Minds On

Fractions with more than one whole

In a forest, a tree harvester is cutting down trees in the area and placing cut trees in piles.

Humans are using up the world’s natural resources at an unsustainable pace.

For example, people are cutting down forests at a faster rate than they can regrow.

At the rate we use resources each year, we are living as if we have 1.6 Earths when we only have 1 planet Earth.

Brainstorm

Brainstrom

Using pictures, numbers, or tools such as fraction strips or circles, algebra tiles, fraction blocks, relational rods, or fraction rods, how might you express 1.6 as a fraction?

Action

Improper fractions and mixed numbers

When we have whole items as well as fractions of items, we can represent this with numbers in a few different ways.

Let’s use the example from the Minds On section of “1.6 Earths.”

The value 1.6 means that we have 1 whole item and then we have 6 tenths of another item.

If we reduce this to lowest terms, we have 1 whole item and 3 fifths of another item.

Press ’Definition’ to access an explanation of simplest terms.

Lowest terms means finding the lowest equivalent fraction possible.

For example, 5 10 in lowest terms is 1 2 .

We can show this as:

Two rectangles, one is shaded and the second is split into ten equal parts with six parts shaded. Labelled one and six over ten. Equals. Two rectangles, one is shaded and the second is split into five equal parts with three parts shaded. Labelled one and three over five.

Let’s work with the value in its lowest terms of 1 3 5 .

There are two ways to express fractions that have more than a whole:

  • as a mixed fraction
  • as an improper fraction

Examine the following.

A rectangle is split into five pieces, and all five a shaded. It is labelled with one and the text “whole number”. A second rectangle is split into five pieces, and three of the five are shaded. It is labelled with three over five, and the text “fraction.” The next text shown is “Mixed Fraction.” Below this is the fraction expression one and three over five. Below is the text “Whole Number Mixed with fraction.” The next text show is “Improper Fraction.” Below this is the fraction expression eight over five, and the text “We count eight fifths.” Below this is the statement “Numerator Bigger than Denominator.”

Check out this video entitled "Improper Fractions and Mixed Numbers" to learn more about these two ways of expressing fractions that have more than a whole.

Your turn!

Let’s explore another example!

Did You Know?

Did You Know?

Did you know?

As the human population increases, our need for resources increases.

There is speculation that by 2050, the rate we use resources could equal two and a half Earths. Some have even speculated that we will require even more than this amount of resources.

Let’s express two and a half as a mixed fraction and as an improper fraction.

Examine the following:

On the left, the text reads “Mixed Fraction.” Below this is the fraction expression two and one over two. Followed by the text “Whole Number Mixed with fraction.” On the right, the text reads “Improper Fraction.” Below this is the fraction expression five over two. Followed by the text “We count five halves. Numerator Bigger than Denominator.” Below everything, there are three circles. The first two circles are shaded and have the fraction two over two inside them. The third circle is split in two, with one of two parts shaded and the fraction one over two inside.

Your turn to try!

Use the Expressing Improper and Mixed Fractions Worksheet to express different given amounts as both improper fractions and mixed fractions.

Expressing Improper and Mixed Fractions Worksheet

Press the Activity button to access the Expressing Improper and Mixed Fractions Worksheet.

Activity (Open PDF in a new tab)
Student Success

Student Success

Create a model or diagram

Select two to three of the fractions from the “Expressing Improper and Mixed Fractions Worksheet” and create a model or a diagram to illustrate the improper fraction or mixed fraction.

Also, consider using algebra tiles, fraction rods, or other tools available to show situations where we have more than one whole and a fraction amount.

Consolidation

Fractions in recipes

Measuring cup with the fractions one fourth, one half, and three fourths listed on the side of the cup.

We often see fractions used in recipes for baking or cooking.

Often the fractions listed in recipes are expressed as mixed fractions.

Sometimes, when we need to double or halve a recipe, it’s easier to express the fraction as an improper fraction so that it’s easier to compare and adjust the amounts.

Let’s practice comparing and ordering different fractions!

Test Your Skills

Test your skills

Explore the following groupings. For each, compare and order the amounts from least to greatest.

You may wish to use fraction rods, algebra tiles or diagrams to assist you.

  • three and one third, four thirds, two and two thirds
  • three and three fourths, seven halves, four and one twelfth
  • one and three fifths, two and two tenths, one and four tenths
  • ten thirds, three halves, eight sixths, five fourths

Explain how you decided which is the smallest amount, and which is the largest amount.

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.