Comparisons using number lines

Lesson

You may have already learned about plotting fractions on a number line.

To plot fractions on a number line we:

• divide the line into the number of parts indicated by the denominator.
• count along the number of parts indicated by the numerator.

The further along the number line the point is, the larger the fraction.

Unit fractions

Unit fractions are fractions with a numerator of one. Watch this video to learn about comparing unit fractions using a number line.

Try these questions for yourself.

Worked examples

Question 1

Think about the fractions $\frac{1}{8}$18 and $\frac{1}{10}$110.

1. Plot the number $\frac{1}{8}$18 on the number line.

2. Plot the number $\frac{1}{10}$110 on the number line.

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

Which number is smaller?

$\frac{1}{8}$18

A

$\frac{1}{10}$110

B

Question 2

Using the given number lines, arrange the following fractions in descending order.

$\frac{1}{3}$13, $\frac{1}{6}$16, $\frac{1}{4}$14, $\frac{1}{2}$12

1. $\editable{},\editable{},\editable{},\editable{}$,,,

Non-unit fractions

Non-unit fractions are fractions that have a numerator other than one. Watch this video to learn about comparing non-unit fractions using a number line.

Try these questions for yourself.

Worked examples

Question 3

Think about the fractions $\frac{3}{4}$34 and $\frac{4}{5}$45.

1. Plot the number $\frac{3}{4}$34 on the number line.

2. Plot the number $\frac{4}{5}$45 on the number line.

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

Which number is bigger?

$\frac{3}{4}$34

A

$\frac{4}{5}$45

B

Question 4

Think about the fractions $\frac{7}{8}$78 and $\frac{8}{9}$89.

1. Plot the number $\frac{7}{8}$78 on the number line.

2. Plot the number $\frac{8}{9}$89 on the number line.

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

Which number is smaller?

$\frac{8}{9}$89

A

$\frac{7}{8}$78

B

Fractions in words

Being able to look at number lines and describe them in many ways shows a good understanding of fractions. Sometimes the fractions can be written in words, so $\frac{1}{8}$18 is written as "one eighth."

Try this question for yourself.

Worked example

Question 5

Using the given number lines, select all correct statements from the following.

1. One quarter is greater than one eighth

A

Three quarters is greater than seven eighths

B

Seven eighths is greater than three quarters

C

One quarter is equal to one eighth

D

Remember!

We use the denominator to divide the number line into equal parts.

We use the numerator to select the number of parts.

The further along the number line, the larger the fraction.

Outcomes

5.NN1.05

Represent, compare, and order fractional amounts with like denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, number lines) and using standard fractional notation