4 ms·

12x12 is the max for most memorized multiplication tables (at least in the US). 16x18 is going to require some actual mental work that is prone to errors.

by hueving 11y ago

kqr 11y ago
For computer people, 16×18 is easily split into 16×20 - 16×2, which in turn is 320 - 32. If you don't know instinctively that 16×2 is 32 it might be a bit harder though.
- Cyph0n 11y ago
  Or a better way for us programmers: 16 * 16 = 256 16 * 2 = 32 256+32 = 288
  - cozzyd 11y ago
    Even better: 16 * 18 = (17-1)*(17+1) = 17^2-1 = 289-1 = 288. Provided of course you know your squares.
    - Cyph0n 11y ago
      Ah that's a good one. I had powers of 2 in mind.
Cyph0n 11y ago
See my edit. The basic tables are all you need.
Someone 11y ago
16x18 = 17x17 - 1 = 289 - 1 = 288 Te squares up to 20x20 everybody should know by head. The only problem is that answer. Seeing 288 (2x12^2) immediately made me spend time double-checking the factors in the multiplicands.
- Joof 11y ago
  Out of curiosity, in what situations does knowing the squares benefit someone later in mathematics / life? Actually curious.
  - Someone 11y ago
    Short version: it is fun. If you do mental math, it makes exercises way more fun if you know more interesting numbers. The 16x18 example is an example. For another example, consider 42x49 When primed by 16x18, one might consider writing it as (45-3)x((45+3)+1) = 45^2-3^2 + 42 = 2025 - 9 + 42 = 2058 (This works for many pairs of numbers that are relatively close together, only requires one 'large' multiplication, and that one is simple, as stated in the article) But of course, half-way through, one may realize it is 6x7 x 7x7 = 7^4 - 7^3 Now, 7^3 = 343 (easy to remember in combination with 3^5 = 243), but 7^4 = 2401, for me, doesn't pop out (when you say 2401, I know it's 7^4, but not vice versa) Meanwhile 49 is close to 50, so we have 42x50 - 42 = 2100 - 42 = 2058 That is faster, but somewhat dull. Meanwhile, as far as we know, the savant calculator just takes the dull road, adding 40x40, 40x(2+9), and 2x9, doesn't get distracted, and produces the right answer in a tenth of the time I take. He has less fun, though, because I take detours to visit tourist attractions. It also can make taxi rides more fun.
  - deleted 11y ago
    [deleted]

12x12 is the max for most memorized multiplication tables (at least in the US). 16x18 is going to require some actual mental work that is prone to errors.

by hueving 11y ago

12x12 is the max for most memorized multiplication tables (at least in the US). 16x18 is going to require some actual mental work that is prone to errors.

kqr 11y ago

For computer people, 16×18 is easily split into 16×20 - 16×2, which in turn is 320 - 32. If you don't know instinctively that 16×2 is 32 it might be a bit harder though.

Cyph0n 11y ago
Or a better way for us programmers: 16 * 16 = 256 16 * 2 = 32 256+32 = 288
- cozzyd 11y ago
  Even better: 16 * 18 = (17-1)*(17+1) = 17^2-1 = 289-1 = 288. Provided of course you know your squares.
  - Cyph0n 11y ago
    Ah that's a good one. I had powers of 2 in mind.

Cyph0n 11y ago

See my edit. The basic tables are all you need.

Someone 11y ago

16x18 = 17x17 - 1 = 289 - 1 = 288 Te squares up to 20x20 everybody should know by head. The only problem is that answer. Seeing 288 (2x12^2) immediately made me spend time double-checking the factors in the multiplicands.

Joof 11y ago
Out of curiosity, in what situations does knowing the squares benefit someone later in mathematics / life? Actually curious.
- Someone 11y ago
  Short version: it is fun. If you do mental math, it makes exercises way more fun if you know more interesting numbers. The 16x18 example is an example. For another example, consider 42x49 When primed by 16x18, one might consider writing it as (45-3)x((45+3)+1) = 45^2-3^2 + 42 = 2025 - 9 + 42 = 2058 (This works for many pairs of numbers that are relatively close together, only requires one 'large' multiplication, and that one is simple, as stated in the article) But of course, half-way through, one may realize it is 6x7 x 7x7 = 7^4 - 7^3 Now, 7^3 = 343 (easy to remember in combination with 3^5 = 243), but 7^4 = 2401, for me, doesn't pop out (when you say 2401, I know it's 7^4, but not vice versa) Meanwhile 49 is close to 50, so we have 42x50 - 42 = 2100 - 42 = 2058 That is faster, but somewhat dull. Meanwhile, as far as we know, the savant calculator just takes the dull road, adding 40x40, 40x(2+9), and 2x9, doesn't get distracted, and produces the right answer in a tenth of the time I take. He has less fun, though, because I take detours to visit tourist attractions. It also can make taxi rides more fun.
- deleted 11y ago
  [deleted]