# Rate

A rate is a type of ratio that compares two quantities expressed in different units. There are many different types of rates that we encounter in everyday life.

Examples

1. 3 pens cost \$1.19. Items (pens) are one kind of unit and money (\$1.19) is another.
2. A jet may travel at the rate of 1,000 miles per hour. Distance (miles) is one kind of unit and time (hour) is another.
3. The speed of light in space is 186,000 miles per second. Distance (miles) is one kind of unit and time (second) is another.
4. The rate of interest on a loan for a new car was advertised as 5.9% per year. This is a more complex kind of rate. It compares a rate (percent, or parts per hundred) with another kind of unit, time (year).

## Rate per unit time

One of the most common type of rates you may encounter is some measure over a period of time. Below are some examples:

• Speed - how far you travel per hour on your bike
• Frequency - how many times your heart beats in a minute
• Volumetric flow rate - the volume of fluid that comes out of your tap per second
• Power - the amount of energy delivered to your residence per hour

## Rates related to economics/finance

Below are just a few of many finance related rates we have experience with at some point in our lives.

• Exchange rate - how much one currency, such as the US dollar is worth relative to another, like the Canadian dollar.
• Inflation rate - how much general prices change during the year relative to the beginning
• Interest rate - the price paid by someone borrowing money for use of the money

## Other mathematical concepts related to rate

Slope is a concept you may already have encountered. It describes the direction and steepness of a line. It is the ratio of vertical change to horizontal change of a line. Slope is also later used in calculus, where the slope of the line tangent to a curve is the derivative of the function at that point. The derivative is also referred to as the "instantaneous rate of change."