Question 122802
Let N represent the unknown number.
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One-fourth of N is N divided by 4 which can be written as {{{N/4}}}
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One-half of N is N divided by 2 which can be written as {{{N/2}}}
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If you subtract one-fourth of N from one-half of N this subtraction can be written as:
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{{{N/2 - N/4}}} 
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and the problem tells you that this equals 3. So, in equation form this subtraction is:
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{{{N/2 - N/4 = 3}}}
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You can now put the first term on the left side over a common denominator of 4 by multiplying
it by {{{2/2}}} ... and since {{{2/2 = 1}}} this is the same as multiplying the first term
by 1 ... so it does not change the term. This multiplication of the first term by {{{2/2}}}
changes the term to:
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{{{N/2 * 2/2 = 2N/4}}}
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and the equation then becomes:
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{{{2N/4 - N/4 = 3}}}
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On the left side you combine the two terms by subtracting their numerators and placing the
result over the common denominator. In other words:
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{{{2N/4 - N/4 = (2N - N)/4 = N/4}}}
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and when you substitute this new reduced form of the terms on the left side, the equation becomes:
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{{{N/4 = 3}}}
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This equation can be solved for N by multiplying both sides by 4 to get rid of the denominator
on the left side. Multiplying both sides by 4 results in:
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{{{N = 4*3 = 12}}}
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So the answer to this problem is that the unknown number N equals 12.
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Check:
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One-half of 12 is 6, and one-fourth of 12 is 3. Then 6 - 3 = 3 which is what the problem says
it should be. So the answer of N = 12 checks.
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Hope this helps you to understand the problem.
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