If there's no operator between two numbers, such as
$$\frac{1}{4}\ \frac{3}{2}$$
is multiplication meant? In other words,
$$\frac{1}{4}\ \frac{3}{2}=\frac{1}{4}\cdot\frac{3}{2}=\frac{3}{8}\tag{1}$$
Is $(1)$ a true statement?
If there's no operator between two numbers, such as
$$\frac{1}{4}\ \frac{3}{2}$$
is multiplication meant? In other words,
$$\frac{1}{4}\ \frac{3}{2}=\frac{1}{4}\cdot\frac{3}{2}=\frac{3}{8}\tag{1}$$
Is $(1)$ a true statement?
If both are fractions then you're correct. The general convention is that there is a multiplication sign between them.
But if one is an integer (particularly the one on the left) then the given number represents a mixed fraction and the sign between them is the"plus" sign.