Question 1144116
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Your presentation of the problem indicates you want a solution using algebra, and this is a good kind of problem to solve using algebra, as a way to get practice using algebra to solve problems.<br>
But you can also solve it using logical reasoning and a bit of simple arithmetic.<br>
In the given fraction 7/9, the difference between the numerator and denominator is 2.  When you add the same number to both numerator and denominator, the difference will still be 2.<br>
So what the question asks you to do is find a fraction equivalent to 5/6 in which the difference between the numerator and denominator is 2.<br>
Since the difference between the numerator and denominator of 5/6 is 1, doubling the numerator and denominator will yield a fraction equivalent to 5/6 in which the difference between the numerator and denominator is 2.<br>
So 5/6 = 10/12.  And we see that 10/12 = (7+3)/(9+3); so the number we are looking for is 3.