# Give a proper fraction :           (a) whose numerator is $5$ and denominator is $7.$                                                                                                                                         (b) whose denominator is $9$ and numerator is$5.$                        (c) whose numerator and denominator add up to $10$. How many fractions of this kind can you make?           (d) whose denominator is $4$ more than the numerator.                (Give any five. How many more can you make?)

H Harsh Kankaria

A proper fraction whose:

(a) numerator is $5$ and denominator is $7.$ = $\frac{5}{7}$

(b) denominator is $9$ and numerator is $5.$  = $\frac{5}{9}$

(c) numerator and denominator add up to $10$

Pairs of numbers having sum 10 = $(1,9),(2,8),(3,7),(4,6)(5,5)$

Therefore, the proper fractions are $\frac{1}{9}, \frac{2}{8}, \frac{3}{7}, \frac{4}{6}$

(d) denominator is $4$ more than the numerator. = $\frac{1}{5}, \frac{2}{6}, \frac{15}{19}, \frac{105}{109}, \frac{199}{203},$

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