Heart 11

Quick and efficent way to learn times tables?

generally, i am good at maths, but i have never been able to remember times tables. Im 16, and am doing a level maths next year, and the first module is non calculator, so i really need to learn!

does anyone know any succesful methods to do this???

thanks

If you are talking about the simple multiplication table from 1..10, here are the tricks I use (for higher numbers, see at end):

a) Multiplying by 10 simply adds a zero.

b) learn the square numbers by heart:
1 4 9 16 25 36 49 64 81
One hint is that the last digits are a symmetric pattern
1 4 9 .6 <.5> .6 .9 .4 .1

c) The product of two numbers that are 2 apart is one less than the square of the middle number:
2 * 4 = 8 = 3^2-1
3 * 5 = 15 = 4^2-1
4 * 6 = 24 = 5^2-1
5 * 7 = 35 = 6^2-1
6 * 8 = 48 = 7^2-1
7 * 9 = 63 = 8^2-1

d) The product of two numbers that are 4 apart is 4 less than the square of the middle number:
2 * 6 = 12 = 4^2 - 4
3 * 7 = 21 = 5^2 - 4
4 * 8 = 32 = 6^2 - 4
5 * 9 = 45 = 7^2 - 4

e) Products with 5: Just halve the other number and add a zero if even; 5 if odd: E.g.
7*5: 7 halved is 3, add 5 -> 35
4*5: 4 halved is 2, add 0 -> 20

f) Multiples of 9:
Write down one less than other number, then rest to 9:
9*2 --> write down 1, then 9-1=8 --> 18
9*3 --> write down 2, then 9-2=7 --> 27
9*4 --> write down 3, then 9-3=6 --> 36
9*5 --> 4..5 --> 45
9*6 --> 5..4 --> 54
9*7 --> 6..3 --> 63
9*8 --> 7..2 --> 72
9*9 --> 8..1 --> 81

g) Products of numbers next to each other:
2*3 -> remember 6
3*4 -> remember 12
4*5 -> see e)
5*6 -> see e)
6*7 -> 42 - "the answer to everything from the Hitch Hiker's Guide ..."
7*8 -> 56 - remember 5 6 7 8
8*9 -> see f)

Also, these products come in "pairs", as I see it:

2*3 and 3*4 - one is double the other

4*5 and 5*6 - one is 20, the other 30

6*7 and 7*8 -
* their difference is 14 (2*7);
* so when you know 56=7*8 (5-6-7-8), you know 56-14=42.
* And 42=3*14, 56=4*14.

Only 8*9 = 72 is "lonely" (or you want to pair it with 9*10=90 - both have sum 9: 7+2 = 9+0).

h) 3 apart:
2*5 --> remember 10
3*6 --> double of 3*3
4*7 --> hard to learn - remember 28
5*8 --> see e)
6*9 --> see f)

i) 5 apart
2*7 = 14 - learn
3*8 = 24 - double of 3*4
4*9 = 36 --- 49 is a square, 36 also!

The hardest part, I find, is actually to quickly put the computation in one of the boxes above. Eg..... fast: What is 5*9?
--> you must decide:
Use "5 rule"? - write down half of other number: 4; and attach 5 because 9 is odd --> 45
Or
Use "9 rule": Write down one less of other number 4; and rest to 9 = 5 --> 45.
Or
"distance 4 rule": middle number is 7 --> 7*7=49; minus 4 is 45.

Really try to do this - put each computation in a "rule bucket". And so you can remember WHY a product is what it is ...

Good luck!

----------

What about numbers above 10?

j) Again, it is very useful to learn all squares by heart. And again, the trailing digits follow the same pattern:

121 144 169 196 225 256 289 324 361: 1 4 9 6 5 6 9 4 1 !

Moreover,
169 and 196 are "somehow reversed".
225 follows from a general rule of squaring x5, where x is a single digit:
Write down x(x+1), then 25: E.g., 65^2 = (6*7, then 25) 4225.
256 is 2^8 - computer people know this; otherwise, learn by heart.
The last ones are all the multiple of 4 of the last digit, then the falling single-digit squares:

17^2 = [7*4] [9] = 289
18^2 = [8*4] [4] = 324
19^2 = [9*4] [1] = 361

Then, b), c), d), e) work there also (e.g.: 13*15 = 14^2-1=195).

k) Multiples of 11:
Squeeze in the sum of the two digits:

34*11 = [3] [3+4] [4] = 374
27*11 = [2] [2+7] [7] = 297

If the sum overflows, increment the leftmost digit:

39*11 = [3] [3+9] [9] = 429

l) * 15:
Times 10, then half of that:

18*15 = 180 + 90 = 270

m) 3 apart:
9*12 = 108 - learn by heart
11*14 --> rule of 11
12 * 15 --> rule of 15
13*16 = mhm - see below
14*17 = also see below
15*18 --> rule of 15
16*19 --> see below

n) Sometimes, (a-1)*(b+1) = ab - b + a - 1 works:

19*16 = (20-1)*(15+1)=300 - 15 + 20 - 1 = 304

13*16 = (14-1)*(15+1)=14*15 - 15 + 14 - 1 = 14^2 + 14 - 15 + 14 - 1 = 196 - 1 + 14 - 1 = 196 + 12 = 208 ... maybe not worth the effort ...

14*17 = (15-1)*(16+1) = 15*16-16+15-1=(rule of 15)160+80-1-1=240-2=238

That's about all I know ...

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