Write a proper fraction whose numerator and denominator add upto $12 .$ How many such fractions are possible?

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Solution

According to the question the sum of the numerator and denominator of the required fraction $= 12$
Intuitively, the required proper fractions are: $\frac{0}{12}, \frac{1}{11}, \frac{2}{10}, \frac{3}{9}, \frac{4}{8}, \frac{5}{7}$ etc.
There can be many proper fractions of such type. Answer

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