Exercise 2 Page 156

A ratio of $3$ to $7$ indicates that for every $3$ of one thing, $7$ of another thing will occur. To compare the lengths of the two line segments, $\overline{AP}$ and $\overline{PB},$ let's say that they are made of units of length $x.$

We see here that $\overline{AP}$ is of length $3x,$ while $\overline{PB}$ is of length $7x,$ thus fulfilling our ratio of $3:7.$ If we combine these two segments into one collinear segment, we can form the segment $\overline{AB}.$