We included HMH Into Math Grade 6 Answer Key PDF **Module 2 Lesson 2 Compare Rational Numbers on a Number Line**to make students experts in learning maths.

I Can compare positive and negative rational numbers using a number line.

**Step It Out**

You can compare fractions by graphing them on a number line.

1. Mrs. Smith and Mr. Jones each have 30 students in their class. If Mrs. Smith corrected \(\frac{3}{4}\) of last week’s math assignments and Mr. Jones corrected \(\frac{5}{8}\) of last week’s science assignments, which teacher corrected the greater portion of the assignments?

Answer:

The fraction of homework assignments corrected by Mrs. Smith is \(\frac{3}{4}\).

The fraction of homework assignments corrected by Mr. Jones is \(\frac{5}{8}\).

In order to check who corrected a greater portion of the assignments, we have to convert them into fractions.

Now, LCM of 4, 8 is 8.

Thus, \(\frac{3}{4}\) = \(\frac{3× 2}{4 × 2}\) = \(\frac{6}{8}\).

\(\frac{5}{8}\) = \(\frac{5 × 1}{8 × 1}\) = \(\frac{5}{8}\).

Since 6 > 5

\(\frac{6}{8}\) > \(\frac{5}{8}\).

Thus, Mr. Jones corrected a greater portion of the assignments.

A. What marks on a number line would you need to graph \(\frac{3}{4}\) and \(\frac{5}{8}\)?

_____________________

_____________________

B. Graph the fractions on the number line.

Answer:

C. Note the locations of the numbers.

\(\frac{3}{4}\) is to the ____ of \(\frac{5}{8}\) on the number line, so \(\frac{3}{4}\) is ____ \(\frac{5}{8}\).

Answer:

\(\frac{3}{4}\) is to the left of \(\frac{5}{8}\) on the number line, so \(\frac{3}{4}\) is greater \(\frac{5}{8}\).

D. Write an inequality statement.

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

So, Mrs. Smith corrected Mr. Jones.

Answer:

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

Explanation:

By comparing the given inequality statement the fraction \(\frac{3}{4}\) < \(\frac{5}{8}\). Hence Mrs. Smith corrected less than Mr. Jones.

E. Use the number line to help you write an inequality comparing –\(\frac{5}{8}\) and –\(\frac{3}{4}\).

Answer:

**Turn and Talk** How do the numbers in Parts D and E compare? How can a number line help you to determine the relationship between the numbers in Parts D and E? Explain.

You also can compare decimals using a number line.

2. The record low temperatures for five cities are Ashton -0.6 °F, Barres -1.7 °F, Carl 0.7 °F, Davison 0.4 °F, and Edgeville -1.5 °F. Graph the temperatures on the number line and label each with the first letter of the city’s name.

A. Note the locations of the numbers for Barres and Edgeville.

-1.7 is to the of -1.5, so Barres’s low temperature is than the low temperature for Edgeville.

B. Complete the inequality in two different ways.

-1.7 -1.5 -1.5 -1.7

Answer:

-1.7 >-1.5

-1.5 <-1.7

**Turn and Talk** What do you notice about the rational numbers as you move from left to right on a number line? Use examples to support your answer.

**Check Understanding**

Question 1.

Researchers measure the thickness of the ice at several locations in the Antarctic and compare the measures to a long-term average thickness. A set of ice-level data from the Antarctic Weather Station is shown measured in meters.

-1.2, 2.6, -1.3, 1.8, 2.1, -0.9, 1.5

A. Graph the numbers on the number line to compare the data.

Answer:

B. Use the number line to complete the inequalities.

2.6 -0.9 1.8 2.1 -1.2 -1.3

Answer:

2.6 > -0.9, 1.8 < 2.1, -1.2 < -1.3

C. Is 1.5 to the left or right of -0.9?

______________________

Answer:

Right of -0.9

Explanation:

The number 1.5 is right of -0.9.

D. Is -1.2 to the left or right of -2.1?

______________________

Answer:

Right of -2.1

Explanation:

The number -1.2 is to the right of -2.1.

**On Your Own**

Question 2.**Use Tools** Diego is participating in a cooking competition in which the judges rate performance for various criteria using fractions between -1 and 2. The scores for four competitors are shown.

\(\frac{1}{8}\), –\(\frac{1}{4}\), 1\(\frac{1}{2}\), –\(\frac{3}{4}\)

A. Complete the number line to compare the four scores.

Answer:

B. How do the locations of –\(\frac{3}{4}\) and –\(\frac{1}{4}\) compare? Which number is less? Explain.

Answer:

–\(\frac{3}{4}\) < –\(\frac{1}{4}\)

Explanation:

The given numbers are –\(\frac{3}{4}\) and –\(\frac{1}{4}\)

–\(\frac{3}{4}\) = -0.75

–\(\frac{1}{4}\) = -0.25

-0.75 < -0.25

Question 3.

A sprint triathlon consists of a 750-meter swim, a 20-kilometer bicycle ride, and a 5-kilometer run. The race organizers recorded the difference between 5 athletes’ times and the average time to complete the triathlon. Each value is the amount of time above or below the average in minutes.

2.5, -1.25, 0.8, 1.5, -1.2

A. Graph the athletes’ differences from the average time on the number line.

Answer:

B. Compete the inequality statements.

-1.2 -1.25 0.8 1.5 2.5 -1.25

Answer:

-1.2 < -1.25

0.8 < 1.5

2.5 > -1.25

C. Which inequality in Part B is comparing the differences from the average time for the slowest and fastest athletes in the group? Explain.

