8. Fractions

Lesson

Being able to plot a fraction on a number line can help us compare fractions in this lesson. Let's try this problem as a review.

Plot \dfrac{1}{10} on the number line.

Worked Solution

Idea summary

When plotting a fraction on a number line:

the denominator (bottom number) shows how many parts there should be between each whole number.

the numerator (top number) shows the number of parts to move to the right from the previous whole number.

This video looks at comparing fractions using area models.

Which fraction is smaller?

A

B

Worked Solution

Idea summary

When comparing fractions, if the denominators are the same, then we can compare the numerators.

The denominator also tells us how many parts make up one whole.

This video shows how to use number lines to compare fractions.

Think about the fractions \dfrac{3}{4} and \dfrac{4}{5}.

a

Plot the number \dfrac{3}{4} on a number line.

Worked Solution

b

Plot the number \dfrac{4}{5} on the number line.

Worked Solution

c

The two numbers can be shown on the same number line like this:

Which number is bigger?

A

\dfrac{3}{4}

B

\dfrac{4}{5}

Worked Solution

Idea summary

To plot a proper fraction on a number line:

Start the number line at 0 and end it at 1.

Divide the number line into the number of parts equal to the denominator.

From 0, count to the right the number of parts equal to the numerator.

Plot the point.

To compare fractions on a number line, the fraction furthest to the right is the largest.

What about mixed numbers or improper fractions? This video shows us how to compare using these.

Compare the two fractions by using the greater than (\gt) or less than (\lt) symbol. 1 \dfrac{8}{9} \, ⬚ \, 1 \dfrac{4}{9}

Worked Solution

Idea summary

To plot a mixed number on a number line:

Start the number line at the whole number and end it at the next whole number.

Divide the number line into the number of parts equal to the denominator.

From the start, count to the right the number of parts equal to the numerator.

Plot the point.

To plot an improper fraction on a number line, convert the improper fraction to a mixed number. Then follow the above steps.

represents, models and compares commonly used fractions and decimals