Aimathic
Login | English | Deutsch

Grade 4 math worksheets

Build your own math worksheets from 35,000+ problems for grades 3 to 12, from fractions to AP Calculus. Every problem comes with step-by-step solutions.

Line plots with fraction data

Learning goals

  • Constructs line plots using fractional measurement scales.
  • Marks each fractional measurement at its position on the line plot.
  • Combines and compares fractional measurements represented on the plot.
  • Uses the plot to solve addition and subtraction problems with the data.

Click problems to add them to your worksheet.

Line plots with fraction data 1
The line plot shows craft-stick lengths measured to the nearest \(\frac{1}{4}\) inch. How many sticks are \(1\frac{3}{4}\) inches long?
Figure for problem 551184

Hints

- Follow the evenly spaced quarter-inch ticks to the requested measurement. - Each X-mark represents one craft stick. - Count only the X-marks directly above \(1\frac{3}{4}\).

Solution

1. Locate \(1\frac{3}{4}\) inches on the number line. 2. Count the stacked X-marks above that tick. There are \(2\) X-marks.

Answer

\(2\) sticks
Line plots with fraction data 2
The line plot shows ribbon lengths measured to the nearest \(\frac{1}{4}\) inch. What ribbon length occurs most often?
Figure for problem 552242

Hints

- Look for the tick with the greatest number of stacked X-marks. - Read the fractional measurement directly below that stack. - The question asks for a length, not the number of X-marks.

Solution

1. Find the tallest stack of X-marks. 2. The tallest stack is above \(2\) inches, so \(2\) inches is the most frequent length.

Answer

\(2\,\text{in}\)
Line plots with fraction data 3
The line plot shows ribbon lengths measured to the nearest \(\frac{1}{2}\) inch. Which length has exactly \(3\) ribbons?
Figure for problem 554862

Hints

- Count the X-marks in each stack until you find a stack of exactly \(3\). - Then read the measurement at the tick directly below that stack. - Give the measurement, not the frequency.

Solution

1. Find the stack containing exactly \(3\) X-marks. 2. That stack is above \(1\frac{1}{2}\) inches.

Answer

\(1\frac{1}{2}\,\text{in}\)
Line plots with fraction data 4
Each X stands for one measured bead. How many beads were measured altogether?
Figure for problem 558762

Hints

- Try counting one vertical stack at a time. - How can you check that you included both the shortest and longest lengths?

Solution

1. The plot has two Xs at one-quarter, one at one-half, and three at three-quarters. 2. The total is \(2+1+3=6\) beads.

Answer

\(6\) beads
Line plots with fraction data 5
Which ribbon length appears most often in the plot?
Figure for problem 558763

Hints

- Each height shows how many ribbons have one particular length. - Read the fraction directly below the tallest stack.

Solution

1. Find the tallest stack of Xs. 2. The stack at one-half inch has four Xs, more than at any other length.

Answer

\(\frac{1}{2}\,\text{in}\)
Line plots with fraction data 6
The line plot shows seedling heights measured to the nearest \(\frac{1}{2}\) inch. Which height occurs most often, and how many more seedlings have that height than are \(5\) inches tall?
Figure for problem 551185

Hints

- Read the measurement under the tallest stack. - Then find the stack above \(5\) inches. - Compare the two frequencies, not the two height values.

Solution

1. The tallest stack is above \(6\frac{1}{2}\) inches, with \(4\) X-marks. 2. The stack above \(5\) inches has \(2\) X-marks. 3. The difference is \(4 - 2 = 2\) seedlings.

Answer

\(6\frac{1}{2}\) inches; \(2\) more seedlings
Line plots with fraction data 7
The line plot shows cord lengths measured to the nearest \(\frac{1}{8}\) yard. Add the least length that occurs and the greatest length that occurs.
Figure for problem 551186

Hints

- Use the number-line positions to find the leftmost and rightmost measurements that actually occur. - Express both lengths in eighths before adding. - Check whether the fractional parts combine to a whole yard.

