# Just curious

#### DunceCap

##### New member
Hi. I am curious after seeing a gif with a child using a technique to multiply 9. Is there a name for what I found while playing with multiplying other numbers.....or is it just an insignificant fluke?
For example:
7 x1= 7 27
X2=14 24
X3=21 21
X4=28 18
X5=35 15
X6=42 12
X7=49 9
X8=56 6
X9=63 3
Where the second digit seems to be or part of a multiple of 3 in reverse order (or from 9 back to 1).
If I do this with multiplying 3, the second digits are multiples of 7 in reverse order. I did this with all numbers from 1-9 and they all had this type of partnership with another number.
1 and 9
2 and 8
3 and 7
4 and 6
5 with itself
Again, does this have a name/significance or is it just a coincidence and irrelevant?
TIA

#### lev888

##### Full Member
7 = 10 - 3
7n = (10-3)n
Since we are interested in going backwards let's replace n with k = 10 - n
n = 10 - k
7n = (10 - 3)*(10-k) = 100 - 10k - 30 + 3k = 70 - 10k + 3k
So as n goes from 9 to 1 the 3k term gives you 3, 6, 9, etc.

• DunceCap

#### DunceCap

##### New member
You created an algebra problem to explain the phenomenon. Kool! So I can plug n play with the rest of the numbers in like fashion with similar results? Thank you for entertaining my query!

#### DunceCap

##### New member
It works! Thank you so much!

#### lev888

##### Full Member
You created an algebra problem to explain the phenomenon. Kool! So I can plug n play with the rest of the numbers in like fashion with similar results? Thank you for entertaining my query!
Have fun!