Tag: Eureka Math Grade 6 Module 3

Engage NY Eureka Math 6th Grade Module 3 Lesson 11 Answer Key

Eureka Math Grade 6 Module 3 Lesson 11 Example Answer Key

Example 1. The Absolute Value of a Number
The absolute value often is written as |10|. On the number line, count the number of units from 10 to 0. How many units is 10 from 0?
Answer:
|10| = 10

Answer:

What other number has an absolute value of 10? Why?
Answer:
|- 10| = 10 because – 10 is 10 units from zero and – 10 and 10 are opposites.

The   absolute   value of a number is the distance between the number and zero on the number line.

Example 2. Using Absolute Value to Find Magnitude
Mrs. Owens received a call from her bank because she had a checkbook balance of – $45. What was the magnitude of the amount overdrawn?
Answer:
|- 45| = 45
Mrs. Owens overdrew her checking account by $45.

The   magnitude    of a measurement is the absolute value of its measure.

Eureka Math Grade 6 Module 3 Lesson 11 Exercise Answer Key

Exercise 1 – 3
Complete the following chart.

Answer:

For each scenario below, use absolute value to determine the magnitude of each quantity.

Exercise 4.
Maria was sick with the flu, and her weight change as a result of it is represented by – 4 pounds. How much weight did Maria lose?
Answer:
|-4| = 4 Maria lost 4 pounds.

Exercise 5.
Jeffrey owes his friend $5. How much is Jeffrey’s debt?
Answer:
|- 5| = 5 Jeffrey has a $5 debt.

Exercise 6.
The elevation of Niagara Falls, which is located between Lake Erie and Lake Ontario, is 326 feet. How far is this above sea level?
Answer:
|326| = 326 It is 326 feet above sea level.

Exercise 7.
How far below zero is – 16 degrees Celsius?
Answer:
|- 16| = 16 – 16°C is 16 degrees below zero.

Exercise 8.
Frank received a monthly statement for his college savings account. It listed a deposit of $100 as + 100. 00. It listed a withdrawal of $25 as – 25.00. The statement showed an overall ending balance of $835. 50. How much money did Frank add to his account that month? How much did he take out? What is the total amount Frank has saved for college?
Answer:
|100| = 100 Frank added $100 to his account.
|- 25| = 25 Frank took $25 out of his account.
|835. 50| = 835. 50 The total amount of Frank’s savings for college is $835. 50.

Exercise 9.
Meg is playing a card game with her friend, lona. The cards have positive and negative numbers printed on them. Meg exclaims: “The absolute value of the number on my card equals 8.” What is the number on Meg’s card?
Answer:
|- 8| = 8 or |8| = 8
Meg either has 8 or – 8 on her card.

Exercise 10.
List a positive and negative number whose absolute value is greater than 3. Justify your answer using the number line.
Answer:
Answers may vary. |-4| = 4 and |7| = 7; 4 > 3 and 7 > 3. On a number line, the distance from zero to – 4 is 4 units. So, the absolute value of – 4 is 4. The number 4 is to the right of 3 on the number line, so 4 is greater than 3. The distance from zero to 7 on a number line is 7 units, so the absolute value of 7 is 7. Since 7 is to the right of 3 on the number line, 7 is greater than 3.

Exercise 11.
Which of the following situations can be represented by the absolute value of 10? Check all that apply.
_________ The temperature is 10 degrees below zero. Express this as an integer.
_________ Determine the size of Harold’s debt if he owes $10.
_________ Determine how far – 10 is from zero on a number line.
_________ 10 degrees is how many degrees above zero?
Answer:
The temperature is 10 degrees below zero. