From the information provided by the statement, you know that
*Ann draws 2/16 of the playground
*Susan draws 6/16 of the playground because she draws 3 times as much as Ann so
[tex]3\cdot\frac{2}{16}=\frac{3}{1}\cdot\frac{2}{16}=\frac{6}{16}[/tex]*Louise draws 3/16 because she draws half as much as Susan, so
[tex]\frac{1}{2}\cdot\frac{6}{16}=\frac{6}{32}=\frac{2\cdot3}{2\cdot16}=\frac{3}{16}[/tex]*Sam draws 2/16 because she draws 1 less section than Louise
[tex]\frac{3}{16}-\frac{1}{16}=\frac{2}{16}[/tex]Now, let x be the fraction of the playground that still needs to be drawn. Then, you have
[tex]\begin{gathered} \frac{2}{16}+\frac{6}{16}+\frac{3}{16}+\frac{2}{16}+x=\frac{16}{16} \\ \text{ Add similar terms} \\ \frac{13}{16}+x=\frac{16}{16} \\ \text{ Subtract }\frac{13}{16}\text{from both sides of the equation} \\ \frac{13}{16}-\frac{13}{16}+x=\frac{16}{16}-\frac{13}{16} \\ x=\frac{3}{16} \end{gathered}[/tex]Therefore, 3/16 of the playground still needs to be drawn.
