The meal cost 0.97 for the drink and 1.85" - instead of 0.97, use 1.00 to get 2.85, then subtract 0.03 to get back to 2.82. See?

Do it in multiple small steps you can handle - it goes very quickly, usually quicker than someone can key it into a calculator or cash register. So you hand them a fiver, and expect back (5-3)+0.18...or 2.18 (0.18 being the diff btwn 1.00 and 0.82). If you want to mess up the cashier, hand them 5.82 so you get back an even 3, or some variation on that, like 5.32 to get back 2.50 - the cashiers usually look pretty befuddled at all of this when they see the nice round numbers show up on their little displays after you handed them some odd assortment of bills and coins.

15 multiplied by 12
15 times 10 = 150
15 times 2 = 30
5 + 3 (or 50 + 30) = 8 (or 80)
So, it's 150 + 30 (5+3 = 8 with nothing carried over, so it's 180)

Work out 8% of 17000:
10% = 1700
5% = 850 (8 + 8 = 16, 5 + 5 = 10, 16 + 1 = 17)
1% = 170
7 x 3 = 21 (we're just multiplying the 7 of 170), so that's really 210
100 x 3 (the 100 part of 170) = 300
210 + that 300 = 510
850 + 510 = 1360
(OK, that's all kind of confusing,because that one's a bit complicated, but I hope you get the idea - break it down into small pieces that you're comfortable with. It's a little harder to explain it than to work it out.)

If you make a game of it, it gets to be a little easier.

Good luck, I fully empathize with you.

Answer 2

8% of 17,000 is 8 + 5.6 and add back the zeros so you have 13.6 or 1,360. I learned the zeros placement by learning a slide rule.
.97 + 1.85 is 2.85 less 3 cents or pence in your case. 2.82. Then .18 and 2.0 is 2.18. The dirrerence between 5 and 2.82.
85 x 85 is 9 x 8 = 7200 plus 25 = 7225.
84 x 84 = xsq (7225) -2x (85 x 2) +1

Answer 3

See if you can find a school or private teacher to teach you how to use an abacus. When you get good at it, you don't need the machine - just make a picture of it in your head. I had a business student in Japan who could do cube roots in his head by imagining his abacus!