## Math Expressions Common Core Grade 4 Unit 7 Lesson 2 Answer Key Fractions on the Number Line

**Math Expressions Grade 4 Unit 7 Lesson 2 Homework**

Question 1.

Use the number line to compare the fractions or mixed numbers. Write > or

a. \(\frac{3}{4}\) \(\frac{5}{8}\)

Answer:

\(\frac{3}{4}\) > \(\frac{5}{8}\)

Explanation:

As shown below in the number line, Green line is greater then Red line

b. 1\(\frac{1}{4}\) \(\frac{3}{2}\)

Answer:

1\(\frac{1}{4}\) < \(\frac{3}{2}\)

Explanation:

As shown in the number line below, the Orange Line is shorter then Blue line

c. \(\frac{9}{4}\) 2\(\frac{1}{2}\)

Answer:

\(\frac{9}{4}\) = 2\(\frac{1}{2}\)

Explanation:

Both the Green line and Red line on the number line are of same length

d. \(\frac{7}{2}\) \(\frac{17}{8}\)

Answer:

\(\frac{7}{2}\) > \(\frac{17}{8}\)

Explanation:

As Green line is greater then the Red line on the number line as shown below

e. 4\(\frac{2}{4}\) 4\(\frac{5}{8}\)

Answer:

4\(\frac{2}{4}\) < 4\(\frac{5}{8}\)

Explanation:

As Green line is less then the Red line on the number line as shown below

f. 4\(\frac{1}{2}\) \(\frac{33}{8}\)

Answer:

4\(\frac{1}{2}\) < \(\frac{33}{8}\)

Explanation:

As Green line is less then the Red line on the number line as shown below

g. 1\(\frac{3}{4}\) 1\(\frac{7}{8}\)

Answer:

1\(\frac{3}{4}\) < 1\(\frac{7}{8}\)

Explanation:

As Green line is less then the Red line on the number line as shown below

h. 1\(\frac{1}{2}\) 1\(\frac{1}{8}\)

Answer:

1\(\frac{1}{2}\) > 1\(\frac{1}{8}\)

Explanation:

As Green line is greater then the Red line on the number line as shown below

Question 2.

Mark and label the letter of each fraction or mixed number on the number line.

a. \(\frac{3}{8}\)

Answer:

Explanation:

First draw a number line, and mark the given numbers on the number line.

After mark \(\frac{3}{8}\) on number line.

b. \(\frac{3}{4}\)

Answer:

Explanation:

First draw a number line, and mark the given numbers on the number line.

After that mark \(\frac{3}{4}\) on number line

c. 1\(\frac{1}{2}\)

Answer:

1\(\frac{1}{2}\) = \(\frac{3}{2}\)

Explanation:

First draw a number line, and mark the given numbers on the number line.

After 1 whole number mark 1\(\frac{1}{2}\) on number line

d. 2\(\frac{1}{8}\)

Answer:

2\(\frac{1}{8}\) = \(\frac{17}{8}\)

Explanation:

First draw a number line, and mark the given numbers on the number line.

After 2 whole number 1th part is marked as 2\(\frac{1}{8}\)

e. 2\(\frac{7}{8}\)

Answer:

Explanation:

First draw a number line, and mark the given numbers on the number line.

After 2 whole number 7th part is marked as 2\(\frac{7}{8}\)

f. 3\(\frac{1}{4}\)

Answer:

Explanation:

First draw a number line, and mark the given numbers on the number line.

After 3 whole number 1th part is marked as3\(\frac{1}{4}\)

g. 3\(\frac{5}{8}\)

Answer:

Explanation:

First draw a number line, and mark the given numbers on the number line.

After 3 whole number 5th part is marked as 3\(\frac{5}{8}\)

h. 4\(\frac{2}{4}\)

Answer:

Explanation:

First draw a number line, and mark the given numbers on the number line.

After 4 whole number half part is marked as 4\(\frac{2}{4}\)

i. 4\(\frac{6}{8}\)

Answer:

Explanation:

First draw a number line, and mark the given numbers on the number line.

After 4 whole number 6th part is marked as 4\(\frac{6}{8}\)

j. 4\(\frac{7}{8}\)

Answer:

Explanation:

First draw a number line, and mark the given numbers on the number line.

