Fraction Line Plots Examples: 45 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Fraction Line Plots.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A fraction line plot displays fractional data by placing marks above a number line scaled in fractional units (halves, quarters, eighths, etc.).

Like a regular line plot, but the number line uses fractions instead of whole numbers — each mark shows a measurement like $\frac{3}{4}$ inch.

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How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A fraction line plot shows how many data values land at each fractional mark.

Common stuck point: The procedure for fraction line plots is the easy part; the trap is connecting the dots like a line graph. Asking "Does each dot represent one data value at a number-line location?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Does each dot represent one data value at a number-line location?

Worked Examples

Example 1

medium

Ribbon lengths (in):

\frac12

(×2),

1

(×1),

1\frac12

(×3). Find the total ribbon length.

Answer

6\text{ in}

First step

Sum:

2\cdot\frac12 + 1\cdot1 + 3\cdot\frac32

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Example 2

medium

Show how to re-scale a halves plot to eighths: where do dots at

\frac12

and

\frac34

land?

Example 3

medium

Bookmarks measured:

\frac34

(×4) and

1\frac14

(×4). Find the mean.

Example 4

hard

Eight pieces of yarn measure

\frac38

in (×3),

\frac58

in (×3),

\frac78

in (×2). If you tied them together end to end, what is the total length?

Example 5

hard

Pour 6 cups of water equally into 8 jars whose levels are shown on a line plot. What level (in cups) does each jar hold?

Example 6

challenge

Lina's plot shows 4 dots at

\frac14

, 2 at

\frac12

, and 2 at

\frac34

. She'll add one more dot. Where must she add it so the mean stays exactly

\frac12

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

A line plot has dots at

\frac{1}{2}

: 3 dots. How many data points at

\frac{1}{2}

Each dot = one data point. How many data points are at 1/2?

Example 2

easy

On a fraction line plot, the ticks are halves. What does a dot above the 2nd tick after 0 represent?

Halves-scaled line plot. What value does a dot above the 2nd tick after 0 represent?

Example 3

easy

Dots:

\frac14

:2,

\frac24

:1,

\frac34

:3. How many data points total?

Add the dot counts. What is the total number of data points?

Example 4

easy

Which value occurs most often:

\frac14

:2,

\frac12

:5,

\frac34

:1?

The tallest stack is the mode. Which value occurs most often?

Example 5

easy

True or false: you connect line-plot dots with a line.

Example 6

easy

How many eighths are between 0 and 1 on a line plot scaled in eighths?

Example 7

easy

Dots at

\frac34

inch: 4 measurements. What length was measured 4 times?

Four measurements land on the same tick. What length was measured 4 times?

Example 8

easy

A plot has values only at

\frac12

and

\frac34

. Is

\frac58

a data value?

Dots appear only at 1/2 and 3/4. Is 5/8 a data value?

Example 9

medium

Dots:

\frac14

:2,

\frac12

:3,

\frac34

:1. What fraction of data is at

\frac12

Example 10

medium

Lengths (in):

\frac12,\frac12,1,1,1

. Plotted, what is the total length of all pieces?

Example 11

medium

Data at

\frac14

:1,

\frac12

:2,

\frac34

:1. Find the range.

Example 12

medium

On an eighths scale, dots at

\frac28

and

\frac68

. Simplify these positions.

Example 13

medium

Three measurements:

\frac12,\frac34,\frac34

inch. Find the mean.

Example 14

medium

A plot shows 2 dots at

\frac14

and 2 at

\frac34

. What is the median?

Example 15

medium

Dots at

\frac18

:1,

\frac38

:2,

\frac58

:1. How many data points and where is the peak?

How many data points in total, and which value has the most dots?

Example 16

challenge

Measurements (in):

\frac12

(×2),

1

(×3),

1\frac12

(×1). Find the total length.

Example 17

challenge

Data at

\frac14

:3,

\frac12

:1,

\frac34

:0,

1

:0. After adding one dot at

\frac34

, does the mode change?

Example 18

challenge

A line plot has dots at

\frac14

(×3) and

\frac34

(×3), plus

n

dots at

\frac12

. The mean is

\frac12

. Find

n

Example 19

medium

Dots:

\frac13

:2,

\frac23

:4. What fraction of the data is at

\frac23

Example 20

medium

Values

\frac14,\frac14,\frac34

inch are plotted. What is their total length?

Example 21

easy

A line plot shows dots at

\frac{1}{4}

: 2 dots and at

\frac{3}{4}

: 5 dots. How many data points are there in all?

Add the dot counts at each position. How many data points are there in all?

Example 22

easy

On a line plot scaled in fourths, what fraction does the third tick after 0 represent?

Fourths-scaled line plot. What fraction does the 3rd tick after 0 represent?

Example 23

easy

On a halves-scaled line plot from 0 to 3, how many tick marks are there counting 0?

Example 24

easy

Pencil lengths (in):

\frac14,\frac14,\frac14

. How many data points are at

\frac14

Example 25

easy

How many sixteenths fit between 0 and 1 on a sixteenths line plot?

Example 26

easy

If a plot uses quarters but a child measures

\frac{5}{8}

in, where should the dot go?

Example 27

medium

Data:

\frac14

: 1,

\frac12

: 3,

\frac34

: 2. Find the median.

6 values ordered left to right. The 3rd and 4th both land on 1/2. What is the median?

Example 28

medium

On a fraction line plot, the smallest value is

\frac14

and the largest is

\frac{7}{8}

. Find the range.

Range = max − min. Find the range of this data.

Example 29

medium

Five seeds measured (in):

\frac14,\frac12,\frac12,\frac34,1

. Find the mean.

Example 30

medium

A plot has values at

\frac18,\frac38,\frac58,\frac78

each with 1 dot. Find the mean.

Four equally spaced values. Notice the pairs: 1/8+7/8

Example 31

medium

On a quarters line plot, dots at

\frac14

: 2,

\frac24

: 1,

\frac34

: 3. Find the mode and median.

Example 32

medium

Plot shows hand-spans (in):

5\frac14

: 1,

5\frac12

: 3,

5\frac34

: 2. How many students measured?

Dot counts show how many students had each hand-span. How many students in total?

Example 33

medium

A class measures pencil lengths to the nearest

\frac14

inch. What scale should the line plot use?

Example 34

medium

Plot has values

\frac12

: 2,

\frac34

: 2,

1

: 2. Find total of all values.

Example 35

hard

Lengths (in):

\frac14

(×2),

\frac12

(×3),

\frac34

(×4),

1

(×1). Find the mean.

Example 36

hard

Plot has data only at

\frac14

and

\frac34

. The median is

\frac12

. What's the relationship between the dot counts?

Example 37

hard

A line plot has these inch measurements:

\frac12,\frac12,\frac34,\frac34,1

. If the longest piece is cut to match the shortest, what's the new total length?

Example 38

hard

Plot of ribbon lengths:

\frac14

:1,

\frac12

:2,

\frac34

:1. After Sam adds a

\frac34

ribbon, does the mean increase, decrease, or stay the same?

Example 39

hard

Plot has measurements that sum to

5\tfrac12

inches over 11 dots. What is the mean?

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Related Concepts

Fractions Fraction on a Number Line Line Plots Adding Fractions with Unlike Denominators

Background Knowledge

These ideas may be useful before you work through the harder examples.

fractionsfraction on number lineline plots