Line Plots with Fractions: Grade 4 Math Worksheet Answer Key – PDF Download

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.

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