Question 272451
Afternoon, thank you in advance...HELP!!! I'm a mom trying to remember how to do this. I gave up. been at it for more than 35 mins...Son is being asked to find the value of n.

352 X 75 = (nX75)+ (50X75) + (2X75)

THANK YOu THANK YOU THANK YOU 
<pre>

{{{352}}}{{{"×"}}}{{{75}}}{{{"="}}}{{{n}}}{{{"×"}}}{{{75}}}{{{"+"}}}{{{50}}}{{{"×"}}}{{{75}}}{{{"+"}}}{{{2}}}{{{"×"}}}{{{75}}}

Using the distributive principle:


{{{352}}}{{{"×"}}}{{{75}}}{{{"="}}}{{{"("}}}{{{n}}}{{{"+"}}}{{{50}}}{{{"+"}}}{{{2}}}{{{")"}}}{{{"×"}}}{{{75}}}

Add the 50 and the 2

{{{352}}}{{{"×"}}}{{{75}}}{{{"="}}}{{{"("}}}{{{n}}}{{{"+"}}}{{{52}}}{{{")"}}}{{{"×"}}}{{{75}}}

Multiply both sides by {{{1/75}}}

{{{352}}}{{{"×"}}}{{{75}}}{{{"×"}}}{{{1/75}}}{{{"="}}}{{{"("}}}{{{n}}}{{{"+"}}}{{{52}}}{{{")"}}}{{{"×"}}}{{{75}}}{{{"×"}}}{{{1/75}}}

Put the {{{75}}}{{{"×"}}}{{{1/75}}}'s in parentheses just for emphasis

{{{352}}}{{{"×"}}}{{{"("}}}{{{75}}}{{{"×"}}}{{{1/75}}}{{{")"}}}{{{"="}}}{{{"("}}}{{{n}}}{{{"+"}}}{{{52}}}{{{")"}}}{{{"×"}}}{{{"("}}}{{{75}}}{{{"×"}}}{{{1/75}}}{{{")"}}}

Replace the {{{75}}}{{{"×"}}}{{{1/75}}}'s by {{{1}}}'s

{{{352}}}{{{"×"}}}{{{1}}}{{{"="}}}{{{"("}}}{{{n}}}{{{"+"}}}{{{52}}}{{{")"}}}{{{"×"}}}{{{1}}}

Since 1 is the identity for multiplication, any number multiplied by 1
gives the same number as the number multip[lied by it, so we can just
eliminate the {{{"×"}}}{{{1}}}'s:

{{{352}}}{{{"="}}}{{{"("}}}{{{n}}}{{{"+"}}}{{{52}}}{{{")"}}}

We can eliminate those parentheses:

{{{352}}}{{{"="}}}{{{n}}}{{{"+"}}}{{{52}}}

Subtract {{{52}}} from both sides:

{{{352}}}{{{"-"}}}{{{52}}}{{{"="}}}{{{n}}}{{{"+"}}}{{{52}}}{{{"-"}}}{{{52}}}

Do the subtractions:

{{{300}}}{{{"="}}}{{{n}}}{{{"+"}}}{{{0}}}

{{{300}}}{{{"="}}}{{{n}}}

Edwin</pre>