Q47. - Algebra 1

Question

REASONING Compare and contrast ratios and rates.

Step-by-Step Solution

Answer

In ratio both numerator and denominator have the same kind of quantity thus it does not have a unit definition, whereas in the expression for rates, the quantities are different.

Step 1. Understanding the concept of ratio.

A ratio is a form of mathematical expression for the comparison of two quantities of the same kind. It is a relation that indicates how many times one quantity is equal to the other.

Alternatively, we can say that a Ratio is a number, which expresses one quantity as a fraction of the other.

For example, the ratio of 3 to 4 is 3 : 4 or $\frac{3}{4}$.

Step 2. Understanding the concept of rate.

A proportion is a comparison between two ratios, we can set a definite amount of a changing quantity to be the standard and use it to quantify how fast or slow this quantity is changing with respect to another quantity. 

For example rate of movement of a vehicle is expressed in miles per hour. Here both quantities; distance and time have been defined using a standard definition, distance is measured in miles and time in hours. So, for example, we can say a car is moving at 50 miles per hour.

Step 3. Compare and contrast the ratio with rates.

In ratio both numerator and denominator have the same kind of quantity thus it does not have a unified definition. Whereas in rates quantities are different for example in the rate of 50 miles per hour or 50mph, the fraction is being defined as $\frac{50}{1}$, here numerator is in miles and denominator is in hours.