Sum and product of numerator of rational number doubt

Question

Given the sum rule: $$ \frac{n}{m}+\frac{r}{s}=\frac{n \cdot s+m \cdot r}{m \cdot s} $$ the product rule: $$ \frac{n}{m} \cdot \frac{r}{s}=\frac{n \cdot r}{m \cdot s} $$ and the quotient rule: $$ \frac{\frac{n}{m}}{\frac{r}{s}}=\frac{n}{m} \cdot \frac{s}{r} $$ why: $$ \frac{m+\frac{r}{s}}{n} = \frac{ms+r}{ns} $$ it is not: $$ \frac{m+\frac{r}{s}}{n} = \frac{\frac{ms+r}{s}}{n} = \frac{n(ms+r)}{s} $$

Answer 1

Note that $n = \frac{n}{1}$ and thus, $$\frac{\frac{ms+r}{s}}{n} = \frac{\frac{ms+r}{s}}{\frac{n}{1}} = \frac{ms+r}{s} \cdot \frac{1}{n} = \frac{ms + r}{ns}.$$

Answer 2

See when you are confused in such cases use brackets

$\frac{m+\frac{r}{s}}{n} =\frac{(m+\frac{r}{s})}{n}= \frac{(\frac{ms+r}{s})}{n} = \frac{(ms+r)}{ns}$