How to Memorize Multiplication Tables

7-minute read • Updated on 6 Oct 2024

This page discusses a few ways to memorize multiplication tables.

Using Chanting to Remember Multiplication Tables

A simple way to learn times tables is to chant them repeatedly. This is how I learned them as a kid, and for most of my life I’ve just gone back to the chant to find the answers.

If I hear “six times eight”, my brain completes it: “six times eight is forty-eight”. If I hear “eight times six” I reverse the numbers so that the sub-vocalization is “six times eight”, which leads me to the answer. If I’m doing a lot of calculations, I don’t need the chant.

I learned the 9s by learning that the 10s place increases by 1 and the 1s place decreases by 1. In the numbers below, notice that the 1s place of the answer decrease: 9, 8, 7, 6, 5, 4, 3, 2, 1, while the 10s place increases: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

 1 × 9 = 09 ← The first digit of the answer is 1 less than the number you multiply by
 2 × 9 = 18 ← The 1st digit increases and the 2nd decreases
 3 × 9 = 27 ← The 1st digit increases and the 2nd decreases
 4 × 9 = 36 ← The 1st digit increases and the 2nd decreases
 5 × 9 = 45 ← etc.
 6 × 9 = 54
 7 × 9 = 63
 8 × 9 = 72
 9 × 9 = 81
10 × 9 = 90

The chanting method is kind of like recalling song lyrics by playing a song back in your mind, making the information easier to remember.

Also check out some tips for using Anki to memorize multiplication tables.

Mental Calculation and Mathematics Guide

Learn more about mental calculation and mathematics.

Using the Major System to Remember Multiplication Tables

MalcolmHyndman taught his 5-year-old son times tables using the Major System:

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.

The discussion about using the Major System for multiplication tables continues below that.

Kinma discusses an alternate method he uses to teach his son multiplication tables:

I am teaching my son the multiplication tables in a Trachtenberg kind of way. The tables until 6 are easy for him. We are now training to do 8-12. 7 is the most difficult for him (as it is for many kids).

We have already done ‘sequences’ for about two years. I started doing those from when they were 3-4 years old.

A sequence is 2, 4, 6, 8, …

Or 3, 6, 9, 12, …

Or 7, 14, 21,…

etc.

My youngest is 5 and with her I only do the sequences.

My oldest is now learning the tables at school.

What I do for numbers close to 10 (8 - 12) is this.

I have him first add a zero to the number (multiplication by 10) and then add or subtract the number or twice the number.

11 = 10 + 1, so:

1 * 11 = 10 + 1 = 11

2 * 11 = 20 + 2 = 22

3 * 11 = 30 + 3 = 33

4 * 11 = 40 + 4 = 44

5 * 11 = 50 + 5 = 55

6 * 11 = 60 + 6 = 66

7 * 11 = 70 + 7 = 77

8 * 11 = 80 + 8 = 88

9 * 11 = 90 + 9 = 99

10 * 11 = 100 + 10 = 110

11 * 11 = 110 + 11 = 121

12 * 11 = 120 + 12 = 132

9 = 10 - 1, so:

1 * 9 = 10 - 1 = 9

2 * 9 = 20 - 2 = 18

3 * 9 = 30 - 3 = 27

4 * 9 = 40 - 4 = 36

5 * 9 = 50 - 5 = 45

6 * 9 = 60 - 6 = 54

7 * 9 = 70 - 7 = 63

8 * 9 = 80 - 8 = 72

9 * 9 = 90 - 9 = 81

10 * 9 = 100 - 10 = 90

11 * 9 = 110 - 11 = 99

12 * 9 = 120 - 12 = 108

12 = 10 + 2, so:

