Why It Matters: Ratios, Rates, Probabilities, and Averages

Why learn how to apply your knowledge of decimals to real world scenarios?

As the long jump coach at Hamilton Middle School, Jeffrey enjoys documenting his students’ progress and helping them set goals for future meets. It’s the start of a new track season, and Jeffrey’s working to establish expectations for the new long jumpers on the team. He thinks it might be helpful to find the average jump of three of his returning long jumpers so he can give the new jumpers an idea of what to aim for.

A female track athlete lunges for the sandpit.

At the first practice, Jeffrey asks Pedro, Elena, and Roy to show the new jumpers how it’s done. He records the following distances for their jumps:

  • Pedro: 5.51 meters
  • Elena: 5.87 meters
  • Roy: 3.92 meters

Now Jeffrey wants to find the mean distance they jumped. And because middle school students sometimes have a tough time visualizing distances written as decimals, he also wants to state the average in terms of a mixed fraction–for example, 4.25 meters is the same as 4 1/4 meters. How can Jeffrey calculate this?

After having the returning team members demonstrate, Jeffrey asks his new long jumpers to give it a try. Here are the distances he records for them:

  • 4.54 meters
  • 3.89 meters
  • 6.02 meters
  • 4.54 meters
  • 5.31 meters
  • 3.91 meters

With this set of data, Jeffrey wants to find the mean and mode of the jumps, rounded to the nearest tenth of a meter.

To come up with the data Jeffrey’s looking for, you’ll need to know the ins and outs of working with decimals. That’s what you’ll learn in this section.


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