How does rearrangement work for pulling out factors












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Given 10(6*3+2) we can rearrange the equation by pulling out the 3 and getting 10((6*3)/3+(2/3))3



Okay I understand that it works. But I don't understand how. I would have assumed to do 10((6*3)/3+2)3 since we are only removing the 3 as a factor to 6. Why does 3 need to be divided by the 2 as well? 3 has nothing to do with the 2.










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  • $begingroup$
    The only way the value of the expression will be unchanged is if you both multiply and divide by $3$.
    $endgroup$
    – saulspatz
    Jan 7 at 21:14






  • 1




    $begingroup$
    Notice that everything in the parentheses is being multiplied by $10$. If you extract a $3$ from the parentheses, each term left in the parentheses is being multiplied by $30$.
    $endgroup$
    – N. F. Taussig
    Jan 7 at 21:21










  • $begingroup$
    Please use MathJax.
    $endgroup$
    – N. F. Taussig
    Jan 7 at 21:24
















1












$begingroup$


Given 10(6*3+2) we can rearrange the equation by pulling out the 3 and getting 10((6*3)/3+(2/3))3



Okay I understand that it works. But I don't understand how. I would have assumed to do 10((6*3)/3+2)3 since we are only removing the 3 as a factor to 6. Why does 3 need to be divided by the 2 as well? 3 has nothing to do with the 2.










share|cite|improve this question









$endgroup$












  • $begingroup$
    The only way the value of the expression will be unchanged is if you both multiply and divide by $3$.
    $endgroup$
    – saulspatz
    Jan 7 at 21:14






  • 1




    $begingroup$
    Notice that everything in the parentheses is being multiplied by $10$. If you extract a $3$ from the parentheses, each term left in the parentheses is being multiplied by $30$.
    $endgroup$
    – N. F. Taussig
    Jan 7 at 21:21










  • $begingroup$
    Please use MathJax.
    $endgroup$
    – N. F. Taussig
    Jan 7 at 21:24














1












1








1





$begingroup$


Given 10(6*3+2) we can rearrange the equation by pulling out the 3 and getting 10((6*3)/3+(2/3))3



Okay I understand that it works. But I don't understand how. I would have assumed to do 10((6*3)/3+2)3 since we are only removing the 3 as a factor to 6. Why does 3 need to be divided by the 2 as well? 3 has nothing to do with the 2.










share|cite|improve this question









$endgroup$




Given 10(6*3+2) we can rearrange the equation by pulling out the 3 and getting 10((6*3)/3+(2/3))3



Okay I understand that it works. But I don't understand how. I would have assumed to do 10((6*3)/3+2)3 since we are only removing the 3 as a factor to 6. Why does 3 need to be divided by the 2 as well? 3 has nothing to do with the 2.







algebra-precalculus arithmetic






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asked Jan 7 at 21:10









SephSeph

1685




1685












  • $begingroup$
    The only way the value of the expression will be unchanged is if you both multiply and divide by $3$.
    $endgroup$
    – saulspatz
    Jan 7 at 21:14






  • 1




    $begingroup$
    Notice that everything in the parentheses is being multiplied by $10$. If you extract a $3$ from the parentheses, each term left in the parentheses is being multiplied by $30$.
    $endgroup$
    – N. F. Taussig
    Jan 7 at 21:21










  • $begingroup$
    Please use MathJax.
    $endgroup$
    – N. F. Taussig
    Jan 7 at 21:24


















  • $begingroup$
    The only way the value of the expression will be unchanged is if you both multiply and divide by $3$.
    $endgroup$
    – saulspatz
    Jan 7 at 21:14






  • 1




    $begingroup$
    Notice that everything in the parentheses is being multiplied by $10$. If you extract a $3$ from the parentheses, each term left in the parentheses is being multiplied by $30$.
    $endgroup$
    – N. F. Taussig
    Jan 7 at 21:21










  • $begingroup$
    Please use MathJax.
    $endgroup$
    – N. F. Taussig
    Jan 7 at 21:24
















$begingroup$
The only way the value of the expression will be unchanged is if you both multiply and divide by $3$.
$endgroup$
– saulspatz
Jan 7 at 21:14




