Aimathic
Login | English | Deutsch

Free math worksheets

Build your own math worksheets from 30,000+ problems for grades 3 to 12, from fractions to AP Calculus. Every problem comes with step-by-step solutions.

Line plots with fraction data

Click problems to add them to your worksheet.

5511844
The line plot shows the lengths of craft sticks measured to the nearest \(\frac14\) inch. The horizontal axis uses decimal equivalents of the fractional measurements. How many sticks are \(2\frac14\) inches long?
Figure for problem 551184

Hints

- Convert \(2\frac14\) to its decimal equivalent on the graph. - Each X-mark represents one craft stick. - Count only the stack above \(2.25\).

Solution

1. \(2\frac14=2.25\), so use the tick at \(2.25\). 2. There are \(4\) X-marks above \(2.25\).

Answer

\(4\) sticks
5522424
The line plot shows ribbon lengths measured in quarter-inch units. Each number on the horizontal axis tells how many \(\frac14\)-inch units long a ribbon is. How many ribbon pieces are represented altogether?
Figure for problem 552242

Hints

- Each X-mark represents one measurement. - Count every X-mark, not just the tallest stack. - You can total the stack heights after counting each stack.

Solution

1. Each X-mark represents one ribbon piece. 2. There are \(2+1+3+1=7\) X-marks altogether.

Answer

\(7\) ribbon pieces
5511854
The line plot shows seedling heights measured to the nearest \(\frac12\) inch. The horizontal axis uses decimal equivalents. Which height occurs most often, and how many more seedlings have that height than are \(5\) inches tall?
Figure for problem 551185

Hints

- Find the tallest stack first. - Then count the X-marks at \(5\) inches. - Compare the two frequencies, not the two measurements.

Solution

1. The tallest stack is at \(6.5\) inches, with \(5\) seedlings. 2. The stack at \(5\) inches has \(2\) seedlings. 3. The difference is \(5-2=3\) seedlings.

Answer

\(6\frac12\) inches; \(3\) more seedlings
5511864
The line plot shows pieces of cord measured to the nearest \(\frac18\) yard. The horizontal axis uses decimal equivalents. Add the least length that occurs and the greatest length that occurs.
Figure for problem 551186

Hints

- Find the leftmost and rightmost ticks that actually have X-marks. - Rewrite both measurements in eighths before adding. - Check whether the fractional parts combine to a whole yard.

Solution

1. The least plotted length is \(\frac58\) yard. 2. The greatest plotted length is \(1\frac38\) yards. 3. \(\frac58+1\frac38=2\) yards.

Answer

\(2\,\text{yd}\)
5511874
The line plot shows shell lengths measured to the nearest \(\frac14\) inch. The horizontal axis uses decimal equivalents. What is the range of the shell lengths?
Figure for problem 551187

Hints

- Use only ticks with X-marks when finding the least and greatest values. - Subtract the least measurement from the greatest measurement. - Rewrite the measurements in fourths before subtracting.

Solution

1. The least plotted length is \(2\frac12\) inches. 2. The greatest plotted length is \(4\frac14\) inches. 3. The range is \(4\frac14-2\frac12=1\frac34\) inches.

Answer

\(1\frac34\,\text{in.}\)
5511904
A carpenter measured the widths of ten wood strips to the nearest \(\frac14\) inch: <table> <tr><th>Width</th><th>Number of strips</th></tr> <tr><td>\(1\frac12\,\text{in.}\)</td><td>2</td></tr> <tr><td>\(1\frac34\,\text{in.}\)</td><td>1</td></tr> <tr><td>\(2\,\text{in.}\)</td><td>4</td></tr> <tr><td>\(2\frac12\,\text{in.}\)</td><td>2</td></tr> <tr><td>\(2\frac34\,\text{in.}\)</td><td>1</td></tr> </table> Draw a line plot of the data. Include every quarter-inch tick from \(1\frac12\) inches through \(2\frac34\) inches, even if no strip has that width.

Hints

- Mark every quarter-inch value in the required interval before plotting the data. - Use the frequency column to decide how many X-marks belong at each listed width. - Do not remove ticks just because no strip has that measurement.

