When two fractions refer to the same whole explain why the fraction with a lesser denominator has larger pieces than the fraction with a greater denominator

Because for a fraction with a small denominator, you don't have to split them up into small pieces and as many pieces. For example: let's say you had 2/3. you draw a circle with 3 equal quadrants. Those quadrants are big because you didn't have to split the circle up into a lot of peices; only 3.

Now for a bigger denominator like 20/32, you have to split the circle into 32 peices. For all of them to fit, you have to make the pieces small.

You have 2 sides that are 2 cms and you have 6 sides that are 1/2 cm and you have 4 sides that are 1 cm. the smallest sides are 1/2 the medium sized sides are 1 and the smallest are 1/2. so to find the perimeter you have to add them all up together so your answer will be 11 cm's

No solution : there is no number of boxes that she bought