$begingroup$
The only way the value of the expression will be unchanged is if you both multiply and divide by $3$.
$endgroup$
– saulspatz
Jan 7 at 21:14




1




1




$begingroup$
Notice that everything in the parentheses is being multiplied by $10$. If you extract a $3$ from the parentheses, each term left in the parentheses is being multiplied by $30$.
$endgroup$
– N. F. Taussig
Jan 7 at 21:21




$begingroup$
Notice that everything in the parentheses is being multiplied by $10$. If you extract a $3$ from the parentheses, each term left in the parentheses is being multiplied by $30$.
$endgroup$
– N. F. Taussig
Jan 7 at 21:21












$begingroup$
Please use MathJax.
$endgroup$
– N. F. Taussig
Jan 7 at 21:24




$begingroup$
Please use MathJax.
$endgroup$
– N. F. Taussig
Jan 7 at 21:24










1 Answer
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$begingroup$

According to the distributive law
$$a(b+c)=ab+ac$$
In your problem
$$a=3,~b=((6cdot3)/3),~c=(2/3)$$
$$((6cdot3)/3+(2/3))cdot3=((6cdot3)/3) cdot3 +(2/3)cdot3=6cdot3+2$$
On the other hand, you are wrong to say that
$$((6cdot3)/3+2)cdot3=6cdot3+2$$
Since according to the distributive law
$$((6cdot3)/3+2)cdot3=(6cdot3/3)cdot3+2cdot3=6cdot3+6$$






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    $begingroup$

    According to the distributive law
    $$a(b+c)=ab+ac$$
    In your problem
    $$a=3,~b=((6cdot3)/3),~c=(2/3)$$
    $$((6cdot3)/3+(2/3))cdot3=((6cdot3)/3) cdot3 +(2/3)cdot3=6cdot3+2$$
    On the other hand, you are wrong to say that
    $$((6cdot3)/3+2)cdot3=6cdot3+2$$
    Since according to the distributive law
    $$((6cdot3)/3+2)cdot3=(6cdot3/3)cdot3+2cdot3=6cdot3+6$$






    share|cite|improve this answer









    $endgroup$


















      0












      $begingroup$

      According to the distributive law
      $$a(b+c)=ab+ac$$
      In your problem
      $$a=3,~b=((6cdot3)/3),~c=(2/3)$$
      $$((6cdot3)/3+(2/3))cdot3=((6cdot3)/3) cdot3 +(2/3)cdot3=6cdot3+2$$
      On the other hand, you are wrong to say that
      $$((6cdot3)/3+2)cdot3=6cdot3+2$$
      Since according to the distributive law
      $$((6cdot3)/3+2)cdot3=(6cdot3/3)cdot3+2cdot3=6cdot3+6$$






      share|cite|improve this answer









      $endgroup$
















        0












        0








        0





        $begingroup$

        According to the distributive law
        $$a(b+c)=ab+ac$$
        In your problem
        $$a=3,~b=((6cdot3)/3),~c=(2/3)$$
        $$((6cdot3)/3+(2/3))cdot3=((6cdot3)/3) cdot3 +(2/3)cdot3=6cdot3+2$$
        On the other hand, you are wrong to say that
        $$((6cdot3)/3+2)cdot3=6cdot3+2$$
        Since according to the distributive law
        $$((6cdot3)/3+2)cdot3=(6cdot3/3)cdot3+2cdot3=6cdot3+6$$






        share|cite|improve this answer









        $endgroup$



        According to the distributive law
        $$a(b+c)=ab+ac$$
        In your problem
        $$a=3,~b=((6cdot3)/3),~c=(2/3)$$
        $$((6cdot3)/3+(2/3))cdot3=((6cdot3)/3) cdot3 +(2/3)cdot3=6cdot3+2$$
        On the other hand, you are wrong to say that
        $$((6cdot3)/3+2)cdot3=6cdot3+2$$
        Since according to the distributive law
        $$((6cdot3)/3+2)cdot3=(6cdot3/3)cdot3+2cdot3=6cdot3+6$$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Jan 7 at 21:37









        LarryLarry

        2,54531131




        2,54531131






























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