Solution

1. Draw a number line from \(1\frac12\) to \(2\frac34\) inches with quarter-inch spacing. 2. Place \(2\) X-marks at \(1\frac12\), \(1\) at \(1\frac34\), \(4\) at \(2\), \(2\) at \(2\frac12\), and \(1\) at \(2\frac34\). 3. Leave the unused quarter-inch ticks with no X-marks.

Answer

A correct line plot has frequencies \(2,1,4,2,1\) at \(1\frac12,1\frac34,2,2\frac12,2\frac34\) inches, with empty ticks at the unused quarter-inch values.
5511884
The line plot shows seven jump distances measured to the nearest \(\frac12\) foot. One eighth jump distance was accidentally erased from the record. The total distance of all eight jumps was \(52\) feet. What was the erased jump distance?
Figure for problem 551188

Hints

- Read every plotted jump distance, including repeated values. - Find the total of the seven visible jumps. - Compare that subtotal with the stated total for all eight jumps.

Solution

1. Add the seven distances shown: \(5+5\frac12+6+6+7+7\frac12+8=45\) feet. 2. The erased jump must make the total \(52\) feet. 3. \(52-45=7\) feet.

Answer

\(7\,\text{ft}\)
5511894
A class recorded these button diameters, in inches: \(\frac38,\frac12,\frac12,\frac58,\frac78,1\). The line plot shown was made from the data, but exactly one X-mark was placed on the wrong tick. Which X-mark should be moved, and where should it go?
Figure for problem 551189

Hints

- Tally the raw measurements before looking for the mistake. - Compare each required frequency with the plotted frequency. - One position has one mark too many and another has one mark too few.

Solution

1. The data require one mark at \(\frac38\), two at \(\frac12\), one at \(\frac58\), one at \(\frac78\), and one at \(1\). 2. The plot shows one mark at \(\frac38\), one at \(\frac12\), two at \(\frac58\), one at \(\frac78\), and one at \(1\). 3. Move one X-mark from \(\frac58\) inch to \(\frac12\) inch.

Answer

Move one X-mark from \(\frac58\,\text{in.}\) to \(\frac12\,\text{in.}\).
5522434
The line plot shows board lengths measured in eighth-foot units. Each number on the horizontal axis tells how many \(\frac18\)-foot units long a board is. The two shortest boards are joined end to end. How much longer is their combined length than the longest board?
Figure for problem 552243

Hints

- Identify the two leftmost X-marks and write each horizontal-axis value as that many eighths of a foot. - Add those two board lengths before making the comparison. - The rightmost X-mark is the longest board; subtract its length from the combined length.

Solution

1. The two shortest X-marks are at \(5\) and \(7\) eighth-foot units, so the two shortest boards measure \(\frac58\,\text{ft}\) and \(\frac78\,\text{ft}\). 2. Their combined length is \(\frac58+\frac78=\frac{12}{8}=1\frac12\,\text{ft}\). 3. The rightmost X-mark is at \(10\) eighth-foot units, so the longest board measures \(\frac{10}{8}=1\frac14\,\text{ft}\). 4. The difference is \(1\frac12-1\frac14=\frac14\,\text{ft}\).

Answer

\(\frac14\,\text{ft}\)
5511914
The line plot shows the lengths of metal pins measured to the nearest \(\frac18\) inch. The horizontal axis uses decimal equivalents. Every pin longer than \(1\frac14\) inches will be trimmed to exactly \(1\frac14\) inches. How much metal will be trimmed off altogether?
Figure for problem 551191

Hints

- Identify only the stacks to the right of \(1\frac14\) inches. - For each affected measurement, find how much one pin must be shortened. - Multiply each shortening by the number of pins in that stack before combining the amounts.

Solution

1. Pins longer than \(1\frac14\) inches are at \(1\frac38\), \(1\frac12\), and \(1\frac58\) inches. 2. Two \(1\frac38\)-inch pins each lose \(\frac18\) inch, for \(\frac14\) inch total. 3. One \(1\frac12\)-inch pin loses \(\frac14\) inch. 4. Two \(1\frac58\)-inch pins each lose \(\frac38\) inch, for \(\frac34\) inch total. 5. The total trimmed length is \(\frac14+\frac14+\frac34=1\frac14\) inches.

Answer

\(1\frac14\,\text{in.}\)

All problems may be used, copied and printed free of charge for school and tutoring, including paid tutoring. Commercial adaptations as well as publication or redistribution on the internet are not permitted.

Building free math worksheets