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Math Help - conjunctures

  1. #1
    Newbie n_duncan2010's Avatar
    Joined
    Apr 2007
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    10

    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.
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  2. #2
    Super Member

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    Hello, n_duncan!

    Did you even try what they suggested ??


    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}\\<br />
101 \times 34 \:=\: {\color{blue}3434} \\<br />
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} \\<br />
111 \times 111 & =& {\color{red}12321} \\<br />
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}\\<br />
33 \times 34 & =&{\color{green}1122}\\<br />
333 \times 334 & = & {\color{green}111222}\end{array}

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

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