何か目からウロコだなぁ

How am I just now seeing this pattern for the first time?

Because we’re not taught to think like this in schools. It’s all memorization, we’re not taught about patterns with numbers.

I was actually taught these tricks in school. Memorization is mandatory for a lot of basic math, even in this case, but these tricks are meant to aid with memorization and speed it up by a lot.

I’ma just list out a few of them. A lot if it is also learning what the factorization works out like. Multiples of 3 have a lot. You often can use these to check your math and sometimes figure out answers easier.

• odd numbers: if an odd number can be factorized, its factors will always be 2 odd numbers. Likewise the multiplication of 2 odd numbers will always be odd as well.
• even numbers: any multiple of 2 will be an even number. If any number is multiplied by at least 1 even number, the result will be even.
• multiples of 3: the digits will add up to a smaller multiple of 3. 27 for instance is 2+7 = 9. 26632, which is huge, will add up to 2+6+6+3+1 = 18, which 1+8 = 9, so you’ll know it’s a multiple of 3 as well (even if you might not know what its factors are right away).
  
• multiples of 4: If the 10′s digit is an even number, then the 1′s digit is gonna be 0, 4, or 8. If it’s an odd number, then it’ll be 2 or 6.
• multiples of 5: end in either 0 or 5. They’ll basically be half of the number you multiply by, times 10. (5*7 = 35)
• multiples of 6 use the same rules as multiples of 3, except the 1′s place needs to be an even number.
• no rules for 7 sadly. 7 was rude and gets no hot dog.
• 8 is just every other multiple of 4. There are technically more patterns for it but they get kinda too long to be useful.
• 9 works like 3, except the addition of the digits will come to a smaller multiple of 9. 27 -> 2+7 = 9. 81 -> 8+1 = 9. 9 also will be 1 multiple less than multiplying by 10. So 9x8 = 10x8 - 8 = 80 - 8 = 72. 9x4 = 10x4- 4 = 40 - 4 = 36. This results in the pattern that the girl is demonstrating.

I also learned these patterns. I’m sorry for those who didn’t; it’s not like these patterns have been new knowledge for many years, so it’s a shame if this wasn’t part of the curriculum in some areas.

I learned this in elementary school too. Granted, I think it was mentioned once by another student who must have gotten it from somewhere else. But when he did, the teacher did encourage everyone to remember it.