After 4 whole number 7th part is marked as 4\(\frac{7}{8}\)

The list below shows the amount of fruit purchased from the market.

Fruit Purchases (lb = pounds)

Question 3.

Decide if each weight is closer to 2 pounds, 2\(\frac{1}{2}\) pounds, or 3 pounds. Write closer to 2 pounds, closer to 2\(\frac{1}{2}\) pounds, or closer to 3 pounds.

a. apples __________

b. bananas _________

c. grapes _________

d. oranges ___________

Answer:

a. apples ____2 pounds_______

b. bananas __2\(\frac{1}{2}\) pounds________

c. grapes ____2\(\frac{1}{2}\) pounds______

d. oranges ___2\(\frac{1}{2}\) pounds________

Question 4.

Which purchase had a greater weight?

a. apples or grapes __________

b. oranges or bananas __________

Answer:

a. Grapes

b. Oranges

Explanation:

a. By subtracting apples from grapes, we come to know that grapes has more weight

Apples = 2pounds

Grapes = 2\(\frac{1}{2}\) pounds

We get, 2 – 2\(\frac{1}{2}\) pounds = \(\frac{1}{2}\) pounds more grapes

b. By subtracting oranges from bananas, we come to know that have more weight

oranges = 3\(\frac{1}{10}\) pounds

bananas = 2\(\frac{3}{8}\) pounds

So, 3\(\frac{1}{10}\) pounds – 2\(\frac{3}{8}\) pounds

\(\frac{31}{10}\) pounds – \(\frac{19}{8}\) pounds

LCM of the denominator 10 and 8 = 40

\(\frac{31 x 4}{40}\)pounds – \(\frac{19 x 5}{40}\) pounds

\(\frac{124}{40}\) pounds – \(\frac{95}{40}\) pounds

\(\frac{29}{40}\) pounds more than oranges

**Math Expressions Grade 4 Unit 7 Lesson 2 Remembering**

**Solve, using any method.**

Question 1.

Answer: 152

Explanation:

Question 2.

Answer: 2383

Explanation:

Question 3.

Answer: 1009

Explanation:

**Solve each comparison problem.**

Question 4.

Mateo read 2,382 pages in a book series over the summer. This is 3 times the number of pages as his younger brother read over the summer. How many pages did Mateo’s brother read over the summer?

Answer:

794 pages did Mateo’s brother read over the summer

Explanation:

Question 5.

In Jen’s town, there was 9 inches of snow in a year. In her cousin’s town, there was 216 inches of snow in the same year. How many times the number of inches of snow was there in the cousin’s town as in Jen’s town?

Answer:

24 times the number of inches of snow was there in the cousin’s town as in Jen’s town

Explanation:

**Write < or > to make each statement true.**

Question 6.

\(\frac{2}{5}\) \(\frac{4}{5}\)

Answer:

\(\frac{2}{5}\) < \(\frac{4}{5}\)

Explanation:

\(\frac{2}{5}\) = 0.4

\(\frac{4}{5}\) = 0.8

\(\frac{2}{5}\) < \(\frac{4}{5}\)

Question 7.

\(\frac{1}{8}\) \(\frac{3}{8}\)

Answer:

\(\frac{1}{8}\) < \(\frac{3}{8}\)

Explanation:

\(\frac{1}{8}\) = 0.1

\(\frac{3}{8}\) = 0.3

So, \(\frac{1}{8}\) < \(\frac{3}{8}\)

Question 8.

\(\frac{4}{5}\) \(\frac{4}{6}\)

Answer:

\(\frac{4}{5}\) > \(\frac{4}{6}\)

Explanation:

\(\frac{4}{5}\) = 0.8

\(\frac{4}{6}\) = 0.6

So, \(\frac{4}{5}\) > \(\frac{4}{6}\)

Question 9.

**Stretch Your Thinking** Dakota says the point on the number line shown here is \(\frac{4}{5}\). His teacher says that he is reading the number line incorrectly. What is Dakota’s error? What is the correct fraction?

Answer:

Dakota’s error is the denominator should be 6, its 6 equal parts

\(\frac{4}{6}\) is the correct fraction

Explanation:

When we observe the number line it clearly shows us that each whole is divided into 6 parts.

But in the above information it shows that \(\frac{4}{5}\)

So, the correct fraction is represented as \(\frac{4}{6}\)