5. Fractions

Lesson

Let's practice finding relatable denominators to help us in this lesson.

Which fraction has a denominator that is a multiple of the denominator in \dfrac{2}{4}.

A

\dfrac{6}{7}

B

\dfrac{8}{9}

C

\dfrac{7}{8}

Worked Solution

Idea summary

Look for common multiples between the denominators of two different fractions as this will help us to find common denominators.

We can compare 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.

We can compare improper fractions and mixed numbers.

Think about the fractions \dfrac{8}{6} and \dfrac{8}{3}.

a

Plot the number \dfrac{8}{6} on the number line.

Worked Solution

b

Plot the number \dfrac{8}{3} on the number line.

Worked Solution

c

Which fraction is bigger?

A

\dfrac{8}{3}

B

\dfrac{8}{6}

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.

Let's see now how to compare fractions that have different denominators.

Let's compare the fractions \dfrac{1}{2} and \dfrac{7}{8}.

a

Change \dfrac{1}{2} into eighths.

Worked Solution

b

Which of the following is the correct number sentence?

A

\dfrac{1}{2}<\dfrac{7}{8}

B

\dfrac{1}{2}=\dfrac{7}{8}

C

\dfrac{1}{2}>\dfrac{7}{8}

Worked Solution

Idea summary

When comparing fractions that are close in value, it helps for them to have a common denominator. Drawing a fraction rectangle shows the value of the fraction.