1. ## Times tables

OK.... Crazy basic for this forum and i didn't really know where to put this question BUT....

I've recently been learning my times tables and i found this site useful for it - Math Trainer - Multiplication

i found the way it questioned really easy to use and learn with, and have learnt my 12 times tables... (*whey...*) But i was wondering about the best way to go on after this, 13 / 14 / 15 / 16 etc... Are they generally committed to memory in the same way as the 12 or do you find it easier to use formula's to work these out, ?

I can't really find a great site for learning them ( i guess because it's so basic... ) and reciting them over and over seemed a bit primitive for some reason, but if this is the only way then i guess ill have to have a bash.

cheers

2. ## Re: Times tables

I learned the multiplication table only for factors <= 10. For larger numbers, I remember squares and the rule for multiplying by 11 ((10m + n) * 11 = 100m + 100(m + n) + n). I could calculate some other products using the formula (a + b)2 = a2 + 2ab + b2, but I have not memorized them.

Be thankful we have a decimal numeral system instead of sexagesimal one as in Babylon!

3. ## Re: Times tables

Originally Posted by silverpen
OK.... Crazy basic for this forum and i didn't really know where to put this question BUT....

I've recently been learning my times tables and i found this site useful for it - Math Trainer - Multiplication

i found the way it questioned really easy to use and learn with, and have learnt my 12 times tables... (*whey...*) But i was wondering about the best way to go on after this, 13 / 14 / 15 / 16 etc... Are they generally committed to memory in the same way as the 12 or do you find it easier to use formula's to work these out, ?

I can't really find a great site for learning them ( i guess because it's so basic... ) and reciting them over and over seemed a bit primitive for some reason, but if this is the only way then i guess ill have to have a bash.

cheers
I only remember the times tables up to 12. Anything bigger I look for factors, or do a halving and doubling, or just multiply them out using short/long multiplication. There's only so much we can be expected to remember.

4. ## Re: Times tables

Hello, silverpen!

There is a trick to multiplying two numbers in the "teens".

The two numbers are: $10 + a$ and $10 + b.$

Their product is: . $(10+a)(10+b) \:=\:100 + 10(a+b) + ab$

We have a 3-digit number: . $|\:1\:|\:a+b\:|\:ab\:|$

The units-digit is the units-digit of $ab.$
Write that down and remember the "carry".

The tens-digit is the units-digit of $a+b$ plus the "carry".

The hundreds-digit is $1$ plus the "carry" from the tens-digit.

Example: . $14 \times 17$

We have: . $|\:1\;|\;\;\;\:|\:\;\;\:|$

Units-digit: . $4\times 7 \,=\,28$
Write down "8", carry the "2": . $|\:1\:|\:\;\;^2\:|\:8\:|$

Tens-digit: . $4+7 \,=\,11$, plus the carry, $13$
Write down "3", carry the "1": . $|\:1\,^1\:|\:3\:|\:8\:|$

Hence, we have: . $|\:2\;|\;3\:|\;8\:|$

Therefore: . $14 \times 17 \,=\,238$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Years ago, I intended to use this trick
. . and eventually memorize the "teens" table.

But I found more tricks and got "lazy".
. . I never commited all the products to memory.

If the two numbers differ by an even number,
. . we can use the "difference of squares" identity:
. . . . . $(a-b)(a+b) \:=\:a^2-b^2$

Example: . $15 \times 17$

We have: . $(16-1)(16+1) \:=\: 16^2 - 1^2 \:=\:256 - 1 \:=\:255$

Example: . $13 \times 17$

We have: . $(15-2)(15+2) \:=\:15^2 - 2^2 \:=\:225 - 4 \:=\:221$

Of course, the two numbers need not be in the "teens" for this trick.

Example: . $29 \times 35 \:=\:(32-3)(32+3) \:=\:32^2 - 3^2 \:=\:1024 - 9 \:=\:1015$

This means you must memorize a lot of squares ... which I did years ago.

You may be wondering: how do we find that "middle number"?
. . Just average the two numbers.

5. ## Re: Times tables

hey, thank's for the reply's all.... So the general consensus seems to be formula's rather than committing things to memory, ? fair enough...

@Soroban - i didn't really understand what you wrote there - can you tell me what it would fall under so that i can go off and learn it please, ?

sos the level pretty basic!

much appreciated though.

- one thing i was doing was dividing both numbers by 2, multiplying them, then multiplying the end result by four..... But this is easier if both the number's are even! (maybe ill learn decimal multiplications after)

6. ## Re: Times tables

going to work through your examples for a bit