Solution

1. The leftmost tick with an X-mark is \(\frac{5}{8}\) yard. 2. The rightmost tick with an X-mark is \(1\frac{3}{8}\) yards. 3. Add: \(\frac{5}{8} + 1\frac{3}{8} = 2\) yards.

Answer

\(2\,\text{yd}\)
Line plots with fraction data 8
The line plot shows shell lengths measured to the nearest \(\frac{1}{4}\) inch. What is the range of the shell lengths?
Figure for problem 551187

Hints

- Find the leftmost and rightmost ticks that have X-marks above them. - Range means greatest measurement minus least measurement. - Rewrite the measurements with fourths if that helps you subtract.

Solution

1. The least represented length is \(2\frac{1}{2}\) inches. 2. The greatest represented length is \(4\frac{1}{4}\) inches. 3. The range is \(4\frac{1}{4} - 2\frac{1}{2} = 1\frac{3}{4}\) inches.

Answer

\(1\frac{3}{4}\,\text{in}\)
Line plots with fraction data 9
Aisha measured the widths of ten wood strips to the nearest \(\frac{1}{4}\) inch: <table> <tr><th>Width</th><th>Number of strips</th></tr> <tr><td>\(1\frac{1}{2}\,\text{in}\)</td><td>2</td></tr> <tr><td>\(1\frac{3}{4}\,\text{in}\)</td><td>1</td></tr> <tr><td>\(2\,\text{in}\)</td><td>4</td></tr> <tr><td>\(2\frac{1}{2}\,\text{in}\)</td><td>2</td></tr> <tr><td>\(2\frac{3}{4}\,\text{in}\)</td><td>1</td></tr> </table> The blank line plot has consecutive quarter-inch ticks. One tick is labeled A instead of with its measurement. What measurement belongs at A, and how many X-marks should be placed above each tick?
Figure for problem 551190

Hints

- Use the equal spacing on the blank number line to determine the value at A. - Then match each measured width to its tick. - A tick remains on the line plot even when its frequency is zero.

Solution

1. The ticks increase by \(\frac{1}{4}\) inch, so A is \(2\frac{1}{4}\) inches. 2. Use the table for the listed widths and include zero for the missing width. 3. From left to right, the frequencies are \(2, 1, 4, 0, 2, 1\).

Answer

A = \(2\frac{1}{4}\,\text{in}\) From left to right: \(2, 1, 4, 0, 2, 1\) X-marks.
Line plots with fraction data 10
The line plot shows pencil lengths measured to the nearest \(\frac{1}{4}\) inch. How many more pencils are \(2\frac{1}{4}\) inches long than \(1\frac{3}{4}\) inches long?
Figure for problem 554863

Hints

- Locate both specified fractional measurements on the number line. - Count the X-marks at each of those ticks. - Subtract the two frequencies, not the two length values.

Solution

1. There are \(4\) X-marks at \(2\frac{1}{4}\) inches and \(2\) X-marks at \(1\frac{3}{4}\) inches. 2. The difference is \(4 - 2 = 2\).

Answer

\(2\) more pencils
Line plots with fraction data 11
The line plot shows board lengths measured to the nearest \(\frac{1}{8}\) foot. What is the range of the lengths?
Figure for problem 554864

Hints

- Find the first and last ticks on the number line that have X-marks above them. - Range is greatest value minus least value. - Rewrite both measurements in eighths before subtracting.

Solution

1. The leftmost plotted measurement is \(\frac{5}{8}\) foot. 2. The rightmost plotted measurement is \(1\frac{1}{8}\) feet, which is \(\frac{9}{8}\) feet. 3. The range is \(\frac{9}{8} - \frac{5}{8} = \frac{1}{2}\) foot.

