Question

Peter has changed his diet to eat healthier. 2/3 of his meals are gluten
free and of these gluten free meals 1/2 are vegan. How much of his total
diet is gluten free and vegan?

Answer 1

2/3 of his diet is gluten free, and 1/2 of that is vegan, so the 1/2 is gluten free and besides being gluten free is also vegan, so is both.

what's 1/2 of 2/3?    $\bf \cfrac{2}{3}\cdot \cfrac{1}{2}\implies \cfrac{2}{6}\implies \cfrac{1}{3}$