Fun and interesting number patterns

[hellokittymania]

I was watching Kate the sleepy teachers YouTube channel and she mentioned that 11 times any double digit number has a really easy pattern to solve it.

For example take 11×15
Split the 15, then add 1+5
Answer is six
Put the six in the middle and you have 165

Another example
11×94
9+4 = 13
Put the three in the middle carry the one over to the first digit on the left
You have 1034

One more example
11×21
2+1 = 3
Equals 231

Are there any other tips or tricks or interesting facts about math that you know or that you use in your classroom or with your children? I have always found mouth to be a nightmare, but I can understand this very easily.

I think divisibility rule is fascinating, especially 7.

www.mathplayground.com/howto_divisibility.html

I can't understand this one for the life of me. Well I can in the examples,but not in a logical way.or well enough to recreate.

11x
15

55

11

165

Now that's easy

But ... a number will divide by 3 if the sum of it's digits divides by 3.

So 125(1+2+5=8)is not divisible by 3 but 135 is(1+3+5=9). Handy in quizzes

To tell whether a big number is divisible by 3 then add the component numbers together to see if the sum is divisible by 3

Eg. 45432
4+5+4+3+2
=18
1+8
=9
9 is a multiple of 3 so the original number will be divisible by 3.

The 9 times table is magic all by itself.

The sums of consecutive odd numbers are square numbers:
1
1+3=4
1+3+5=9

Etc.

iklboo, it's not just 9 times table.
any number multiplied by 9 have an answer with 9 as a digital root.
It's fascinating...

9 x 631 = 5679 5 + 6 + 7 + 9 = 27 2 + 7 = 9
9 x 1165 = 10485 1 + 0 + 4 + 8 + 5 = 18 1+8 = 9

Sorry yes, 9 is a great number

If you put 99999999 / 81 in a calculator you get 1234567.89

Even more fascinating!
I really wish I knew all these stuff when I was a child!
So much more fun than just learning to calculate.

We have been reading 'The Number Devil' ...
I hadn't known:
1x1=1
11x11=121
111x111=12321
1111x1111=1234321
11111x11111=123454321
etc....

My favourite 9x trick is holding 10 fingers up, putting the multiplier finger down and reading off the numbers of fingers before the multiplier (10s number) and the number of fingers after the multiplier (1s number).

If looking at number PATTERNS, for the 9x table, I find this neat:
09
18
27
36
45
54
63
72
81
90

If you look at the tens digit only, from top to bottom, you're counting 0-9. The ones digit is the reverse, counting down from 9-0. The top half flipped/mirrored makes the bottom half.

We've used the fact that 9x (something) is the same as 10x (something) minus 1x (something) for working out the 9x table quickly.
(4x9 = 40-4, 7x9=70-7, 6x9=60-6 etc)

So e.g. 6x9, the tens digit is going to be one less than 6 i.e. 5 (because if you take some ones away from 10x6 / 60, it will always be 50something), and the ones digit is going to be the number bond of 6 to 10 i.e. 4 (because you're distracting 6 from a multiple of 10) -> 54
Or, 7x9: tens digit is one less than 7 ->6, ones digit is number bond of 7 to 10 ->3, --> 63

Similarly if you know the tens digit you can determine the ones digit if you know that the two digits must add up to 9, as mentioned by pp.

I had to prove in my university interview the rule for divisibility for 3, 9, and 11.

As it hasn't been mentioned yet, the rule for divisibility by 11 is add and subtract alternate digits. If the answer is 0 or divisible by 11 then the source number was.
e.g.
134523488

1-3+4-5+2-3+4-8+8=0

For 9x table look at your hands palms facing in. If trying 3x9 put down your 3rd finger. that leaves 2 on the left and 7 on the right, so 3x9=27.

e^i.pi +1 =0 is my favourite equation.

Sorry hippy missed your post re 9x