How many proper fractions can you make whose numerator and denominator add up to $8$ ?

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Solution

Let the numerator of a fraction = $x$
Numerator and denominator add up to $8$ , Denominator = $8 - x$
So, Required fraction = $\frac{x}{8 - x}$
For $x = 1, 2, 3, 4, 5, 6, 7$
Required proper fractions will be $\frac{1}{7}, \frac{2}{6}, \frac{3}{5}$

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