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To divide a fraction by a number is the same as to multiply the fraction by the multiplicative inverse of that number, i.e:

$$\frac{a}{b}/c = \frac{a}{b}*\frac{1}{c}$$

We get:

$$\frac{5}{3}/9 = \frac{5}{3}*\frac{1}{9}$$

We multiply (*) numerator (top) by numerator and denominator (bottom) by denominator:

$$\frac{5}{3}*\frac{1}{9} = \frac{5 * 1}{3*9}= \frac{5}{27}$$