5 ms·

Why 4x8 and 6x8 are, surprisingly, some of the hardest times tables to remember

17 points by JustinSkycak 2y ago

hffffauasddw 2y ago
I typically never remember 6 x 8, so I rearrange it to make it easier to compute in my head, like so: 6(8) = 6(10 - 2) = 60 - 12 = 60 - (10 + 2) = 60 - 10 - 2 = 48
- valiant55 2y ago
  I go: 6x8 5x8+8 40+8 48
- tylerhou 2y ago
  You can also use difference of squares. 6*8 = (7-1)*(7+1) = 7^2-1 = 49-1 = 48.
patrakov 2y ago
The conclusion is (or, rather, was) invalid for Soviet Russia. The reason is that a song for children by Eduard Khil specifically mentioned 6x8=48. https://www.youtube.com/watch?v=WLMHWtregmw https://www.youtube.com/watch?v=WLMHWtregmw (at 1:38).
rossant 2y ago
My own mnemonics relies on arithmetic progressions for these two: - 6x8 = 48 : 4-6-8 - 7x8 = 56 : 5-6-7-8
- BizarroLand 2y ago
  7*8=56 was easy for me since you had 5678 in the given numbers. This is my easy to hard ranking: (I memorized to 15's, not that it was very useful, just more of a self-imposed boredom challenge) 1's, 10's, 2's, 5's, 9's, 3's, 7's, 4's, 11's, 12's, 6's, 8's, 13's, 14's, 15's
Const-me 2y ago
For old-school software developers 4*8 is easy because both numbers are powers of 2. I compute expressions like that as 2 ^ ( log2(4) + log2(8) ) = 2^(2+3) = 2^5
saltcured 2y ago
Maybe I'm a bit abnormal or had some kind of mild defiance disorder as a student in the 80s. Despite testing high and being told I was "gifted", I never could memorize the multiplication table. I learned the diagonal (the squares) up to 11x11, but even as an adult am more likely to fast-forward through some sequential calculations in my mind rather than trust a memorized answer. For something like 6x8 I'll still almost immediately decompose it into either 2x(3x8) or 6x8 = 8x8 - 2x8 = 64 - 16. And if I did the latter, I'd second guess myself as to whether I'm going to make fence-post errors in the subtraction. Even something basic like 5x7 I might mentally turn into 5x5 + 5 + 5 and just mentally step through the answer 25..30..35 on a number line. I get more error prone when incrementing by 7. As an aside, it kind of blew my mind when I discovered that my wife seems to work a completely different way "in floating point". She'll often come out with a good answer for the mantissa but having lost track of the exponent. My mental calculations don't work this way at all.
- Vecr 2y ago
  You can do it with spaced repetition, I think Anki has a pre-made set somewhere that also has division and both ways around (to improve your instant recall).
jasonjamerson 2y ago
I was forced (thankfully) to commit everything under 12x12 to just rote memory, is that not widespread?
zug_zug 2y ago
This is fascinating. So it looks to me like the proposals is that our brain has a map from 6 -> "multiples of 6" and 8 -> "multiples of 8" and it triggers both nodes, and that our brain then finds the MOST stimulated node (i.e. numbers that are multiples of both 6 and 8). Because 24 is a multiple fo 6 and 8 it's causing interference. This seems believable, curious if there's hard data on this (that indeed 6x8 is the hardest and other numbers with shared multiples) but not curious enough to look it up.
- JustinSkycak 2y ago
  Linked in the article: Campbell (1987) The role of associative interference in learning and retrieving arithmetic facts https://www.researchgate.net/publication/247981688_The_role_of_associative_interference_in_learning_and_retrieving_arithmetic_facts https://www.researchgate.net/publication/247981688_The_role_...
fjfaase 2y ago
Took me the longest (about 40 years) to memorize 7x8. Before being able to memorize it, I would usually add 7 to 49. For some reason, the squares stuck in my mind rather easily. So, 7x7 and 8x8 are easier. I cannot remember having problems with 4x8 and 6x8. Maybe because 48 is double of 24, which is double of 12. I have to say that my performance IQ is much higher than my verbal IQ.
- euroderf 2y ago
  Same here! 7x8 was the outlier (and 8x7 also). Stubbornly resistant to memorization.
cozzyd 2y ago
in hex, they're among the easier ones to remember!