Answer

\(\frac{1}{2}\,\text{ft}\)
Line plots with fraction data 12
Seven strips have these widths: \(\frac{3}{8}\,\text{in}\), \(\frac{1}{2}\,\text{in}\), \(\frac{1}{2}\,\text{in}\), \(\frac{5}{8}\,\text{in}\), \(\frac{5}{8}\,\text{in}\), \(\frac{5}{8}\,\text{in}\), and \(\frac{7}{8}\,\text{in}\). The blank line plot has equally spaced eighth-inch ticks from \(\frac{3}{8}\) inch through \(\frac{7}{8}\) inch. The three interior ticks are labeled A, B, and C. Which lettered tick should have \(3\) X-marks, and what measurement does that tick represent?
Figure for problem 554865

Hints

- First identify which width occurs three times in the data. - Use the equal tick spacing to count by eighths from \(\frac{3}{8}\) to \(\frac{7}{8}\). - Match the repeated width to the correct lettered position on the blank line plot.

Solution

1. The value occurring \(3\) times is \(\frac{5}{8}\) inch. 2. Starting at \(\frac{3}{8}\), the consecutive eighth-inch ticks are \(\frac{3}{8}, \frac{1}{2}, \frac{5}{8}, \frac{3}{4}, \frac{7}{8}\). 3. The middle interior tick B represents \(\frac{5}{8}\), so B should have \(3\) X-marks.

Answer

B; \(\frac{5}{8}\,\text{in}\)
Line plots with fraction data 13
Five paper strips measure \(\frac{1}{4}\), \(\frac{1}{2}\), \(\frac{1}{2}\), \(\frac{3}{4}\), and \(1\) inch. One X is at the wrong tick on the line plot. Which length has one X too many? Which length needs one more X?
Figure for problem 558764

Hints

- Each X represents one measurement. - Check how many times each length appears in the list and on the plot.

Solution

1. The list has one strip measuring \(\frac{3}{4}\,\text{in}\), but the plot has two Xs at that tick. 2. The list also has one \(1\,\text{in}\) strip, but the plot has no X at \(1\,\text{in}\).

Answer

\(\frac{3}{4}\,\text{in}\) has one X too many; \(1\,\text{in}\) needs one more X.
Line plots with fraction data 14
The plot shows the widths of five buttons. A notebook lists only four widths: \(\frac{1}{8}\), \(\frac{3}{8}\), \(\frac{5}{8}\), and \(\frac{7}{8}\) inch. Which width is missing from the notebook?
Figure for problem 558765

Hints

- Count the Xs at each value before looking for the gap. - Compare those counts with the values already written in the notebook.

Solution

1. The plot has one button each at \(\frac{1}{8}\), \(\frac{5}{8}\), and \(\frac{7}{8}\) inch, and two at \(\frac{3}{8}\) inch. 2. The notebook lists only one \(\frac{3}{8}\)-inch button, so another is missing.

Answer

\(\frac{3}{8}\,\text{in}\)
Line plots with fraction data 15
If beads in each group are placed end to end, which group has greater total length: the \(\frac{1}{4}\)-inch beads or the \(\frac{1}{2}\)-inch beads? By how much?
Figure for problem 558766

Hints

- The taller stack does not necessarily have the greater combined length. - Think about each bead's length and how many beads have that length.

Solution

1. There are three quarter-inch beads, with combined length \(\frac{3}{4}\,\text{in}\). 2. There are two half-inch beads, with combined length \(1\,\text{in}\). The half-inch group is longer by \(\frac{1}{4}\,\text{in}\).

Answer

The \(\frac{1}{2}\)-inch group, by \(\frac{1}{4}\,\text{in}\).
Line plots with fraction data 16
A strip measures \(\frac{3}{8}\,\text{in}\). Can you place it exactly on a tick of this line plot? If you split each quarter-inch gap into the fewest equal parts needed, how far apart would the new ticks be?
Figure for problem 558767

Hints

- Find the two ticks that the new measurement lies between. - Think about placing equally spaced new ticks within that gap.

Solution

1. The plotted ticks are quarter inches apart, but three eighths lies between one-quarter and one-half. 2. A scale with ticks every one-eighth inch includes three-eighths exactly.

Answer

No. Use \(\frac{1}{8}\)-inch tick spacing.
Line plots with fraction data 17
What length does tick A stand for, and how many strips have that length? Each tick is \(\frac{1}{8}\,\text{in}\) from the next.
Figure for problem 558768

Hints

- Look at the labeled ticks on either side of A. - Count the one-eighth steps instead of measuring the picture with a ruler.

Solution

1. Tick A lies one eighth past \(1\frac{1}{4}\,\text{in}\). 2. Add \(\frac{1}{8}\) to \(1\frac{2}{8}\) to get \(1\frac{3}{8}\,\text{in}\).

Answer

\(1\frac{3}{8}\,\text{in}\); \(2\) strips.
Line plots with fraction data 18
The line plot shows bead lengths. Are there more beads shorter than \(\frac{1}{2}\,\text{in}\), more beads longer than \(\frac{1}{2}\,\text{in}\), or the same number? How many beads are exactly \(\frac{1}{2}\,\text{in}\)?
Figure for problem 558769

Hints

- Use the half-inch tick as a dividing point. - Count the Xs on both sides; remember that a measurement on the dividing tick is neither shorter nor longer.

Solution

1. Three Xs are below \(\frac{1}{2}\,\text{in}\), and three Xs are above it. 2. One X is exactly at \(\frac{1}{2}\,\text{in}\).

Answer

The same number: \(3\) shorter and \(3\) longer; \(1\) is exactly \(\frac{1}{2}\,\text{in}\).
Line plots with fraction data 19
Four pebbles have lengths of \(\frac{1}{8}\), \(\frac{3}{8}\), \(\frac{3}{8}\), and \(\frac{1}{2}\) inch. Which line plot, a), b), or c), shows these measurements? Explain one mistake in a wrong plot.
Figure for problem 558770

Hints

- All three plots show four Xs. Are the Xs above the right tick marks? - Check both the position and the height of the stack for a repeated measurement.

Solution

1. The list has one \(\frac{1}{8}\)-inch pebble, two \(\frac{3}{8}\)-inch pebbles, and one \(\frac{1}{2}\)-inch pebble. 2. Plot b) has an X at \(\frac{1}{8}\), two Xs at \(\frac{3}{8}\), and one X at \(\frac{1}{2}\). 3. Plot a) puts one of the \(\frac{3}{8}\)-inch pebbles at \(\frac{1}{4}\). Plot c) puts the \(\frac{1}{2}\)-inch pebble at \(\frac{5}{8}\).

Answer

b). For example, plot a) wrongly has an X at \(\frac{1}{4}\,\text{in}\) instead of a second X at \(\frac{3}{8}\,\text{in}\).
Line plots with fraction data 20
The line plot shows seven jump distances measured to the nearest \(\frac{1}{2}\) foot. One eighth jump distance was 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 X-mark as one measurement at the tick directly below it. - Include a repeated measurement once for each stacked X-mark. - Compare the subtotal of the visible jumps with the total for all eight jumps.

Solution

1. Read the seven plotted measurements: \(5, 5\frac{1}{2}, 6, 6, 7, 7\frac{1}{2}, 8\) feet. 2. Their total is \(45\) feet. 3. The erased jump is \(52 - 45 = 7\) feet.

Answer

\(7\,\text{ft}\)
Line plots with fraction data 21
A class recorded these button diameters, in inches: \(\frac{3}{8}, \frac{1}{2}, \frac{1}{2}, \frac{5}{8}, \frac{7}{8}, 1\). The line plot 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 first. - Compare those tallies with the stacked X-marks at the corresponding fractional ticks. - One tick has one extra X-mark and another has one missing X-mark.

