Can you give me a visual representation on 1/6 of 4/5 to get 4/30?

Question

I'm trying to understand fractions more by using a visual representation, and I having a hard time making a visual representation of the 1/6 of 4/5 and getting a visual understandable representation of the answer 4/30.

I'd appreciate If somebody could represent it for me.

Answer 1

Look at the following grid:

Suppose you want to take $\frac{1}{6}$ of it, then just take one of the rows, as shown in the following drawing:

Now, suppose we only want $\frac{4}{5}$ of that $\frac{1}{6}$. Then just take $4$ of the $5$ squares that make up that row:

At the end we ended up with $4$ squares, while the entire grid has a total of $30$. therefore $\frac{1}{6}\cdot\frac{4}{5}=\frac{4}{30}$

Answer 2

Divide a cake into $30$ equal slices. $\frac45$ of the cake is represented by $\frac45\times 30=24$ slices. $\frac16$ of these $24$ slices is $\frac16\times 24=4$ slices, which is also $\frac{4}{30}$ of the whole cake.

Answer 3

Take 15 squares and shade 12 of them. Then you have shaded 4/5 of the squares. Now divide the 12 shaded squares into 6 equal pieces. Then each piece consists of two squares. So two squares represents 1/6 of 4/5 and two squares out of 15 squares equals 4/30.