1 * 12 = 10 + 2 = 12

2 * 12 = 20 + 4 = 24

3 * 12 = 30 + 6 = 36

4 * 12 = 40 + 8 = 48

5 * 12 = 50 + 10 = 60

6 * 12 = 60 + 12 = 72

7 * 12 = 70 + 14 = 84

8 * 12 = 80 + 16 = 96

9 * 12 = 90 + 18 = 108

10 * 12 = 100 + 20 = 120

11 * 12 = 110 + 22 = 132

12 * 12 = 120 + 24 = 144

8 = 10 - 2, so:

1 * 8 = 10 - 2 = 8

2 * 8 = 20 - 4 = 16

3 * 8 = 30 - 6 = 24

4 * 8 = 40 - 8 = 32

5 * 8 = 50 - 10 = 40

6 * 8 = 60 - 12 = 48

7 * 8 = 70 - 14 = 56

8 * 8 = 80 - 16 = 64

9 * 8 = 90 - 18 = 72

10 * 8 = 100 - 20 = 80

11 * 8 = 110 - 22 = 88

12 * 8 = 120 - 24 = 96

We have not yet done a lot with the 7 table.

We do the 7 sequence from time to time.

For the table I plan to use the following.

He is quick to halve.

7 is 5 + 2. 5 is halve of ten and 2 is double of one.

So I call it ’ halve and double’. There is a shift between halve and double, but ‘halve and double’ just sounds better.

In the case of 4 (times 7), we do halve of 4 (2) and double 4 (8).

I have him picture the 2 next to the 8 to form 28.

In the case of 8, again we do halve of 8 (4) and double (16).

He knows by then he needs to concatenate them, effectively picturing 4|16 = 56. Or he can just do 40+16.

Btw, I don’t force him to do anything. I just show him options.

Until now he just picks them up easily.

For even numbers ‘halve plus double’ is easy:

2 * 7 = 1|4 = 14

4 * 7 = 2|8 = 28

6 * 7 = 3|12 = 42

8 * 7 = 4|16 = 56

10 * 7 = 5|20 = 70

12 * 7 = 6|24 = 84

For odd numbers I just have him get the next number in the sequence.

Either that or have him multiply the number by 10, halve and then double:

1 * 7 = 5 + 2 = 7

2 * 7 = 10 + 4 = 14

3 * 7 = 15 + 6 = 21

4 * 7 = 20 + 8 = 28

5 * 7 = 25 + 10 = 35

6 * 7 = 30 + 12 = 42

7 * 7 = 35 + 14 = 49

8 * 7 = 40 + 16 = 56

9 * 7 = 45 + 18 = 63

10 * 7 = 50 + 20 = 70

11 * 7 = 55 + 22 = 77

12 * 7 = 60 + 24 = 84

Kinma also posted some good tips in the Multiplication Tables Revisted discussion.

Going Past the Basic 9x9 Multiplication Table

Daniel_360 suggests:

…learning the 1–99 × 1–9 multiplication tables is medium-difficult, but for sure means you can shortcut through a lot of small mental calculations.

Firstly, consider why you want to know them. If it’s just for a party trick or a memory challenge, then feel free to use standard mnemonic techniques.

If you want to use them in other calculations, you need to have the result directly, and mnenomic techniques won’t be suitable for this due to the demand on visual working memory. You might use them initially, but ultimately you will have to train to shortcut any mnemonic techniques.

Some things that might help you:

Start with the most useful and simplest times tables first (e.g. 24, 51, 99).

Look for patterns within the data (e.g. 3 × 37, 6 × 37, 9 × 74 etc. fall in a pattern; the 99-times table is also easy).

Regardless of whether you use mnemonics, palaces, patterns, or none of these, the last part of your training would be to use some flashcard system to ensure you can answer any of these multiplications in less than about 1.5 seconds (including typing). I have made such a tool for my personal training and for my students, although originally I used to use Anki.

Discussions About Remembering Your Multiplication Tables

Here are some longer discussions about memorizing multiplication tables:

Free Multiplication Table Worksheets

We also have a page with free multiplication table worksheets.