Part of a Group

A jar holds 27 marbles, and 2/3 of them are red. How many are red? In a story, "2/3 of" a number means 2/3 times that number. Use r for red: r = (2/3) × 27. 27 divided into 3 equal groups gives 9 in each, and 2 of the groups hold 18, so the next line is r = 18.

The word of turns into a multiplication because that is what a fraction of something is: the bottom splits the group into equal parts, and the top says how many of the parts you take. Dividing by the bottom first keeps the numbers small, which is why the 27 was split into threes before anything was multiplied.

A quick sense check: a fraction less than 1 of a group is less than the whole group. 18 red marbles out of 27 is believable; 40 would not be.