That’s what I do in my head if I need an exact result. If I’m approximateing I’ll probably just do something like 70 * 15 which is much easier to compute (70 * 10 + 70 * 5 = 700 + 350 = 1050).
No it doesn’t, multiplication and division always take precedence over addition and subtraction. You’d need parentheses to clarify what is in the divisor since that can be ambiguous with line notation.
OK, I’ve been willing to just let the examples roll even though most people are just describing how they’d do the calculation, not a process of gradual approximation, which was supposed to be the point of the way the LLM does it…
…but this one got me.
Seriously, you think 70x5 is easier to compute than 70x3? Not only is that a harder one to get to for me in the notoriously unfriendly 7 times table, but it’s also further away from the correct answer and past the intuitive upper limit of 1000.
Times 5 and times 10 tables are really easy for me. So yeah, in my mind it’s an easier comuptation.
That being said having a result of a little over a 1000 gives me an estimate for the magnitude of a number – it’s around a thousand. It might be more or less but it’s not far from there.
See, for me, it’s not that 7*5 is easier to compute than 7*3, it’s that 5*7 is easier to compute than 7*3.
I saw your other comment about 8’s, too, and I’ve always found those to be a pain, so I reverse them, if not outright convert them to arithmetic problems. 8x4 is some unknown value, but X*8 is always X*10-2X, although do have most of the multiplication tables memorized for lower values.
8*7 is an unknown number that only the wisest sages can compute, however.
I’ve always hated it and eight. I can only remember the ones that are familiar at a glance from the reverse table and to this day I sometimes just sum up and down from those “anchor” references. They’re so weird and slippery.
Going back to the “being friends” thing, I think you and I could be friends due to applying qualities to numbers; but I think it might be challenging because I find 7 and 8 to be two of the best. They’re quirky, but interesting.
72 * 10 + 70 * 3 + 2 * 3
That’s what I do in my head if I need an exact result. If I’m approximateing I’ll probably just do something like 70 * 15 which is much easier to compute (70 * 10 + 70 * 5 = 700 + 350 = 1050).
(72 * 10) + (2 * 3) = x
There, fixed, because otherwise order of operation gets fucky.
No it doesn’t, multiplication and division always take precedence over addition and subtraction. You’d need parentheses to clarify what is in the divisor since that can be ambiguous with line notation.
OK, I’ve been willing to just let the examples roll even though most people are just describing how they’d do the calculation, not a process of gradual approximation, which was supposed to be the point of the way the LLM does it…
…but this one got me.
Seriously, you think 70x5 is easier to compute than 70x3? Not only is that a harder one to get to for me in the notoriously unfriendly 7 times table, but it’s also further away from the correct answer and past the intuitive upper limit of 1000.
Times 5 and times 10 tables are really easy for me. So yeah, in my mind it’s an easier comuptation.
That being said having a result of a little over a 1000 gives me an estimate for the magnitude of a number – it’s around a thousand. It might be more or less but it’s not far from there.
See, for me, it’s not that 7*5 is easier to compute than 7*3, it’s that 5*7 is easier to compute than 7*3.
I saw your other comment about 8’s, too, and I’ve always found those to be a pain, so I reverse them, if not outright convert them to arithmetic problems. 8x4 is some unknown value, but X*8 is always X*10-2X, although do have most of the multiplication tables memorized for lower values.
8*7 is an unknown number that only the wisest sages can compute, however.
For me personally, anything times 5 can be reached by halving the number, then multiplying that number by 10.
Example: 66 x 5 = Y
(66/2) x (5x2) = Y
cancel out the division by creating equal multiplication in the other number
66/2 = 33
5x2 = 10
33 x 10 = Y
33 x 10 = 330
Y = 330
The 7 times table is unfriendly?
I love 7 timeses. If numbers were sentient, I think I could be friends with 7.
I’ve always hated it and eight. I can only remember the ones that are familiar at a glance from the reverse table and to this day I sometimes just sum up and down from those “anchor” references. They’re so weird and slippery.
Huh.
Going back to the “being friends” thing, I think you and I could be friends due to applying qualities to numbers; but I think it might be challenging because I find 7 and 8 to be two of the best. They’re quirky, but interesting.
Thank you for the insight.