Tran and Noah are each given the same amount of clay in art class. Tran divides his clay into 3 equal pieces. He uses 2 pieces to make a bowl. Noah divides his clay into 4 equal pieces, He also uses 2 pieces to make a bowl. Tran says that he has more clay left over than Noah. Is Tran correct? Explain,

- Let the total amount of clay be \( C \) for both Tran and Noah. - **Tran's clay:** - Tran divides his clay into 3 equal pieces, so each piece is \[ \frac{C}{3}. \] - He uses 2 pieces to make a bowl. The remaining clay is: \[ C - 2 \left(\frac{C}{3}\right) = C - \frac{2C}{3} = \frac{C}{3}. \] - **Noah's clay:** - Noah divides his clay into 4 equal pieces, so each piece is \[ \frac{C}{4}. \] - He uses 2 pieces to make a bowl. The remaining clay is: \[ C - 2 \left(\frac{C}{4}\right) = C - \frac{2C}{4} = C - \frac{C}{2} = \frac{C}{2}. \] - **Comparison:** - Tran's leftover clay is \( \frac{C}{3} \). - Noah's leftover clay is \( \frac{C}{2} \). - Since \[ \frac{1}{3}C < \frac{1}{2}C, \] Noah has more leftover clay than Tran. - **Conclusion:** Tran is not correct; he actually has less clay left over than Noah.