Comparisons using number lines
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 shown by the denominator.
- count along the number of parts shown 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}{2}$12 and $\frac{1}{4}$14.
Plot the number $\frac{1}{2}$12 on the number line.
Plot the number $\frac{1}{4}$14 on the number line.
The two numbers can be shown on the same number line like this:
Which number is smaller?
$\frac{1}{4}$14
A$\frac{1}{2}$12
B
Question 2
Using the given number lines, arrange the following fractions in descending order.
$\frac{1}{3}$13, $\frac{1}{4}$14, $\frac{1}{5}$15, $\frac{1}{2}$12
$\frac{\editable{}}{\editable{}},\frac{\editable{}}{\editable{}},\frac{\editable{}}{\editable{}},\frac{\editable{}}{\editable{}}$,,,
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.
Plot the number $\frac{3}{4}$34 on the number line.
Plot the number $\frac{4}{5}$45 on the number line.
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{4}{3}$43 and $\frac{4}{4}$44.
Plot the number $\frac{4}{3}$43 on the number line.
Plot the number $\frac{4}{4}$44 on the number line.
The two numbers can be shown on the same number line like this:
Which number is bigger?
$\frac{4}{3}$43
A$\frac{4}{4}$44
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}{4}$14 is written as "one quarter."
Try this question for yourself.
Worked example
Question 5
Using the given number lines, select all correct statements from the following.
Three quarters is less than one half
AOne half is less than one quarter
BThree quarters is greater than one half
COne half is greater than one quarter
D
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.