# Rates

18.01.2019

Episode #2 of the course Everyday math by Jenn Schilling

Welcome back! In Lesson 2, we will expand on our knowledge of ratios to discuss rates, a special type of ratio. A rate is a comparison or relationship between two quantities that have different units. For example, miles per hour is a rate. First, we will discuss the math behind rates, then we will look at everyday examples of rates. Let’s get started!

The Math

Yesterday’s lesson focused on ratios, which we learned describe relationships between two or more quantities. Rates are a type of ratio in which the quantities have different units, such as miles per gallon. The term unit rate was also used in yesterday’s lesson, without much explanation. A unit rate is a rate for a single quantity and is particularly useful when making comparisons. For example, miles per hour is a unit rate; a car travels 25 miles per 1 hour. Rates can be scaled similarly to ratios, by multiplying both parts of the rate by the same quantity, so 25 miles per 1 hour turns into 50 miles per 2 hours.

Everyday Applications

There are a large number of rates used in everyday life. Whenever you travel, you use rates. Speed is a rate, as is fuel consumption. But you also use rates when determining how long it will take you to get to your destination based on the distance and the speed.

For example, if you are traveling 50 miles at an average rate of 40 miles per hour, how long will it take you to get to your destination? We know that 40 miles per 1 hour is a unit rate and that we are traveling 50 miles. To determine the time, we have to compute (1 hour/40 miles) × 50 miles, since we need to cancel out the miles units and end up with hours. The answer will be 50/40 hours, or 5/4 of an hour, which is equivalent to 1.25 hours, or 1 hour and 15 minutes.

Rates are also used when considering which route to take; the time to travel on each route depends on the speed (a rate) along that route.

Rates are seen in the workplace. Salaries can be broken down into pay rate of dollars per hour. The unemployment rate is the number of people unemployed compared to the number of people in the labor force. In project management, people keep track of the time it will take to complete different tasks; there is a rate at which work will be completed.

Money often involves rates. For example, when saving or investing, there is an interest rate or rate of return, which tells you how your money will grow as a percentage of how much money you save or invest. If you travel abroad, you will see an exchange rate, which tells you how much money you can get of another currency based on the currency of your home country.

Rates are even seen in fitness! Many people wear fitness trackers that show their heart rates, or beats per minute. This is actually a unit rate—the number of beats in one minute. When exercising, people often keep track of their pace in minutes per mile, another unit rate!

Many demographic statistics about countries, states, and cities are also presented as rates. For example, the birth rate shows the number of births per a certain population. The income per capita tells us the average income in a location and is determined by dividing total income by total population—another unit rate!

As you can see, rates are everywhere! It is important to understand rates to make sense of travel, work, money, fitness, and statistics. Understanding rates can also help you determine useful information, such as how long it will take you to travel to your destination.

I look forward to continuing our travels around everyday math tomorrow when we will dive into percentages!

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