# conjunctures

• August 20th 2007, 02:21 PM
n_duncan2010
conjunctures
Geometry
haha i misspelled the topic. oops.... its supposed to be conjectures
Use a calculator to explore the pattern write a conjecture based on what you observe

10. 101x25= ?
101x34 =?
101x49=?

11. 11x11=?
111x111=?
1111x1111=?

12. 3x4=?
33x34=?
333x334=?

does anybody know how to do this??? haha because... i dont.
• August 20th 2007, 03:31 PM
Soroban
Hello, n_duncan!

Did you even try what they suggested ??

Quote:

Use a calculator to explore the pattern write a conjecture based on what you observe,

$10)\;\;\begin{array}{c}101 \times 25\:=\:{\color{blue}2525}\\
101 \times 34 \:=\: {\color{blue}3434} \\
101 \times 49\:=\:{\color{blue}4949} \end{array}$

Just a wild guess . . .

But it looks like 101 times any two-digit number $ab$ is equal to $abab$.

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

$11)\;\;\begin{array}{ccc}11 \times 11 &= & {\color{red}121} \\
111 \times 111 & =& {\color{red}12321} \\
1111 \times 1111&=&{\color{red}1234321}\end{array}$

I bet that: . $11111 \times 11111 \:=\:123454321$

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

$12)\;\;\begin{array}{ccc}3 \times 4 &= & {\color{green}12}\\
33 \times 34 & =&{\color{green}1122}\\
333 \times 334 & = & {\color{green}111222}\end{array}$

And I bet that: . $3333 \times 3334 \:=\:11112222$