Let's say there are $x$ skateboards in the shop. Thus, there are $x\cdot\frac{1}{4}=\frac{1}{4}x$ red skateboards and $\frac{2}{3}x $ red scooters. Since the number of red skateboards is equal to the number of red scooters, this means that, \begin{align*}
\frac{1}{4}x&=\frac{2}{3}x
\\\Rightarrow\qquad12\cdot\frac{1}{4}x&=12\cdot\frac{2}{3}x
\\\Rightarrow\qquad3x&=8x
\\\Rightarrow\qquad-5x&=0
\end{align*}Thus, $x=0.$ A skateboard and a scooter are both defined as non-zero, so both $x$ and $0$ are defined as zero. This means that there are zero skateboards, and hence, zero scooters, in the skate shop. Thus, the fraction of the total skateboards and scooters that are red is $\frac{0}{0}=\boxed{0.}$
In the FreeWheelin' Skate Shop, exactly 1/4 of the skateboards are red and exactly 2/3 of the scooters are red. If there are equal numbers of red skateboards and red scooters in the shop, what fraction of the total skateboards and scooters together are red? Express your answer as a simplified fraction.
anonymous
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