See fraction multiplication with a grid, and watch how division turns into "multiplying by the reciprocal."
When multiplying fractions, multiply the numerators together and the denominators together: (a/b) × (c/d) = (a×c)/(b×d). Draw a grid b columns by d rows, shade a of the columns and c of the rows, and the number of overlapping squares is exactly the numerator (a×c), while the total number of squares is the denominator (b×d).
Fraction division can feel a little different, but there's actually a very simple rule: flip the fraction you're dividing by (its reciprocal) and multiply. (a/b) ÷ (c/d) = (a/b) × (d/c). Why you flip and multiply becomes clear naturally once you think about "how many times does c/d fit."