# Into Math Grade 6 Module 2 Lesson 1 Answer Key Interpret Rational Numbers

We included HMH Into Math Grade 6 Answer Key PDF Module 2 Lesson 1 Interpret Rational Numbers to make students experts in learning maths.

## HMH Into Math Grade 6 Module 2 Lesson 1 Answer Key Interpret Rational Numbers

I Can find and use absolute values and the opposite of a number to solve real-world problems.

The magnitude of a star is a number that is a measure of its brightness as seen on Earth. The brighter the star, the lower its magnitude. The data below show the magnitudes of five stars in our galaxy. Between what two consecutive integers is the magnitude of each star located? In most applications, the magnitude of a number is its size or amount. However, when talking about the magnitude of a star, magnitude includes negative numbers.

Polaris (The North Star): 1.97
Sirius (The Dog Star): -1.45
Arcturus: -0.04
Canopus: -0.72

Turn and Talk How many decimals are between the numbers 0 and -1? Explain your thinking.
-0.1, -0.2, -0.3, -0.4, -0.5, -06, -0.7, -0.8, -0.9 and -1

Build Understanding
1. The average low temperature in Nome, Alaska, in a number that can be January, is the rational number -2.8 °F.
A. Consecutive marks on a number line increase and decrease by the same amount. What marks would you need to graph -2.8 on a number line?
B. Between what two consecutive integers is -2.8 located on a number line?
-2.8 is between the integers and .
-2.7 and -2.9

Explanation:
The two consecutive integer is -2.8 located on a number line is -2.7 and -2.9.
C. How would you graph -2.8 on a number line?
I would plot a point tenths to the ___ of -2.
I would plot a point on -2.8 tents to the left of -2

D. Complete the statement to describe the position of -2.8 compared to 0.
-2.8 is units to the ___ of 0.
-2.8 is 17 th unit to the left of 0.

E. What is the opposite of -2.8?
The opposite of -2.8 will be units to the ____ of 0.
The opposite of -2.8 will be 2.8 units to the right of 0.
So, the opposite of -2.8 is 2.8.
F. Graph —2.8 and its opposite on the number line.

2. The legs of a display swing set are buried in the ground as shown.
A. What marks on a number line would you need to graph ?
_________________
B. Describe the position of $$\frac{1}{2}$$ on a number line.
$$\frac{1}{2}$$ is between the integers and .
$$\frac{1}{2}$$ is unit to the ___ of 0.
$$\frac{1}{2}$$ is between the integers 0 and 1.
$$\frac{1}{2}$$ is 5 unit to the right of 0.
C. The opposite of $$\frac{1}{2}$$ will be unit to the ___ of 0. So, the opposite of $$\frac{1}{2}$$ is .

The opposite of $$\frac{1}{2}$$ will be 5 units to the right of 0. So, the opposite of $$\frac{1}{2}$$ is – $$\frac{1}{2}$$.
D. Graph $$\frac{1}{2}$$ and its opposite on the number line.

Turn and Talk What marks on a number line would you need to graph -3.75? Explain.
The number -3.75 is located to the left of the 0 on the line. The numbers are decreasing going from right to left and it is located 0 to -3.75

Step It Out
In a previous lesson, you found the absolute values of integers. You can find the absolute values of rational numbers in the same way.

3. The lowest elevation at Death Valley National Park is approximately -0.05 mile.
A. What distance is this from sea level?
_________________
The distance is this from sea level is 0.05 mile.
B. Between what two consecutive integers is -0.05 located on a number line?
_________________
0 to -1

C. Complete the number sentence.
|-0.05| =
0.05

4. Mrs. Suffer withdraws money from the bank. The withdrawal transactions are recorded on her bank statement.
A. Find the absolute value of each withdrawal amount.
|-5.25| = ___ |-7.10| = ____
|-3.50| = ___ |-4.75| = ____
|-5.25| = 5.25 |-7.10| = 7.10
|-3.50| = 3.50 |-4.75| = 4.75
B. Which is greater, -7.10 or -3.50? Which is a greater withdrawal, -$7.10 or -$3.50? Explain.

-$7.10 > -$3.50

Explanation:
The number -$7.10 is greater than -$3.50.

Check Understanding

Question 1.
The average weight of a newborn panda is 0.2, or $$\frac{2}{10}$$, pound. Between what two integers is the weight of a newborn panda?
_____________________
$$\frac{2}{10}$$ lies between 0 and 1.

Explanation:
The weight of a newborn panda lies between two integers are 0 and 1.

For Problems 2-4, graph each number on the number line and then find the absolute value.

