Before we start representing this product of fractions 2/3 x 3/5
we recall that the meaning of that product is: we need to find "2/3" OF "3/5"
(that "x" symbol can be interpreted as "OF". So we are trying to find with the product of the fractions what is two thirds of three fifths.
So we start by representing with a rectangle our unit, and dividing that rectangle in 5 equal parts, where we are going to represent in the second step the "3/5" (three fifths):
Now we mark three of these portions to represent the "3/5":
Now we need to divide our model in 3 equal parts in order to find two thirds of the 3 /5 (yellow squares). We use horizontal divisions this time:
And now we highlight with a different color what corresponds to the yellow sections now divided in three equal parts:
We see that two thirds of the yellow fractions now is highlighted in green. What do these new smaller squares represent? Notice that our original rectangle is now divided in (3 x 5 = 15) fifteen equal parts, and the answer we want (the green sections) total 6 of them
Then we conclude that the answer should be: 6 / 15
which coincides with what we have learned about multiplication of fractions:
2 / 3 * 3 / 5 = ( 2 * 3 ) / ( 3 * 5 ) = 6 / 15