A Fraction of a Fraction

2/3 of a garden is planted, and 1/4 of the planted part is tomatoes. What fraction of the whole garden is tomatoes? The word of is your signal. You already know that 1/4 of 12 is $\frac{1}{4}\cdot 12$. In the same way, 1/4 of 2/3 is $\frac{1}{4}\cdot \frac{2}{3}$.

Pick a letter, t for tomatoes, and write t equal to the calculation: $t = \frac{1}{4}\cdot \frac{2}{3}$. Work it out: $t = \frac{2}{12}$, then simplify, $t = \frac{1}{6}$. A sixth of the whole garden is tomatoes.

The answer is smaller than 2/3, as it must be: the tomatoes are only part of the planted part. If a story like this comes out bigger than the fraction it started from, an of was turned into an addition.