3 ms·

Do people just memorise their times tables up to 100? Is that what it takes?

ColinWright 5y ago
It's a sense of what numbers are. As a decimal, 1/6 is 0.1666.., so that will mean that 6 times 16 is around 100. How many seconds in a day? It's 60 times 60 times 24, but 24 is around 25, which is 100/4. So it's 60 times 15 times 100, and 6 times 15 is about 6 times 16, which is 100, so it's 10 times 100 times 100, which is 100,000. But that's too big by about 4% (because we used 25 instead of 24) and another 6% or 7% (from using 16 instead of 15) so it's about 11% smaller. So seconds in a day is about 88,000. All small numbers, few facts, but being comfortable in using them quickly with a side order of sanity checking.
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tombert 5y ago
I can't speak for anyone else, but for my mental math (which admittedly is only so-so, not spectacular), I make pretty liberal use of factoring. Want to multiply a number by 15? Multiply it by ten, then multiply it by five, and add them together. Usually that's good enough to get me a rough number, if I need a precise number I whip out my phone.
- ColinWright 5y ago
  Or if you want to multiply by 15, multiply by ten, then add on half again. So 34 times 15 is 340 plus half of 340, which is 170, so the answer is around 500 (actually 510). But if you want 34 (specifically) times 15 there are other ways to go. Or (34 times 15) is (17 times 30). Six times 16 is around 100, so three times 15 will be half that, or around 50. So 34 times 15 is around 500. Or 34 is about 100/3, so multiply that by 15 is 100/3 times 15, which is 100 times 15/3, which is about 500. Being good at mental arithmetic and estimation isn't about being able to do sums quickly and accurately, it's about being happy with rough calculations, retaining a sense of how accurate you are so you can fix it later (if necessary).
  - jonsen 5y ago
    > So 34 times 15 is ... We who knows our powers of two do 34 ~= 2^5 15 ~= 2^4 2^5 * 2^4 = 2^9 = 512
    - tombert 5y ago
      I'm embarrassed to admit that I know my powers of two pretty well, and I didn't even think of this trick.
shadowofneptune 5y ago
Memorizing the tables past 12 is something stressed in older education, but isn't necessary. It really comes down to knowing strategies to simplify the calculation. If you can round the operands to a more easily used number, say 23 becomes 22 or 20, it's much simpler to do the mental math.
chousuke 5y ago
Do people actually do that? I never bothered and made up my own method instead. 10x is trivial. 9x is 10x - x, which is also trivial. 5x is also trivial because it's 10x / 2. For the rest I just memorized whatever stuck the easiest and calculate the rest. For example, 7*4 is not automatic for me but it becomes 7*2*2 which is easy.

It's a sense of what numbers are. As a decimal, 1/6 is 0.1666.., so that will mean that 6 times 16 is around 100. How many seconds in a day? It's 60 times 60 times 24, but 24 is around 25, which is 100/4. So it's 60 times 15 times 100, and 6 times 15 is about 6 times 16, which is 100, so it's 10 times 100 times 100, which is 100,000. But that's too big by about 4% (because we used 25 instead of 24) and another 6% or 7% (from using 16 instead of 15) so it's about 11% smaller. So seconds in a day is about 88,000. All small numbers, few facts, but being comfortable in using them quickly with a side order of sanity checking.

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tombert 5y ago

I can't speak for anyone else, but for my mental math (which admittedly is only so-so, not spectacular), I make pretty liberal use of factoring. Want to multiply a number by 15? Multiply it by ten, then multiply it by five, and add them together. Usually that's good enough to get me a rough number, if I need a precise number I whip out my phone.

ColinWright 5y ago
Or if you want to multiply by 15, multiply by ten, then add on half again. So 34 times 15 is 340 plus half of 340, which is 170, so the answer is around 500 (actually 510). But if you want 34 (specifically) times 15 there are other ways to go. Or (34 times 15) is (17 times 30). Six times 16 is around 100, so three times 15 will be half that, or around 50. So 34 times 15 is around 500. Or 34 is about 100/3, so multiply that by 15 is 100/3 times 15, which is 100 times 15/3, which is about 500. Being good at mental arithmetic and estimation isn't about being able to do sums quickly and accurately, it's about being happy with rough calculations, retaining a sense of how accurate you are so you can fix it later (if necessary).
- jonsen 5y ago
  > So 34 times 15 is ... We who knows our powers of two do 34 ~= 2^5 15 ~= 2^4 2^5 * 2^4 = 2^9 = 512
  - tombert 5y ago
    I'm embarrassed to admit that I know my powers of two pretty well, and I didn't even think of this trick.

shadowofneptune 5y ago

Memorizing the tables past 12 is something stressed in older education, but isn't necessary. It really comes down to knowing strategies to simplify the calculation. If you can round the operands to a more easily used number, say 23 becomes 22 or 20, it's much simpler to do the mental math.

chousuke 5y ago

Do people actually do that? I never bothered and made up my own method instead. 10x is trivial. 9x is 10x - x, which is also trivial. 5x is also trivial because it's 10x / 2. For the rest I just memorized whatever stuck the easiest and calculate the rest. For example, 7*4 is not automatic for me but it becomes 7*2*2 which is easy.