To determine the amount of clay left over after making the mugs, we need to subtract the total pounds of clay needed for the mugs from the initial amount of clay.
The total pounds of clay needed for the mugs is given by the sum of the values in the "Pounds of Clay Needed" column. Let's calculate this:
![\[ 0 + (1)/(4) + (1)/(2) + (3)/(4) + 1 + (3)/(2) + (1)/(4) = (19)/(4) \text{ pounds}\]](https://img.qammunity.org/2024/formulas/mathematics/college/pviyrcs9mtmc4n2qcymh3bkb4dtctlxol5.png)
Now, subtract this total from the initial 6 pounds:
![\[6 - (19)/(4) = (24)/(4) - (19)/(4) = (5)/(4) \text{ pounds}\]](https://img.qammunity.org/2024/formulas/mathematics/college/u422jx3qjmm9p23iqm8e36d4pek6f99uvx.png)
Therefore, after making the mugs, there is
pounds of clay left over.