Question 1159720
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A solution using logical reasoning and a bit of trial and error with simple arithmetic....<br>
When the denominator is decreased by 7, the fraction becomes 1.  That means the denominator is 7 more than the numerator.  So the fraction is of the form {{{n/(n+7)}}}.<br>
When the numerator is increased by 3, the fraction becomes (equivalent to) 3/4.  So the fraction {{{(n+3)/(n+7)}}} is equivalent to 3/4.<br>
From there you can solve the problem algebraically:<br>
{{{(n+3)/(n+7) = 3/4}}}
{{{3(n+7) = 4(n+3)}}}
{{{3n+21 = 4n+12}}}
{{{n = 9}}}<br>
The original fraction is {{{n/(n+7) = 9/16}}}<br>
If you have excellent number sense, you can also work the last part of the problem informally.  You know the fraction {{{(n+3)/(n+7)}}} is equivalent to 3/4.  In the fraction 3/4, the difference between numerator and denominator is 1; you want the difference to be 4 (the difference between n+3 and n+7).<br>
So the fraction after you increase the numerator by 3 is {{{(3*4)/(4*4) = 12/16}}}; and that makes the original fraction 9/16.<br>