, 2020

Solution 1

Between 0 and 1.0, the number line is divided by tick marks (at $P$, $Q$, $R$) into 4 equal lengths. Thus, the distance between adjacent tick marks is $\frac{1.0-0}{4}=0.25$. Since $R$ is the 3$^{rd}$ tick mark moving right from 0, the value of $R$ is $3\times0.25=0.75$. Since $U$ is the 6$^{th}$ tick mark moving right from 0, the value of $U$ is $6\times0.25=1.5$. The value of $R$ divided by the value of $U$ equals $\frac{0.75}{1.5}=0.5$. Solution 2 The number $R$ is located at the 3$^{rd}$ tick mark to the right of 0. The number $U$ is located at the 6$^{th}$ tick mark to the right of 0. The tick marks are equally spaced along the number line, and so the value of $R$ must be half the value of $U$ (since 3 is half of 6). The value of $R$ divided by the value of $U$ equals $\frac12$ or 0.5.