What do you know about ratios, rates and percentages?

Often, you may be aware that there are maximum speed limits in different places, such as school zones and main streets. The speed limits in these areas are often 50km/h. Many people read data in the news that describes a study where 1 in every 6 Canadians respond to something. We can describe population growth as increasing 0.3% each year. Each of these are examples of rates, ratios, and percents. Although they might seem very different, they’re actually very similar and very much related. What do you know about percentages? What do you know about ratios? What do you know about rates?

Ratios, fractions and percents

Let’s review the relationship between ratios, fractions and percentages first before we begin our task for today.

Ratios

Ratios compare one part to another. For example, the ratio of large tip to fine tip in a marker pack is 8:12 and represents a part to part ratio. Given that information, I know that there are 20 markers in the package, 8 are large tip and 12 are fine tip. For every 8 large tip markers there will be 12 fine tip markers. I could also record a ratio that compare the large tip to all the markers 8:20, 8 out of the 20 markers in total are large tip, this is a part to whole ratio. Ratios could also be represented as a fraction form, 8:20 can be written as $\frac{8}{20}$.

Since ratios can be represented as a fraction, we can create an equivalent fraction out of 100 to generate a percentage that matches our fraction.

Equivalent fractions

To create an equivalent fraction, you multiply the denominator and numerator by the same number $\frac{1}{2}$ is equivalent to $\frac{2}{4}$ because when you multiply both the numerator and denominator by 2, you get $\frac{2}{4}$. This is also the case when you multiply the numerator and denominator of $\frac{1}{2}$ by 4, you get $\frac{4}{8}$. The fraction $\frac{1}{2}$ is also equivalent to $\frac{4}{8}$. The following image represents these equivalencies.

Equivalent ratios and rates

Creating equivalent rates and ratios is basically the same as creating equivalent fractions. You first convert your ratio or rate into a fraction, then multiply or divide your numerator and denominator by the same amount. The following image represents this rule.

Task 1: Physical activity in Canada

The following table contains data that describes the self-reported physical activity of Canadian adults by age group. Convert the data into one standard form so it’s easier to interpret and understand the comparison (e.g., fractions, percents, or ratios). What do you notice about these numbers? Using this data, could you make any recommendations to improve the physical fitness of adults?

Source: Physical activity, self reported, adult, by age group (statcan.gc.ca)

Task 2: Future trends in physical activity

If we know that the physical activity of all adult age groups has decreased by 2% since 2015, what could the percentage of adults doing physical activity be like in 5 years if this trend continues? What could it be in 10 years? Show the rationale for your thinking.

Road trip

Real World Problem

Imagine a family is driving around the city or going on a road trip. Use an online map (or another distance measuring tool) to determine the distance and speed limit to outline the routes to two different destinations. Estimate how long each route will take the family to get to their destination and determine which route would be best under different circumstances. Choose places, locations and distances that are interesting to you to compare, or you can use the ones listed in the example.

Here’s an example:

There are 2 drives they can do outside the city. The speed limit is important to note. If they were driving at 50km/h and their friend lived about 20 km away, I could compare this to driving on the highway at 90 km/h for a relative who lives 250 km away.

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.

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