Fractions on Line Plots

Content Fractions on Line Plots
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Learning text on the topicFractions on Line Plots

Line plots with fractions are a type of graph that shows data on a fractional number line. There are crosses created above the line to indicate the frequency of each unit of data.

Line Plots with Fractions – Example

In this example, we want to look at how much snow fell on different days. We have given data and the question is “What was the least amount of snow accumulated in a day?” With the help of using line plots, we can answer questions about the data.

Our line does not indicate the fraction for the day with the least amount of snow, so we need to count how many increments the line is divided into. The line plot is divided into eighths, so the denominator of our fraction will be 8. Our date is on the first increment on the line plot. The position of the increment is the numerator of the fraction we want to find out. Combining our data, we see that numerator 1 and denominator 8 are the fraction $\frac{1}{8}$, so the least amount of snow fallen in a day is $\frac{1}{8}$ feet!

If the question now commands us to find the greatest amount of snowfall accumulated in a day, we look at our line plot again and search for the rightmost entry on the line.

Using our counted increments from earlier, we see that the greatest amount of snowfall in a day accumulated up to $\frac{7}{8}$ feet of snow!

Line Plots with Fractions – Summary of Steps

Step # What to do
1 Look at the data on the line plot to understand
what you need to find.
2 If the line does not indicate the fraction you
are looking for, count the number of increments
on the line plot.
3 The number of increments total is the denominator
and the specific increment is the numerator

Line Plots with Fractions – Further Practice

Now it’s your turn! What is the difference in the amounts of snow between the greatest and the least?

Have a look at our interactive exercises and worksheets which will provide you with continued practice using line plots to record data and answer questions about the fractional data.

Fractions on Line Plots exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the learning text Fractions on Line Plots.
• How do we answers questions about fractions on a line plot?

Hints

The data needs plotting first before any further steps.

Solution
1. Plot data on the line plot.
2. Read questions and identify keywords that tell you what to look for on the line plot.
3. Count how many increments the line is divided into if the fraction is not listed on the line plot.
4. Simplify fractions as necessary.
• What was the greatest amount of snowfall accumulated in a day?

Hints

What does greatest amount of snow accumulation mean?

We are not looking for the most frequent amount of snow.

Which fraction on the line plot represents the most snowfall accumulation?

Fractions with the same numerator and denominator are equal to 1.

Solution
• The greatest amount of snowfall accumulated in a day was $\frac{8}{8}$.
• $\frac{8}{8}$ is simplified to 1.
• The answer is 1 foot.
• Find the difference.

Hints

What does difference mean?

To find the difference subtract the lowest (or least) amount from the greatest amount.

$\frac{1}{8}$ is the lowest amount and $\frac{8}{8}$ is the greatest amount.

Solution
• Difference means to subtract so you need to find the fractions on the line plot that represent the least and greatest amount of snowfall accumulation and subtract them.
• $\frac{1}{8}$ is the least.
• $\frac{8}{8}$ is the greatest.
• $\frac{8}{8}$ - $\frac{1}{8}$ is $\frac{7}{8}$.
• The answer is $\frac{7}{8}$.
• Combining fractions.

Hints

Simplify the fractions on the line plot to work out which fractions are less than $\frac{1}{4}$.

There are two fractions that need adding together.

Solution
• Combine means to add so you need to add the fractions that represent less than $\frac{1}{4}$ of a foot of snow on the line plot.
• $\frac{1}{8}$ is less than $\frac{1}{4}$ of a foot of snow.
• You add $\frac{1}{8}$ two times since there are two Xs above $\frac{1}{8}$ on the line plot.
• $\frac{1}{8}$ + $\frac{1}{8}$ = $\frac{2}{8}$
• $\frac{2}{8}$ is simplified by dividing the numbers by 2.
• The answer is $\frac{1}{4}$.
• Can you complete the number line?

Hints

Which data point on the line plot illustrates the least amount of e.g. snowfall accumulation?

Which data point on the line plot illustrates e.g. the most amount of snowfall accumulation?

Solution

The image pictured illustrates the fractions in order from least to greatest on the line plot.

• Can you solve the problem?

Hints

What does combine tell you to do?

What does the difference tell you to do?

Solution
• First, you need to find the combined amount for the days with less than a quarter of a foot of snow accumulation.
• Combine tells you to add.
• $\frac{1}{8}$ + $\frac{1}{8}$ = $\frac{2}{8}$
• Next, you need to find the difference in the amount of snow between the combined amount and the greatest.
• Difference means to subtract.
• $\frac{8}{8}$ - $\frac{2}{8}$ = $\frac{6}{8}$
• Finally, you need to simplify $\frac{6}{8}$ since 6 and 8 can be divided by 2.
• The answer is $\frac{3}{4}$.
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