To solve the given expression \(\frac{p}{q} \div \frac{r}{s}\), let's follow the required steps, ensuring each step is clearly explained:
1. Understanding Division of Fractions:
Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of a fraction \(\frac{r}{s}\) is \(\frac{s}{r}\). Therefore:
[tex]\[
\frac{p}{q} \div \frac{r}{s} = \frac{p}{q} \times \frac{s}{r}
\][/tex]
2. Multiplying the Fractions:
To multiply two fractions, you simply multiply their numerators (the top numbers) together and their denominators (the bottom numbers) together. This gives us:
[tex]\[
\frac{p}{q} \times \frac{s}{r} = \frac{p \cdot s}{q \cdot r}
\][/tex]
3. Combining the Numerators and Denominators:
Combine the numerators \(p\) and \(s\) by multiplying them together, and combine the denominators \(q\) and \(r\) by multiplying them together:
[tex]\[
\frac{p \cdot s}{q \cdot r}
\][/tex]
So, the simplified form of the expression \(\frac{p}{q} \div \frac{r}{s}\) is:
[tex]\[
\frac{p \cdot s}{q \cdot r}
\][/tex]
Thus, the solution to the problem is:
[tex]\[
\frac{p}{q} \div \frac{r}{s} = \frac{p \cdot s}{q \cdot r}
\][/tex]
