Minds On

Decimals and fractions: What do they mean?

Reflect on the terms “decimals” and “fractions.” What do they mean? What is a decimal? What is a fraction? When would you decide to use a decimal instead of a fraction? When would you choose to use a fraction? Why are we learning about them together?

Action

Decimals and fractions

Decimals and fractions are very similar, because they are both representations that show parts of whole numbers. The visual provided might help you understand how they are related.

Let’s examine the following images that represent different parts of a whole as both fractions and decimals.

The images represent circles and rectangles that are divided into equal parts such a one quarter, one half, three quarters and one whole.

Decimals and fractions allow us to accurately describe parts of a whole. Decimals can easily be converted into fractions and vice versa. Let’s think about decimals in the place value chart. We know that when we use a place value chart with whole numbers, it is divided into hundreds, tens, and ones. When using decimals, the chart is further divided into tenths, hundredths and thousandths.

Representing decimals as fractions

Let’s explore the following decimal place value chart!

This place value chart is helpful because when we represent decimals as fractions the place value chart tells us more specifically about the fraction. For example, in the number 0.4, 4 is in the tenths spot, this tells us what the denominator of our fraction would be. In this case since 4 is in the tenths, our fraction is out of 10. The fraction that represents 0.04 would be 4 100     because the last number is in the hundredths, we know our fraction is out of 100. Here are some more examples and a visual representation of how decimals and fractions are related. The following images represent this learning as explained here.

Practice

Use your learning to convert the following decimals into fractions in your notebook, or in a method of your choice: 0.9, 0.04, 0.36 and 200.

Comparing fractions with the same denominator

An important part of comparing fractions is that they must have the same denominator. Access the video Homework Zone: Math – Comparing Fractions to learn how to compare the fractions once they have a common denominator.

Comparing and ordering decimals

Here are some quick steps to remind you how to compare and order decimals:

  1. Create a place value chart. Place the following numbers into the appropriate columns: 0.23, 0.08, 0.29, 0.378
  2. Compare the numbers in the greatest place value. First recognize the whole number. If there isn’t a whole number, you can refer to the tenths place.
  3. If you notice a set of numbers that are similar, refer to the next place value position to determine which number is greater.

Analyzing data

Now that you are developing a better understanding of fractions and decimals, use the following information in the following chart to compare and order the data. This chart contains the total area of each province and territory in Canada in relation to the total area of Canada.

Please order the data beginning with the Province or Territory that has the smallest total area. How could you represent this data in fractions? Is it easier to compare the data in its fraction or decimal form? Explain your thinking.

If you would like, you can complete this activity using TVO Mathify. You can also use your notebook or the following fillable and printable document.

Province / Territory Percentage of the area in decimals
Nunavut 0.21
Quebec 0.15
Northwest Territories 0.14
Ontario 0.11
British Columbia 0.09
Alberta 0.07
Saskatchewan 0.06
Manitoba 0.07
Yukon 0.07
Newfoundland and Labrador 0.04
New Brunswick 0.007
New Scotia 0.007
Prince Edward Island 0.007

Press the ‘TVO Mathify' button to access this interactive whiteboard and the ‘Activity’ button for your note-taking document. You will need a TVO Mathify login to access this resource.

TVO Mathify (Opens in new window) Activity (Open PDF in a new window)

Beyond the math

Who might find the numbers in the chart about the area of each province and territory in relation to the total area of Canada important? How can you use the data to take action and further investigate the ways resources or supports are being distributed? What inferences can you make or what questions do you have about the area, resources and land use in the provinces/territories?

Consolidation

Data in our daily lives

Complete either Task 1 or Task 2. You can record your work in an audio recording, on paper, or on a computer.

Task: Real world problem 1

Throughout the year, companies compete for consumers. Find similar products in a flyer such as computers, video games or food items and order their values from greatest to least. You can even compare the prices from different stores. In what ways does this comparison change where you shop or what you purchase? How does our learning from today’s lesson support you in this activity?

If you would like, you can complete this activity using TVO Mathify. You can also use your notebook or the following fillable and printable document.

Press the ‘TVO Mathify' button to access this interactive whiteboard and the ‘Activity’ button for your note-taking document. You will need a TVO Mathify login to access this resource.

TVO Mathify (Opens in new window) Activity(Open PDF in a new window)

Task: Real world problem 2

You may or may not realize, but there is a lot of data collected in sports. Choose a sport and collect some information that you are interested in analyzing. It could be anything from misses and buckets of basketball players on a team to the wins and losses of a soccer team compared to the rest of the league. Use fractions or decimals based on the researched data and order them. You should use a minimum of ten numbers.

If you would like, you can complete this activity using TVO Mathify. You can also use your notebook or the following fillable and printable document.

Press the ‘TVO Mathify' button to access this interactive whiteboard and the ‘Activity’ button for your note-taking document. You will need a TVO Mathify login to access this resource.

TVO Mathify (Opens in new window) Activity(Open PDF in a new window)

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.

I feel...

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

Connect with a TVO Mathify tutor

Think of TVO Mathify as your own personalized math coach, here to support your learning at home. Press ‘TVO Mathify’ to connect with an Ontario Certified Teacher math tutor of your choice. You will need a TVO Mathify login to access this resource.

TVO Mathify (Opens in new window)