Solution

1. The data require one X-mark at \(\frac{3}{8}\), two at \(\frac{1}{2}\), one at \(\frac{5}{8}\), one at \(\frac{7}{8}\), and one at \(1\). 2. The plot has one X-mark too few at \(\frac{1}{2}\) and one too many at \(\frac{5}{8}\). 3. Move one X-mark from \(\frac{5}{8}\) inch to \(\frac{1}{2}\) inch.

Answer

Move one X-mark from \(\frac{5}{8}\,\text{in}\) to \(\frac{1}{2}\,\text{in}\).
Line plots with fraction data 22
The line plot shows board lengths measured to the nearest \(\frac{1}{8}\) foot. 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

- Use horizontal position on the number line to identify the two shortest observations and the longest observation. - Add the two shortest measurements before comparing with the longest. - Express the measurements in compatible fractional units before subtracting.

Solution

1. The two shortest boards are the two leftmost plotted observations: \(\frac{5}{8}\) foot and \(\frac{7}{8}\) foot. 2. Their combined length is \(\frac{5}{8} + \frac{7}{8} = 1\frac{1}{2}\) feet. 3. The rightmost plotted observation is \(1\frac{1}{4}\) feet. 4. The difference is \(1\frac{1}{2} - 1\frac{1}{4} = \frac{1}{4}\) foot.

Answer

\(\frac{1}{4}\,\text{ft}\)
Line plots with fraction data 23
The line plot shows wire lengths measured to the nearest \(\frac{1}{4}\) inch. One new wire that is \(1\frac{1}{2}\) inches long is added to the data. Does the range change? What happens to the most frequent length?
Figure for problem 554866

Hints

- Range depends only on the leftmost and rightmost plotted measurements. - Decide whether the added wire changes either extreme. - Then examine the stack at \(1\frac{1}{2}\) inches and compare its frequency with the other stacks.

Solution

1. Before the new wire is added, the leftmost plotted length is \(1\) inch and the rightmost is \(2\) inches, so the range is \(1\) inch. 2. Adding another \(1\frac{1}{2}\)-inch wire does not create a new minimum or maximum, so the range stays \(1\) inch. 3. The tallest stack was already at \(1\frac{1}{2}\) inches. Its frequency rises from \(3\) to \(4\), so it remains the most frequent length.

Answer

The range does not change; it stays \(1\,\text{in}\). The most frequent length remains \(1\frac{1}{2}\,\text{in}\), and its frequency becomes \(4\).
Line plots with fraction data 24
The line plot shows metal-pin lengths measured to the nearest \(\frac{1}{8}\) inch. Every pin longer than \(1\frac{1}{4}\) inches will be trimmed to exactly \(1\frac{1}{4}\) inches. How much metal will be trimmed off altogether?
Figure for problem 551191

Hints

- Use the number line to identify every stack to the right of \(1\frac{1}{4}\) inches. - For each affected tick, find how much one pin must be shortened. - Multiply each trimming amount by the number of X-marks in that stack before combining the results.

Solution

1. The affected stacks are at \(1\frac{3}{8}\), \(1\frac{1}{2}\), and \(1\frac{5}{8}\) inches. 2. Two \(1\frac{3}{8}\)-inch pins each lose \(\frac{1}{8}\) inch, for \(\frac{1}{4}\) inch total. 3. One \(1\frac{1}{2}\)-inch pin loses \(\frac{1}{4}\) inch. 4. Two \(1\frac{5}{8}\)-inch pins each lose \(\frac{3}{8}\) inch, for \(\frac{3}{4}\) inch total. 5. The total trimmed length is \(\frac{1}{4} + \frac{1}{4} + \frac{3}{4} = 1\frac{1}{4}\) inches.

Answer

\(1\frac{1}{4}\,\text{in}\)

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