Minds On
Youth triathlon

An athlete is training for a youth triathlon race. A triathlon consists of three events: swimming, bicycling, and running (marathon).
As they train for the triathlon, their distances in kilometres are recorded as both improper fractions and mixed fractions.
Press the following tabs to access explanations of improper and mixed fractions.
An improper fraction has a numerator that is higher than the denominator.
Some examples are:
An mixed fraction is a whole number and a fraction combined.
Some examples are:
Triathlon training
The following table lists the training distances in kilometres for each event.
Use the Triathlon Part 1 Worksheet to record the missing distance either as a mixed or improper fraction.
Youth Event | Distance km (Mixed Fraction) | Distance km (Improper Fraction) |
---|---|---|
Marathon 1 | ||
Marathon 2 | ||
Triathlon 1 swim | ||
Triathlon 2 swim | ||
Bicycling 1 | ||
Bicycling 2 |
Press the ‘Activity’ button to access Triathlon Part 1 Worksheet.
Action
Equivalent fractions
Let’s explore how to find equivalent fractions!
Examine the following diagram that shows how is an equivalent fraction to In other words, the fractions are equal.
Two rectangles split into two parts each. One rectangle has two parts shaded; the second rectangle has one of two parts shaded. Labelled one and one over two. Equals. Two rectangles split into four parts each. One rectangle has four parts shaded; the second rectangle has two of four parts shaded. Labelled one and two over four.
Hint!
When finding an equivalent fraction for mixed fractions, the whole number stays the same!
We can also find equivalent fractions for improper fractions.
Examine the following diagram that shows how is an equivalent fraction to . In other words, the fractions are equal.
Three circles equally split into two parts each. The first two circles are shaded, and the third circle has one of two parts shaded. Labelled five over two. Equals. Three circles equally split into four parts each. The first two circles are shaded, and the third circle has two of four parts shaded. Labelled ten over four.
We can also show equivalent fractions using mixed fractions and their improper fraction form.
Examine the following diagram that shows how the mixed fraction of is an equivalent fraction to the improper fraction of .
Two rectangles split into eight parts each. The first rectangle is shaded, and the second rectangle has four of eight parts shaded. Number statement reads one and four over eight, equals, twelve over eight.
Let’s practice 1
Fraction expression reads one and four over eight equals a fraction with a blank numerator and a denominator of four. Below each number are two blank rectangles split into eight parts each, two rectangles on the left and two on the right.
Find the equivalent fraction to using quarters as the denominator.
Represent your answer using a tool of your choice, such as fraction strips, fraction circles, or relational rods.
Express your answer as both mixed fraction and an improper fraction.
Press ‘Answer’ to access a sample answer.
Fraction expression reads one and four over eight equals one and two over four or six over four. Below one and four over eight are two rectangles split into eight parts each. One rectangle is fully shaded, and the second rectangle has four parts shaded. Below the fraction expression one and two over four or six over four, are two rectangles split into eight parts each. One rectangle is fully shaded, and the second rectangle has four parts shaded. The rectangles are outlined to show how the rectangle could be split into four parts each.
As a mixed fraction:
As an improper fraction:
Let’s practice 2
Fraction expression reads two and one over two equals a fraction with a blank numerator and a denominator of eight. Below each fraction are three blank rectangles for each. The first fraction expression has two whole rectangles, and one rectangle split in two parts. The second fraction expression has three blank rectangles split into eight parts.
Find the equivalent fraction to uisng eights as the denominator.
Represent your answer using a tool of your choice, such as fraction strips, fraction circles, or relational rods.
Express your answer as both mixed fraction and an improper fraction.
Find the equivalent fraction thirty-seven twelfths in thirds and express in both mixed and improper fraction form.
Press ‘Answer’ to access a sample answer.
Fraction expression reads two and one over two equals a fraction with a blank numerator and a denominator of eight. Below each fraction are three blank rectangles for each. The first fraction expression has two whole rectangles, and one rectangle split in two parts. The second fraction expression has three blank rectangles split into eight parts.
As a mixed fraction:
As an improper fraction:
Test Your Skills
Test your skills
For the following two questions:
- find the equivalent fraction asked for
- represent your thinking using a tool or method of your choice
- express your answer as a mixed fraction and as an improper fraction
Question 1
Find the equivalent fraction to three and one twelfth, or thirty-seven twelfths, using thirds as the denominator.
Four rectangles split into twelve parts each. Three whole rectangles are shaded, and the fourth rectangle has one of twelve parts shaded. The fraction expression reads three and one over twelve, equals, thirty-seven over twelve.
Question 2
Find the equivalent fraction to twenty-six sixths, in using thirds as the denominator.
Five rectangles split into six parts each. Four whole rectangles are shaded, and the fifth rectangle has two of six parts shaded. The fraction expression reads twenty-six over six, equals, a fraction with a blank numerator and a denominator of six.
Consolidation
Triathlon part 2

Consider the triathlon event mentioned earlier in Minds On. Now use Triathlon Part 2 Worksheet to express the missing distances in improper and mixed fraction form. The first row has been completed for you.
Youth Event | Distance km (Mixed Fraction) | Distance km (Improper Fraction) | Distance km (Equivalent Mixed Fraction) |
---|---|---|---|
marathon 1 | twelfths: | sixths: 1 | |
marathon 2 | eighths: | twelfths: | |
triathlon 1 swim | fifths: | halves: | |
triathlon 2 swim | fourths: | halves: | |
bicycling 1 | ninths: | twelfths: | |
bicycling 2 | thirds: | sixths: |
Press the ‘Activity’ button to access Triathlon Part 2 Worksheet.
Student Success
Think
Choose two of the events from the activity “Triathlon Part 2 Worksheet”. For example, marathon 1 and bicycling 1.
Represent each of the three fractions for your chosen events using a tool of your choice. You may create diagrams, or use tools such as fraction strips, fraction circles, or relational rods.
Record your thinking in print or digitally. If possible, share your thinking with a partner.
Reflection
What did you learn in this lesson?
What was the most helpful part of this lesson? Why?
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.