Hey, i am 30 years old and never learned my times tables. Looking just to do the standard ones you find on a school chart ( 1 x 1 - 9 x 9?). I am teaching myself math, eventually for programming and it is really holding me back (and always has).
So you have 81 different facts, but the actual memory work isn’t as much as you might think.
First of all, about half of the facts are inverses of each other, so if you know 7 x 4, you know 4 x 7. If you know 9 x 3, you know 3 x 9, and so on. The only ones that don’t invert are the perfect squares, which involve the same number, like 6 x 6, 3 x 3, 9 x 9, etc. This cuts down your memorization from 81 to 45 unique facts.
0 times anything is 0, so if you see a 0, the answer is automatically 0.
The first 9 facts are very easy - anything times 1 is itself (and 1 times anything is itself). 5 x 1 = 5. 1 x 7 = 7. 8675309 x 1 = 8675309.
The 2s aren’t too hard either. Assuming you can add the same number to itself (2 times a number is twice that number), these shouldn’t be too hard. 2 x 7 is just twice 7, so 7 + 7, or 14. 8 x 2 is twice 8, so it’s 16.
If you can read a clock face, the 5s should be no problem. If the minute hand is pointing at the 6, it’s 30, or if it’s at the 2, it’s 10. 5 x 2 = 10, 6 x 5 = 30, 5 x 8 = 40, etc.
The 9s are some of the most fun. Here’s a trick. Hold out your hands. 9 x 6. Bend down your 6th finger. There are 5 fingers to the left and 4 to the right, so it’s 54. 3 x 9. Bend down your 3rd finger. There are 2 to the left and 7 to the right, so 27.
With that, we’ve knocked out more than half of the table!
From here, I’d advise you to memorize the perfect squares and know what one number multiplied by itself is.
1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
6 x 6 = 36
7 x 7 = 49
8 x 8 = 64
9 x 9 = 81
The low 3s and 4s aren’t too much of a problem, and here, you just need to know 3 x 4 = 12 (one-two equals three times four), in addition to the two squares next to it (3 x 3, 4 x 4)
The remaining twelve facts tend to be the most difficult to memorize, so pay special attention to them (as well as their inverses). The first six involve 3 and 4, and are usually considered to be the easier part of this group.
3 x 6 = 18
3 x 7 = 21
3 x 8 = 24
4 x 6 = 24
4 x 7 = 28
4 x 8 = 32
The second part are the ones that involve the larger numbers 6, 7, and 8. These tend to be the most difficult to memorize. Of all of the 81 facts, these are the most common ones to get wrong.
6 x 6 = 36 (a square)
6 x 7 = 42
6 x 8 = 48
7 x 7 = 49 (a square)
7 x 8 = 56 (this is the one that is THE most commonly missed. I have a little jingle to help me with this one. Five, six, seven, eight. Fifty-six equals seven times eight.)
8 x 8 = 64 (a square)
And with that, the entire table is done. It’s not as bad as you think, right?t
When I was a kid I learned them by chanting them. Even today, if I forget one, I can chant “six times eight is ___” and the answer will appear in memory like recalling the lyrics to a song.
I only chanted them in one direction, so if I see 8x6, I’ll think of it as 6x8 to recall it.
Another trick with 9s is that the 10s increase and the ones decrease.
1 x 9 = 09 ← The first digit of the answer is 1 less than the number you multiply by 2 x 9 = 18 ← The 1st digit increases and the 2nd decreases 3 x 9 = 27 ← The 1st digit increases and the 2nd decreases 4 x 9 = 36 ← The 1st digit increases and the 2nd decreases 5 x 9 = 45 ← etc. 6 x 9 = 54 7 x 9 = 63 8 x 9 = 72 9 x 9 = 81 10 x 9 = 90
Another fact is if we multiply any number with ‘6’ then the the first no is the half of second or last number.
Ex - 6 × 2 = 12 ( we write half of last no is 1 and same last no.)
6 × 2 = 12
6 × 4 = 24
6 × 6 = 36
6 × 8 = 48
6 × 10 = 5 | 10
= 6 | 0 = 60 (we always give carry and write only one no in last)
6 × 48 = 24 | 48
6 × 408 = 204 | 408
When you understand this you can easily do this without any problem.