17 points by JustinSkycak 2y ago

I typically never remember 6 x 8, so I rearrange it to make it easier to compute in my head, like so: 6(8) = 6(10 - 2) = 60 - 12 = 60 - (10 + 2) = 60 - 10 - 2 = 48

valiant55 2y ago
I go: 6x8 5x8+8 40+8 48
tylerhou 2y ago
You can also use difference of squares. 6*8 = (7-1)*(7+1) = 7^2-1 = 49-1 = 48.

patrakov 2y ago

The conclusion is (or, rather, was) invalid for Soviet Russia. The reason is that a song for children by Eduard Khil specifically mentioned 6x8=48. https://www.youtube.com/watch?v=WLMHWtregmw https://www.youtube.com/watch?v=WLMHWtregmw (at 1:38).

rossant 2y ago

My own mnemonics relies on arithmetic progressions for these two: - 6x8 = 48 : 4-6-8 - 7x8 = 56 : 5-6-7-8

BizarroLand 2y ago
7*8=56 was easy for me since you had 5678 in the given numbers. This is my easy to hard ranking: (I memorized to 15's, not that it was very useful, just more of a self-imposed boredom challenge) 1's, 10's, 2's, 5's, 9's, 3's, 7's, 4's, 11's, 12's, 6's, 8's, 13's, 14's, 15's

Const-me 2y ago

For old-school software developers 4*8 is easy because both numbers are powers of 2. I compute expressions like that as 2 ^ ( log2(4) + log2(8) ) = 2^(2+3) = 2^5

saltcured 2y ago

Maybe I'm a bit abnormal or had some kind of mild defiance disorder as a student in the 80s. Despite testing high and being told I was "gifted", I never could memorize the multiplication table. I learned the diagonal (the squares) up to 11x11, but even as an adult am more likely to fast-forward through some sequential calculations in my mind rather than trust a memorized answer. For something like 6x8 I'll still almost immediately decompose it into either 2x(3x8) or 6x8 = 8x8 - 2x8 = 64 - 16. And if I did the latter, I'd second guess myself as to whether I'm going to make fence-post errors in the subtraction. Even something basic like 5x7 I might mentally turn into 5x5 + 5 + 5 and just mentally step through the answer 25..30..35 on a number line. I get more error prone when incrementing by 7. As an aside, it kind of blew my mind when I discovered that my wife seems to work a completely different way "in floating point". She'll often come out with a good answer for the mantissa but having lost track of the exponent. My mental calculations don't work this way at all.

Vecr 2y ago
You can do it with spaced repetition, I think Anki has a pre-made set somewhere that also has division and both ways around (to improve your instant recall).

jasonjamerson 2y ago

I was forced (thankfully) to commit everything under 12x12 to just rote memory, is that not widespread?

zug_zug 2y ago

This is fascinating. So it looks to me like the proposals is that our brain has a map from 6 -> "multiples of 6" and 8 -> "multiples of 8" and it triggers both nodes, and that our brain then finds the MOST stimulated node (i.e. numbers that are multiples of both 6 and 8). Because 24 is a multiple fo 6 and 8 it's causing interference. This seems believable, curious if there's hard data on this (that indeed 6x8 is the hardest and other numbers with shared multiples) but not curious enough to look it up.

JustinSkycak 2y ago
Linked in the article: Campbell (1987) The role of associative interference in learning and retrieving arithmetic facts https://www.researchgate.net/publication/247981688_The_role_of_associative_interference_in_learning_and_retrieving_arithmetic_facts https://www.researchgate.net/publication/247981688_The_role_...

fjfaase 2y ago

Took me the longest (about 40 years) to memorize 7x8. Before being able to memorize it, I would usually add 7 to 49. For some reason, the squares stuck in my mind rather easily. So, 7x7 and 8x8 are easier. I cannot remember having problems with 4x8 and 6x8. Maybe because 48 is double of 24, which is double of 12. I have to say that my performance IQ is much higher than my verbal IQ.

euroderf 2y ago
Same here! 7x8 was the outlier (and 8x7 also). Stubbornly resistant to memorization.

cozzyd 2y ago

in hex, they're among the easier ones to remember!