Question

If 2/5 of the macaroni and cheese provides 16 pieces to the table,how many pieces were in the pan when it was full? Support you answer with models.

Answer 1

Bearing in mind that a whole will be 5/5, so the full pan is 5/5.

$\bf \begin{array}{ccll} macaroni&pieces\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{2}{5}&16\\\\ \frac{5}{5}&p \end{array}\implies \cfrac{\quad\frac{2}{5} \quad }{\frac{5}{5}}=\cfrac{16}{p}\implies \cfrac{2}{5}\cdot \cfrac{5}{5}=\cfrac{16}{p} \\\\\\ \cfrac{2}{5}=\cfrac{16}{p}\implies 2p=80\implies p=\cfrac{80}{2}\implies p=40$