I described it long only for understanding when you used it then it becomes the second nature
I have been many times to the calculation world cup and I have met people who have memorized the whole 100 x 100 table. (Willem Bouman, Jerry Newport and a few others).
Personally I am a bit more proficient just with memorizing the following 50x50 table which is 4 times smaller than the 100x100:
Using colors like the above 12x12 and 50x50 tables, can help memorizing.
To learn all these information, there are a few conditions:
- You have to like numbers
- You have to put the effort into it.
- You have to dislike using the calculator all the time.
Good luck, regardless of your level !
From novice level to genius level, we all use the same brain processes to store these output into our long-term memory.
I showed my 11-year old son this post, and it really helped him to memorize the multiplication table; thanks for sharing. Really liked: 1, 2, 3,4: 12 = 3 * 4 and 5,6,7,8: 56 = 7 * 8. Love it.
I love it. Never heard that one before!
I will use it when teaching my kids.
Kinma , you can also used this hand method on table 19.
In this table one little change.
When you bend your fingers than , we also count the bend finger.
The value of bend finger = 0.5
19 × 2 = Bend your second finger and see bend finger + leftmost finger and double it.
1.5 + 1.5 = 3 (double
And count the rightmost finger = 8
Answer = 38
19 × 4 = bend your 4th finger and count the left finger + bend finger and double it.
3.5 + 3.5 = 7
Rightmost fingers = 6
19 × 4 = 76
I learned that trick myself as a child, interestingly enough.
Love it. Keep them coming, please.
My son and daughter are on the verge of learning the tables.
Jerry Newport? I guess he isn’t a natural after all. Thanks for the info
I met Jerry Newport during the world cup 2010 in Madgeburg, when we both competed.
He was 62 yo back then, and I was 26 yo. I remember, when we were hanging out, I gave him 3 different times , a set random 2 x 2 digit numbers and he found the result instantly. (less than a second, and he had no signs, of calculating. Just pure memory). Most other mental calculators, need around 3 to 4 seconds to find those, but I think for Jerry it was just memory.
I also asked him random 4 digit numbers, and he could instantly tell their factorization or if they were primes. I remember I told him, check 1403 and he instantly replied, that it is ‘61 times 23’. (1403 = 61 x 23 ). He did not use divisibility rules or modulars. Just instant reply.
He told me, he worked a cab driver and he used to factorize all the time , all the licence plates of the cars that were in front of him.
But now in 2020, Jerry is 72 yo and I am not sure if he has the same abilities, because he has not competed for 10 years. So, I just mentioned what I witnessed in 2010. Also, note that Jerry has a mathematics degree so he has some theoretical knowledge already.
The other person I mentioned, the Dutch Willem Bouman, is 81 yo now in 2010, I met him at various world cups, when he was 73, 75 , 77 and 79 yo respectively, and he could definitely instantly factorize 4 digit numbers. In fact, he only was starting thinking/calculating, when he was a given a 5 digit number to factorize (i.e from 10000 to 99999). So I am sure Willem also knows the 100x100 multiplication table as well (by memory recall and not by calculation, like most of us do.).
I don’t think these people, utilize the ‘Major system’, the ‘Ben system’ or whatever ‘image system/memory palace’, but rather, they memorize the whole multiplication table per se, like associating numbers just with each other, and memorizing their multiples, their symmetries and especially noticing the patterns in the last 2 digits, which repeat often.
Finally, for the multiplication’s WR holder, 24 yo Marc from Spain, I think he can solve these 2x2 in around 1.5" (definitely less than 2 seconds each), but it is still calculation and not memory.
Most people, if they met Jerry or Marc they probably could not tell apart who is calculating fast and who has memorized the table, because they are both super fast in their answers. But I have competed against both of them and I talked to both of them , so I know a few more things behind the scenes of the calculation world.
(Please forgive me for my poor English)
I wonder if Marc uses the Soroban system when dong calculation as same as Ms. Jeonghee Lee?
And your calendar calculating is pretty fast, is there any special trick you use for it?
And I haven’t found any Chinese ever took part in Memoriad or MCWC, Is there any reason for it?
Marc does not use the soroban. He “visualizes” the numbers in another way.
This is the human calendar algorithm. The fastest of us use many shortcuts and memorized values to speed up the process (e.g., to cut through the green calculation on the link by just recalling one memorized value).
I’m sure one day there will be Chinese competitors in the competitions.
Thanks for your reply!