Exercise 47 Page 116

Let's begin by reviewing the definitions of ratio and rate. A ratio is the comparison of two numbers by division. There are a few ways to express the ratio of $x$ and $y.$ A rate, on the other hand, is a specific type of ratio. It is the ratio of measurements having different units of measure. In the table below are a few examples of each.

Ratio	Rate
There are $5$ boys and $7$ girls in a class. The ratio of boys to girls is $\frac{5}{7}.$	A car burns $20$ liters of gas for every $200$ km traveled. Gas is burned at a rate of $\frac{2\text{ liters}}{200\text{ hours}}.$
There are $3$ teachers for every $12$ children at a school. The ratio of teachers to children is $\frac{3}{12}.$	A runner runs $2$ km in $20$ minutes. The rate at which the runner runs is $\frac{2\text{ km}}{20\text{ minutes}}.$
There are $100$ cars for every $150$ people in a city. The ratio of cars to people is $\frac{100}{150}.$	A woman works $60$ hours every $3$ weeks. The rate at which she works is $\frac{60\text{ hours}}{3\text{ weeks}}.$

As we can see, both ratios and rates compare two numbers using division. However, rates compare two measurements that involve different units of measure.