This grade 4 line worksheet answer key solves all 22 problems of the line plots with fractions worksheet step by step.
Every solution shows how each value is read from the line plot and how the fractions are added or subtracted. Compare each step with your own work, and check that the number of dots matches the data.
Grade 4 Line Worksheet Answer Key: problems 1–5
Problem 1: Reading points on a number line
The number line has 8 equal steps from 0 to 1, so each step is \(\frac{1}{8}\). Point A is 3 steps from 0: \(\frac{3}{8}\). Point B is 7 steps from 0: \(\frac{7}{8}\).
Problem 2: Counting marks above a value
(a) Count the dots above \(1\frac{1}{2}\): there are 3 plants.
(b) The dots above values greater than 1 are 3 at \(1\frac{1}{2}\), 1 at 2, and 1 at \(2\frac{1}{2}\): 3 + 1 + 1 = 5 plants.
Problem 3: How many data values?
(a) Count all the dots: 1 + 2 + 3 + 2 = 8 strips.
(b) Three dots are above \(\frac{3}{4}\), so 3 strips.
Problem 4: The most common length
The tallest stack is above \(3\frac{3}{4}\). It has 4 dots.
The most common length is \(3\frac{3}{4}\text{ in.}\), and 4 crayons have it.
Problem 5: Shortest and longest
(a) The leftmost dot is at \(\frac{3}{8}\text{ in.}\).
(b) The rightmost dot is at \(\frac{7}{8}\text{ in.}\).
Grade 4 Line Worksheet Answer Key: problems 6–10
Problem 6: Longer than a given length
Look only at dots to the right of \(1\frac{1}{4}\). There is 1 dot at \(1\frac{3}{8}\), 3 dots at \(1\frac{1}{2}\), 1 dot at \(1\frac{3}{4}\), and 1 dot at \(1\frac{7}{8}\).
1 + 3 + 1 + 1 = 6 nails.
Problem 7: Comparing two groups
Shorter than \(\frac{1}{2}\): 2 seeds (both at \(\frac{1}{4}\)). Longer than \(\frac{1}{2}\): 1 + 1 + 1 = 3 seeds.
3 − 2 = 1, so there is 1 more seed longer than \(\frac{1}{2}\) inch.
Problem 8: Make a line plot
Make one dot for each piece and count at the end: there must be 7 dots. 2 at \(\frac{1}{2}\); 3 at \(\frac{3}{4}\); 1 at \(1\); 1 at \(1\frac{1}{4}\).
Problem 9: Longest minus shortest
Longest: \(1\frac{7}{8}\) in. Shortest: \(1\frac{1}{8}\) in.
\(\frac{15}{8} – \frac{9}{8} = \frac{6}{8} = \frac{3}{4}\)
The longest is \(\frac{3}{4}\text{ in.}\) longer.
Problem 10: Adding two lengths
(a) \(\frac{6}{4} + \frac{2}{4} = \frac{8}{4} = 2\). The total is \(2\text{ ft}\).
(b) \(\frac{5}{4} + \frac{5}{4} = \frac{10}{4} = 2\frac{1}{2}\). The total is \(2\frac{1}{2}\text{ ft}\).
Grade 4 Line Worksheet Answer Key: problems 11–15
Problem 11: Total of all the pieces
The values are \(\frac{1}{4}\), \(\frac{1}{2}\), \(\frac{1}{2}\), \(\frac{3}{4}\), \(1\).
\(\frac{1}{4} + \frac{2}{4} + \frac{2}{4} + \frac{3}{4} + \frac{4}{4} = \frac{12}{4} = 3\)
The total is \(3\text{ ft}\).
Problem 12: Subtracting with regrouping
Write 3 as a fraction in fourths: 3 = 2 + \(\frac{4}{4}\). So \(3 – 2\frac{1}{4} = 2\frac{4}{4} – 2\frac{1}{4} = \frac{3}{4}\).
The 3 inch wire is \(\frac{3}{4}\text{ in.}\) longer.
Problem 13: Adding eighths
\(\frac{1}{8} + \frac{3}{8} + \frac{3}{8} + \frac{4}{8} + \frac{5}{8} + \frac{6}{8} = \frac{22}{8} = 2\frac{3}{4}\)
\(\frac{22}{8} = 2\frac{6}{8} = 2\frac{3}{4}\).
The total is \(2\frac{3}{4}\text{ in.}\).