_________________

_________________

Answer:

The inequality is 0.8 < 1.5

Question 4.**Open Ended** A cave system inside a mountain has caves at different elevations above and below sea level. One cave has an elevation of -4\(\frac{1}{4}\) meters. How can you use a vertical number line to determine whether the elevation of a second cave is greater than or less than -4\(\frac{1}{4}\) meters?

Answer:

By measuring the height of the elevation and compare it to greater or less.

Question 5.

On this map of Main Street, distances are in miles. The plotted points indicate the locations of landmarks. The library is located at point 0.

A. Find the locations of the other landmarks and record them in the table in decimal form.

Answer:

B. How do the locations of the city park and the library compare? Write an absolute value inequality to compare the distances from point 0 to the two buildings.

______________________

Answer:

The distance of the city park and library is -0.5

-0.5 > 0

C. How do the locations of the bookstore and the courthouse compare? Write an absolute value inequality to compare the distances from point 0 to the two buildings.

______________________

______________________

Answer:

1.3 > -1.5

Explanation:

The location of the bookstore and the courthouse is 1.3 > -1.5

D. How do the locations of the museum and the bookstore compare? Write an absolute value inequality to compare the distances from point 0 to the two buildings.

______________________

______________________

Answer:

1.3 > 0.8

Explanation:

The absolute value inequality to compare the distances from point 0 to the two buildings is 1.3 > 0.8.

**Use the number line to compare the rational numbers.**

Question 6.

-1\(\frac{3}{4}\) –\(\frac{1}{2}\)

Answer:

– \(\frac{7}{4}\) > –\(\frac{1}{2}\)

Explanation:

Question 7.

–\(\frac{1}{10}\) –\(\frac{4}{5}\)

Answer:

–\(\frac{1}{10}\) <–\(\frac{4}{5}\)

Explanation:

Question 8.

-1\(\frac{3}{7}\) -1\(\frac{1}{2}\)

Answer:

-1\(\frac{3}{7}\) <-1\(\frac{1}{2}\)

Explanation:

Question 9.

-1.45 -0.5

Answer:

-1.45 > -0.5

Explanation:

Question 10.

1.5 -2

Answer:

1.5 > -2

Explanation:

Question 11.

-0.5 0.75

Answer:

-0.5 < 0.75

Explanation:

**Lesson 2.2 More Practice/Homework**

**Compare Rational Numbers on a Number Line**

Question 1.

The high temperature of four different towns in Norway were measured on the same day. The temperatures are 0.9 °C,

-0.5 °C, -1.3 °C, and 1.2 °c.

A. Graph the temperatures on the number line.

Answer:

B. Complete each statement.

-0.5 °C is ____ than -1.3 °C, because -0.5 is to the ____ of -1.3.

0.9 °C is ___ than 1.2 °C, because 0.9 is to the ____ of 1.2.

Answer:

-0.5 °C is < than -1.3 °C, because -0.5 is to the right of -1.3.

0.9 °C is < than 1.2 °C, because 0.9 is to the left of 1.2.

Question 2.**STEM** A circuit board manufacturer rejects a 100-ohm resistor if its measured resistance is 0.15 ohm or more away from 100 ohms. Resistors A and B are rejected. Resistor A’s resistance differs from 100 ohms by +0.15 ohm. Resistor B’s resistance differs from 100 ohms by -0.78 ohm. Which resistor has a resistance closer to 100 ohms?

__________________

__________________

__________________

__________________

Answer:

Resistor A has resistance closer to 100.

Explanation:

Resistor A has a resistance closer to 100 ohms.

Question 3.

Graph the numbers on the number line and complete the inequalities.

Answer:

For Problems 4-5, use the number line to write two different inequalities to compare the numbers.

Answer:

Question 4.

-1.25 and -1\(\frac{1}{8}\)

________________

Answer:

-1.25 and -1.125

-1.25 > -1.125

-1.25 and -1\(\frac{1}{8}\).

Explanation:

Question 5.

–\(\frac{2}{5}\) and -0.5

________________

Answer:

–\(\frac{2}{5}\) and -0.5

-0.4 < -0.5

Explanation:

**Test Prep**

Question 6.

Use the number line to locate 1.6 and -1\(\frac{1}{5}\). Then complete the inequality.

Answer:

1.6 > \(\frac{6}{5}\).

Explanation:

Question 7.

Using the number line, select all the inequality statements that are true.

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

B. -1.25 < -0.75

C. 1.75 < –\(\frac{1}{4}\)

D. 1.75 > 0.5

E. 2\(\frac{1}{2}\) > 2\(\frac{3}{4}\)

F. -1.25 > –\(\frac{1}{4}\)

Answer:

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

B. -1.25 < -0.75

D. 1.75 > 0.5

F. -1.25 > –\(\frac{1}{4}\)

Question 8.

Which inequality is correct?

A. 0.6 < -0.3

B. 0.5 > 0.6

C. -0.8 > 0.4

D. -0.3 > -0.8

Answer:

D. -0.3 > -0.8

Explanation:

The given option D inequality is correct.

**Spiral Review**

Question 9.

The average elevation of New Orleans, Louisiana, is 8 feet below sea level. What integer is used to represent this elevation?

Answer:

-8.

Explanation:

The integer used to represent this elevation is -8

Question 10.

During a football game, a team lost 10 yards on its first play and 20 yards on its third play. Write two integers to represent these losses. Which play had the greater loss? Explain.

Answer:

-10 yards and -20 yards.

The third play has a greater loss.

Explanation:

The two integers to represent these losses are -10 yards and -20 yards.

Question 11.

Write an inequality to compare |-5| and |4|.

Answer:

>

Explanation:

An inequality to compare |-5| and |4| are >.

|-5| = 5

|4| = 4