Best Way To Learn The Multiplication Table Using (PAO, M.P)

So this is something that’s been haunting me since the second grade.
I’ve been bullied (in a nice way) by friends and family for not knowing the multiplication table and quite frankly I could’ve saved A LOT of time on many occasions If I knew it.
Is there’s a good, effective way to memorize the basic multiplication table 1-9?
My skillset consists of PAO and Memory Palaces.
Thanks!

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I taught my son his times tables when he was 5 using the major system. It amazed me then and now how he remembers it so easily. Oh for a mind like a child.

eg. 6x4 = (ch + r) = chair.

“Now Jacob, imagine Nero is sitting on a chair, perhaps waiting to burn down Rome, which coincidently also happened in 64AD (ChaiR)”

NeRo = 24

Jacob would learn one set of the tables each night for just over a week and they were stuck for ever.

Job Done.

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Just a note that if you want to use the times tables to improve your mental maths, you’ll need to recall them very fast otherwise the overhead of using the memory technique will distract from the calculation at hand.

E.g. $140 x 6

  • $100 x 6 is $600
  • $40 x 6 is… okay now remember what 4x6 is…
  • 4x6 is something about a chair (e.g. with @MalcolmHyndman 's neat suggestion)
  • 24… and I’ve forgotten what I was doing before!

At the beginning, using palaces, mnemonics, Major system, patterns etc. can help learn this data, but once you’re comfortable with that you need to graduate to having immediate recall, where you see 4x6 and immediately know it’s 24.

I’ve made some tools that help me directly with this, not just for the times tables but for example learning the 2-digit squares and the year codes for calendar date calculations. For these I absolutely used some mnemonic techniques at the start but that was only the first half of the story.

Any sort of active-recall flashcard drill (paper flashcards, Anki, etc.) will do the trick.

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Agree. I cannot look inside my son’s head now, and he tells me that he no longer relys on chairs and Nero, but he knows both the dates and the Maths. Something else has happened and I would be fascinated to know what that is…anyone? Certainly spaced repetition and active recall must lead to something else.

If you are trying to memorize the math’s table 1 - 10.

There is no need to use major, pao system.

There are total of 100 combinations in multiplication table (1 to 10)

Multiply by 1 & 10
It’s very easiest task to do.

Multiply by 2
We have to double the number , By little practice you can easily able to double any numbers.
Like 35 × 2 = 70

Multiply by 5

There are two situations for 5’s table -

  1. If no. is even - like 8, 4, 12, 48.

Method - half the number and put 0 at the end.

Example - 8 × 5

Half of 8 = 4
At the end = 0
So 8 × 5 = 40

Other example - 46 × 5
Half of 46 = 23
At the end = 0
So 46 × 5 = 230

  1. If no. is odd - like 3 , 5 , 7, 9.

Method - subtract 1 from original no. and then half it & at the end put 5.

Example - 7 × 5

Subtract 1 and then half it -
7 - 1 = 6
Half of 6 = 3
At the end = 5
So 7 × 5 = 35

Other example - 35 × 5
35 - 1 = 34
Half of 34 = 17
At the end = 5

hence 35 × 5 = 175

Multiply by 4 & 8

For 4 = 2 times double
Ex - 4 × 4
Double of 4 = 8
Double of 8 = (16 answer)

For 8 = 3 times double
Example - 7 × 8
Double of 7 = 14
Double of 14 = 28
Double of 28 = (56 answer)

Multiplly by 9

No. 9 has some interesting properties -

  1. If we multiply any no. by 9 -
    The end result of their digit sum is also 9.

Example - 2 × 9 = 18 (digit sum of 18 = 1+8 = 9)

3 × 9 = 27 (digit sum of 27 = 2+7 = 9)

5 × 9 = 45 (digit sum of 45 = 4+5 = 9)

  1. In the case of 1 to 10 table - any number multiplied by 9 starts with 1 less number.

Example - 5 × 9

Starts with 1 less number = 4
Their digit sum has to be 9 so = 5 (because 4 + 5 = 9)

Example - 7 × 9

Starts with 1 less number = 6
Their digit sum has to be 9 = 3
So 7 × 9 = 63

Now we know how to multiply any no with 1, 10, 5, 2, 4, 8 , 9 (we learned 70 combinations)

So there are 30 combinations left (100 - 70 = 30)

3 × 1
3 × 2
3 × 3
3 × 4
3 × 5
3 × 6
3 × 7
3 × 8
3 × 9
3 × 10

6 × 1
6 × 2
6 × 3
6 × 4
6 × 5
6 × 6
6 × 7
6 × 8
6 × 9
6 × 10

7 × 1
7 × 2
7 × 3
7 × 4
7 × 5
7 × 6
7 × 7
7 × 8
7 × 9
7 × 10

As you can see there is not 30 combinations left we already memorized all of them - only 9 combinations left ( In which 3 is same just reversed)

3 square numbers -

  1. 3 × 3 = 3^2 = 9
  2. 6 × 6 = 6^2 = 36
  3. 7 × 7 = 7^2 = 49

3 last combinations -
3 × 6 / 6 × 3 = 18
3 × 7 / 7 × 3 = 21
6 × 7 / 7 × 6 = 42

Tip - 1 last thing I forgot to mention is that -

6’s number rule

If no is even -

Procedure - half the number and put the same number in the end.

Example = 4 × 6
Half of 4 = 2
Put the same no in the end = 4
So 4 × 6 = 24

Example - 6 × 6
Half of 6 = 3
Put the same number in the end = 6
So 6 × 6 = 36

Other big example = 478 X 6
Half of 478 = 239
Put the same no (last no of original) in the end and rest of the no. add in the first part.

      239 | 8
     + 47
  = 286 | 8

So 478 × 6 = 2868.

I hope you like it…

Raja.

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I have written about how I teach the tables to my kids, here:

A quick example.
For the 7 table we a thing we call: halve and double.
7 = 5 + 2 = 10/2 + 2

An example:
4 X 7
Halve of 4 is 2 (2 is the digit for the tens).
Double 4 is 8 (8 is the digit for the ones).
Halve and double is then 28. Done.

So halve is the first digit (tens) and double the second (ones).

Another example:
6 X 7
Halve of 6 is 3. This is the first digit or tens.
Double 6 is 12. This is the second digit. Of course digits end in 9, so the second digit is the 2 in ‘12’ and the 10 left goes into the second digit:

So ‘3’ | ‘12’ becomes 42.

5 X 7
Halve of 5 is 2.5
Double 5 is 10.

First digit: 2.5 (Think we have ‘2.5 tens’ or 25)
Second digit is 10.
25+10 = 35.

See how easy this is?

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@Kinma

For number 7 ,

I am using this , and it looks like very similar

7 = 5+2

Example - 6 × 7

• 6 × 5 = 30 (Method - half the no and put 0 in the end.)
• 6 × 2 = 12

Add = 30 + 12 = 42

Other example = 678 × 7

• 678 × 5 = 3390 (half the no. and put 0 in the end.)
• 678 × 2 = 1356

Add = 3390 + 1356 = 4746

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You are right. 7 = 5 + 2 = 10/2 + 2
10/2 is the halve part. Since I use it for the tens digit, it becomes 1/2 or halve.
And +2 is the double part of course.

Indeed. It is basically the same method.
I just call it halve and double, because it is easy to remember that way for kids.