Problem 14: Repeated addition
\(\frac{3}{4} + \frac{3}{4} + \frac{3}{4} = \frac{9}{4} = 2\frac{1}{4}\).
The total is \(2\frac{1}{4}\text{ ft}\).
Problem 15: Choosing a scale
The value \(\frac{3}{4}\) is not a multiple of \(\frac{1}{2}\), so halves do not work. Every value is a multiple of \(\frac{1}{4}\): \(\frac{2}{4}, \frac{3}{4}, \frac{5}{4}, \frac{6}{4}\).
Use fourths. Eighths also work but add tick marks that are not needed.
Grade 4 Line Worksheet Answer Key: problems 16–20
Problem 16: Find the missing count
Add the known marks: 3 + 2 + 4 = 9.
10 − 9 = 1 mark is at \(1\frac{1}{4}\).
Problem 17: Ribbon for a banner
(a) \(\frac{3}{4} + \frac{3}{4} + \frac{3}{4} = \frac{9}{4} = 2\frac{1}{4}\). The ribbon is \(2\frac{1}{4}\text{ ft}\) long.
(b) \(2\frac{1}{4} – 2 = \frac{1}{4}\). It is \(\frac{1}{4}\text{ ft}\) longer.
Problem 18: Rainfall over 10 days
(a) Three days had \(\frac{1}{8}\) inch: \(\frac{1}{8} + \frac{1}{8} + \frac{1}{8} = \frac{3}{8}\). Answer: \(\frac{3}{8}\text{ in.}\).
(b) Wettest: \(\frac{5}{8}\). Driest: 0. \(\frac{5}{8} – 0 = \frac{5}{8}\). Answer: \(\frac{5}{8}\text{ in.}\).
(c) In eighths: 0 + 1 + 1 + 1 + 2 + 2 + 3 + 4 + 4 + 5 = 23, so \(\frac{23}{8} = 2\frac{7}{8}\). Answer: \(2\frac{7}{8}\text{ in.}\).
Problem 19: Two garden plots
(a) Jamal’s longest is \(3\frac{1}{4}\) in. and Mei’s longest is \(2\frac{3}{4}\) in. \(\frac{13}{4} – \frac{11}{4} = \frac{2}{4} = \frac{1}{2}\). Answer: \(\frac{1}{2}\text{ in.}\).
(b) Jamal: \(\frac{10}{4} + \frac{11}{4} + \frac{12}{4} + \frac{12}{4} + \frac{13}{4} = \frac{58}{4} = 14\frac{1}{2}\). Mei: \(\frac{8}{4} + \frac{9}{4} + \frac{9}{4} + \frac{10}{4} + \frac{11}{4} = \frac{47}{4} = 11\frac{3}{4}\).
\(\frac{58}{4} – \frac{47}{4} = \frac{11}{4} = 2\frac{3}{4}\). Answer: Jamal’s total is \(2\frac{3}{4}\text{ in.}\) greater.
Problem 20: Rope and a knot
(a) The two longest pieces are \(1\frac{1}{4}\) ft each. \(\frac{5}{4} + \frac{5}{4} + \frac{4}{4} = \frac{14}{4} = 3\frac{1}{2}\). Answer: \(3\frac{1}{2}\text{ ft}\).
(b) \(4 – 3\frac{1}{2} = \frac{1}{2}\). Answer: \(\frac{1}{2}\text{ ft}\) shorter.
Grade 4 Line Worksheet Answer Key: problems 21–22
Problem 21: Find the mistake
Noah added the denominators too. The two fractions are both eighths, so the unit stays the same: only the numerators are added.
\(\frac{5}{8} + \frac{7}{8} = \frac{12}{8} = 1\frac{4}{8} = 1\frac{1}{2}\).
The correct sum is \(1\frac{1}{2}\text{ in.}\).
Problem 22: Make a plot and solve
Plot one dot for each seed.
(a) \(\frac{2}{8} + \frac{3}{8} + \frac{3}{8} + \frac{4}{8} + \frac{5}{8} + \frac{5}{8} + \frac{7}{8} = \frac{29}{8} = 3\frac{5}{8}\). Answer: \(3\frac{5}{8}\text{ in.}\).
(b) \(\frac{7}{8} – \frac{2}{8} = \frac{5}{8}\). Answer: \(\frac{5}{8}\text{ in.}\) longer.
How to use this grade 4 line worksheet answer key
Read this grade 4 line worksheet answer key after trying each problem yourself, and redo any problem you missed.
See every chapter on the Grade 4 math page.