Lesson 5 — Activity 1: Introducing Ratios and Rates

Getting Ready

Have you ever been compared to a friend? Have you ever compared hamburgers from two fast food restaurants? People have a tendency to compare things. One way of comparing numbers is by using ratios. In this activity, you will learn how to use different rates and ratios.

Courtesy of Pixabay

Ratios help us compare two numbers of the same type. Think of a typical classroom. There may be 22 students and 1 teacher. Another way to say this is there are 22 students for every 1 teacher. This is a ratio.

A ratio can be written four different ways.

  • as a fraction: 22/1
  • or like this: 22 to 1
  • or like this: 22:1
  • or like this: twenty-two to one

These four different ways of writing 22 students to 1 teacher all mean the same thing.

Let's look at another example.

The school cafeteria conducted a survey of students to determine their favourite fruit. The results are in the circle graph below.

Answer the questions below based on the graph.

1. What is the ratio of plums to apples as the favourite fruit of students?
2. What is the ratio of pears to grapes as the favourite fruit of students?
3. What is the ratio of cherries to oranges as the favourite fruit of students?

1. The ratio of plums to apples is 8:12.
2. The ratio of pears to graphs is 15:10.
3. The ratio of cherries to oranges is 49:6.

Answer these questions to learn more about ratio.

What is a ratio?

A ratio is a comparison of two numbers.

A rice package has the following instructions: "one cup of rice for every 2 cups of water." What are 3 ways to write this ratio of 1 cup of rice for every 2 cups of water?
  • 2:1
  • 2 to 1
  • 2/1

Reduce the ratio 9:3 to its lowest terms by finding the greatest number that divides into both numbers.

3:1 (3 divides into 9 three times and 3 divides into 3 one time)

A ratio is great for comparing two numbers of the same type. For example, ratios can be used to show how many peanuts to cashews in a bowl.

The ratio 5 to 1 means 5 peanuts and 1 cashew. The units are the same since they are both kinds of nuts and you can count them individually.

What do you do when you need to compare numbers of different types? For example, how do you compare the distance a car travels in kilometres to the time it takes to get somewhere?

When the units or types are different, we use a special ratio called a RATE .
A rate is a comparison of two numbers with DIFFERENT UNITS. We have to write the units with the numbers. When using rates, we are usually comparing units of time.

For example:

    100 km driven in 1 hour.

The rate is written like this:

  100 km  
1 hour

But it is most often seen written like this 100 km/1 hr.

Other examples of rates that compare units of time include:

  • metres per second
  • dollars per hour
  • meals per day
  • games per year

Note, when writing rates, the bottom number will always be the period of time as follows:

Courtesy of ADLC


Try this!

Digging Deeper

Click on the Play button below to watch a video on rates and ratios.