This depends on what meaning you give to fractions. One approach is to give fractions the meaning of shares or portions of some unit e.g. a rectangle.
Multiplication is mostly equal to the word of.
Examples:
$\frac{5}{8}=\frac{5}{8}\cdot 1$ are five eights of the unit.
$\frac{2}{3}\cdot\frac{3}{4}$ means two thirds of $\frac{3}{4}$. Show a rectangle, divide it into 4 equal parts and mark three of them red. Now, take two thirds of the red area.
- Variant 1: Divide the red area into three equal parts. Hey, it's already divided into three equal parts. Mark two of them blue. The blue area is $\frac{2}{3}\cdot\frac{3}{4}$ of the rectangle. If you ignore the red part, you can see, that it's also $\frac{2}{4}=\frac{1}{2}$ of the rectangle.
- Variant 2: Divide each of the quarters into three equal parts. How many small parts is the rectangle composed of? It's $3\cdot 4=12$, so we're talking twelths here. In each of the red quarters, mark two of the three parts blue. How many are those? It's $3\cdot 2=6$. So, what's the blue share of the full rectangle? It's $\frac{6}{12}=\frac{1}{2}$. That's the same as variant 1, so our thinking was right.
If you write the numbers in different colors, you can show the students by this generalizable example, that $\frac{a}{b}\cdot\frac{c}{d}=\frac{a\cdot c}{b\cdot d}$ and that they can cancel out the 3s as they are not needed in the end of each variant.
All this should be constructed as much as possible.
Division
In contrast to multiplication, we work formally here, revisiting the technique of inverse operations.
Example: $\frac{5}{7}:\frac{2}{3}=\frac{a}{b}$ and we want to know, what $a$ and $b$ are. The inverse operation to division is multiplication. $\frac{a}{b}$ is the fraction, for which $\frac{2}{3}\cdot\frac{a}{b}=\frac{5}{7}$. We know now, that then $2\cdot a$ must be $5$ and $3\cdot b$ must be 7, but that's not possible for integers $a$ and $b$. But expanding the fraction is our friend here. We just expand $\frac{5}{7}$ by $2$ and by $3$, then it's no problem anymore to find integers $a$ and $b$:
$$\frac{2}{3}\cdot\frac{a}{b}=\frac{5}{7}=\frac{5\cdot 2}{7\cdot 2}=\frac{5\cdot 2\cdot 3}{7\cdot 2\cdot 3}$$
So now we have $2\cdot a =5\cdot 2\cdot 3$, which means $a=5\cdot 3$, and $3\cdot b=7\cdot 2\cdot 3$, which means $b=7\cdot 2$. So:
$$\frac{5}{7}:\frac{2}{3}=\frac{5\cdot 3}{7\cdot 2}=\frac{5}{7}\cdot\frac{3}{2}$$
Compare the leftmost and the rightmost side and you can see:
One divides by a fraction by multiplying with the reciproke of this fraction.
Let them do another example this way on their own. Let them countercheck their results by multiplication.
Important notice Use lots of colors. Every number or associated variable gets the same color.
