Exactly 4

Exactly 1/6 of the kids are playing on the playground. Exactly 3/5 of the kids are playing soccer. Jack adds 1/6 + 3/5 to find the total fraction of kids at the park playing on the playground or playing soccer. Is he correct?

Result

x=

Yes

No

Step-by-step explanation:

$$\begin{gathered} a=\frac{1}{6}+\frac{3}{5}=\frac{5}{30}+\frac{18}{30}=\frac{5+18}{30}=\frac{23}{30}\doteq 0.7667 \\ b=\frac{1}{6}\cdot \frac{3}{5}=\frac{1\cdot 3}{6\cdot 5}=\frac{3}{30}=\frac{1}{10}=0.1 \\ c=a-b=\frac{23}{30}-\frac{1}{10}=\frac{23}{30}-\frac{3}{30}=\frac{23-3}{30}=\frac{20}{30}=\frac{2}{3}\doteq 0.6667 \\ a\ne c \\ \frac{23}{30}\ne \frac{20}{30} \\ x=0 \end{gathered}$$

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