Question 2.
|-0.2| = ___
The absolute value is 0.2

Question 3.
|-1.5| = ____
The absolute value is 1.5

Question 4.
|0.8| = ____
The absolute value is 0.8

Question 5.
A bank statement shows transactions of -$10.40 and$8.50.
A. Do these transactions represent deposits or withdrawals?
_______________________
A negative value means when the money is taken out that is withdrawals.
A positive value means when the money us deposited that is deposits.
From the given question the transactions represent deposits or withdrawals.
B. How can you use absolute value to decide which transaction represented the greater change?
_______________________
_______________________
_______________________
The absolute values of -$10.40 and$8.50 are $10.40 and$8.50.
Therefore the transaction represented the greater change are $10.40. Question 6. Two deep-sea divers are exploring shipwrecks in Lake Erie, one of the Great Lakes. Write the depth of the shipwreck as an integer. What is the absolute value of the depth of the shipwreck? Answer: 200 feet Explanation: The absolute value of the depth of the shipwreck is 200 feet. For Problems 7-9, use the number line to graph the opposite of each number. Label each point. Question 7. -3.25 Answer: Question 8. 0.25 Answer: Question 9. -1.5 Answer: Question 10. Use Structure Graph each number and its opposite on the number line. -1$$\frac{2}{10}$$, –$$\frac{5}{10}$$, $$\frac{3}{10}$$, $$\frac{9}{10}$$ Answer: For Problems 11-13, find the absolute value of each number. Question 11. |$$\frac{6}{5}$$| ______ Answer: $$\frac{6}{5}$$ Explanation: The absolute value of given number is $$\frac{6}{5}$$. Question 12. |-5.10| _____ Answer: 5.10 Explanation: The absolute value of given number is 5.10 Question 13. |-2$$\frac{3}{4}$$| ______ Answer: 2$$\frac{3}{4}$$ Explanation: The absolute value of given number is |2$$\frac{3}{4}$$| I’m in a Learning Mindset! How can I use marks on the number line to effectively compare rational numbers? _________________________ _________________________ Lesson 2.1 More Practice/Homework Question 1. Graph 1.7, -0.3, and 0.5 and their opposites on the number line. Answer: The opposite on the number line are -1.7, 0.3 and -0.5 Explanation: Question 2. Use Tools A marine biologist collects coral species from the bottom of a coral reef. The biologist swims to depths of 3$$\frac{1}{4}$$ meters, 2$$\frac{5}{8}$$ meters, and 4$$\frac{1}{2}$$ meters below sea level. A. Represent these depths as rational numbers. ______________________ Answer: 3$$\frac{1}{4}$$ meters = $$\frac{13}{4}$$ 2$$\frac{5}{8}$$ meters = $$\frac{21}{8}$$ 4$$\frac{1}{2}$$ = $$\frac{9}{2}$$ Therefore these are the given rational numbers. B. Graph and label these depths and their opposites on the number line. Answer: Answer: Question 3. STEM Liquids freeze at different temperatures as shown in the table. Complete the table by finding the absolute value of each temperature. Answer: Question 4. Construct Arguments Hector says that -3.8 °C and 3.8 °C are not the same in terms of their relationship with 0 °C. Is Hector correct? Explain. Answer: Hector is correct. -3.8 °C -3.8 °C Question 5. Reason On Friday, the value of one stock changed by -$2.75. and the value of a second stock changed by \$2.75. How can you use a number line to show that these values are opposites?
5.5

Explanation:
Based on the given conditions calculate 2.75 – – 2.75
= 2.75 + 2.75
Calculate the sum = 5.5
The result is 5.5

Find the opposite and absolute value of each number.

Question 6.
$$\frac{3}{10}$$ _____
absolute value is $$\frac{3}{10}$$
The opposite value is –$$\frac{3}{10}$$

Question 7.
-4.06 _____
The absolute value is 4.06
The opposite value is 4.06

Question 8.
-1$$\frac{1}{5}$$ _____
The absolute value is 1$$\frac{1}{5}$$
The opposite value is 1$$\frac{1}{5}$$

Question 9.
2.19 _________________
The absolute value is 2.19
The opposite value is -2.19

Question 10.
2$$\frac{1}{2}$$ _____
The absolute value is 2$$\frac{1}{2}$$
The opposite value is -2$$\frac{1}{2}$$

Question 11.
0.75 ____
The absolute value is 0.75
The opposite value is -0.75

Test Prep

Question 12.
A stock market index drops by 1.38 points. What rational number represents the change in the index?
_________________
–$$\frac{69}{50}$$

Explanation:
stock market index drops by 1.38 points.
We need to find the rational number that represents the change in the index.
The drop means the stock becomes less and the value of change will be negative.
-1.38 = –$$\frac{138}{100}$$
= $$\frac{69}{50}$$.

Question 13.
An ampere is a unit used to measure electric current. The electrical current is -2.5 amperes in one part of a circuit and 0.6 ampere in another part. Graph the values on the number line.

Question 14.
Amos says that the opposite and the absolute value of a number are always the same. Which rational number can be used to show that this statement is incorrect?
A -0.9
B. 0
C -1.1
D. $$\frac{1}{10}$$
$$\frac{1}{10}$$

Explanation:
$$\frac{1}{10}$$ opposite is –$$\frac{1}{10}$$
$$\frac{1}{10}$$ absolute is $$\frac{1}{10}$$
$$\frac{1}{10}$$ is not equal to –$$\frac{1}{10}$$
Hence the opposite and absolute are not same.
So the given statement is incorrect.

Question 15.
Use the number line to match each point with its opposite.

s

Spiral Review

Question 16.
A pond loses water from evaporation each week. Week 1 had a change in water level of -6 inches. Week 2 had a change in water level of -7 inches. Week 3 had a change in water level of -3 inches. Write the numbers from least to greatest.
_________________
-7, – 6, -3

Explanation:
When we are using negative numbers, we need to write least to the greatest backward from positive numbers. The numbers from least to greatest are -7, – 6, and -3.

Question 17.
Write an inequality to compare the numbers 11 and -9.
_________________
11 > -9

Explanation:
The inequality to compare the numbers 11 and -9 is >
11 > -9

Question 18.
The low temperature in St. Paul, Minnesota, was -9 °F while the low temperature in Minot, North Dakota, was -1 °F on the same day. Which has a smaller magnitude?
_________________