Fair sharing

When something is shared equally, each part of the total has to be the same amount.

Fractions

A fraction is a number that shows equal parts of a whole unit or set of units.

Let’s examine the following image to learn different ways to represent a fraction.

Parts of a fraction

When we work with fractions to solve word problems, it is important to know what the parts of the fraction represent. The two parts of a fraction are the numerator and the denominator.

Denominator

The denominator represents the total parts of the whole.

You will now explore the following Homework Zone: Mathematics segment entitled “All About the Denominator” to learn about the importance of the denominator in a fraction. 

Numerator

The numerator represents the number of parts in the fraction.

You will now explore the following Homework Zone: Mathematics segment entitled “All About the Numerator” to learn about the importance of the numerator in a fraction.

Equivalent fractions

Equivalent fractions mean they are equal.

Fractions are equivalent if:

• they are the same size
• they are at the same point on the number line
• have the same value or amount

Students are working in groups to solve a problem. The teacher says that: a group of two working together will share one piece of paper, four students working together will share two pieces of paper. The teacher also says that eight students working together will share four pieces of paper. The teacher says this is a "fair share" because all students will get the same amount of paper.

Are they correct? Show you thinking using pictures, numbers and words.

Comparing fractions

We can more easily compare fractions with the same denominator.

You will now explore the following Homework Zone: Mathematics segment entitled “Comparing fractions” to learn more about comparing fractions with the same denominator.

Creating equivalent fractions to compare fractions

When denominators are different, it is more difficult to compare fractions. So, we can find equivalent fractions, and then we can compare the fractions.

The following examples show how we can separate each fraction into more equal parts that have the same value.

Example 1

By separating each third into two more equal parts, we get a total of six equal parts. Of these, two are shaded, so we know that $\frac{1}{3}$ is equivalent to $\frac{2}{6}$ .

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Example 2

By separating each fourth into two more equal parts, we get a total of eight equal parts. Of these, six are shaded, so we know that $\frac{3}{4}$ is equivalent to $\frac{6}{8}$ .

If we separate each fourth into three equal parts, we get a total of twelve equal parts. Of these, nine are shaded, so we know that $\frac{3}{4}$ is equivalent to $\frac{9}{12}$ .

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Example 3

By separating each fifth into two more equal parts, we get a total of ten equal parts. We can count on the number line to show that $\frac{3}{5}$ is equivalent to $\frac{6}{10}$ .

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Solving fair-share problems

Solve the problem below.

There are four sandwiches for six children to share equally. How much of a sandwich will each child get?

Here are two possible solutions. Which is correct? Are they both correct?

Solution A

We know that there are six children to share four sandwiches, so we can use a box to represent each sandwich as shown in the following image.

We can divide the box into six equal parts to represent each child. We can then number each part from one to six and count that each number is repeated four times.

So, we can conclude that each child will get $\frac{4}{6}$ of the sandwich.

Solution B

We know that there are six children to share four sandwiches, so we can use a box to represent each sandwich as shown in the following image.

We can divide the box into three equal parts to represent each child. We can then number each part from one to six until all parts are numbered. We can count that each number is repeated two times.

So, we can conclude that each child will get $\frac{2}{3}$ of the sandwich.

Both solutions are correct because $\frac{4}{6}$ and $\frac{2}{3}$ are equivalent fractions and show the same amounts.

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Let's practice!

Work on the next problem. Then, share your thinking in your notebook.

Reader #1 has read $\frac{2}{5}$ of her book. Reader #2 has read $\frac{4}{10}$ of her book. Reader #2 believes she has read more than Reader #1. Is she correct?

Use pictures, numbers, and words in your solution.

Problem solving

Reflection

How do you feel about what you have learned in this activity?  Which of the next four sentences best matches how you are feeling about your learning? Press the button that is beside this sentence.

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