Explanation:
the picture and its text explain it actually already.
each block (or square) on each side represents a fraction.
the whole block is 1. the colored parts are the fraction of that whole (1).
we see the example 2/3 × 3/4
the left block with 2 out of 3 strips marked in pink shows us 2/3 (2/3 of the block is pink).
the right block with 3 out of 4 strips marked in purple shows us 3/4 (3/4 of the block is purple).
it is essential for this method to orient the strips in one block to be at a right angle with the strips of the other block.
now, to do the multiplication you overlay the strips of both blocks.
you see this creates a chess board pattern. the total number of little squares or rectangles is the denominator (bottom part) of the result. in this case 12.
the number of little squares or rectangles that are in both original strips is the numerator (the top part) of the result. in this case 6.
so, yes, 2/3 × 3/4 = 6/12, which can then be refined to 1/2.
now, you have to do the same thing with the actual examples (I cannot draw here, sorry) :
1/4 × 3/5 = 3/20
the left block with 4 strips (one in pink, or whatever color you want), the right block with 5 strips (and 3 marked in e.g. purple).
and then the result block with 4 columns and 5 rows creating 20 little squares or rectangles, and 3 of them are in all original strips.
and the same
3/5 × 2/3 = 6/15 = 2/5
1/2 × 2/5 = 2/10 = 1/5