Divide Unit Fractions by Whole Numbers Practice Test

A baker has $\tfrac{1}{4}$ of a cake left. She shares it equally in two different ways: (1) among 2 kids and (2) among 4 kids. Imagine the cake is first divided into 4 equal pieces, and then that one piece is partitioned again into equal smaller parts. Dividing a fraction by a whole number creates smaller equal parts. Which statement is correct when you compare $\tfrac{1}{4} \div 2$ and $\tfrac{1}{4} \div 4$?

A student says: “To find $\tfrac{1}{4} \div 2$, I divided the denominator by 2 and got $\tfrac{1}{2}$.” But dividing a fraction by a whole number creates smaller equal parts. Use a model idea: split 1 whole into 4 equal parts, then split one of those parts into 2 equal smaller parts. Which claim about the result is incorrect?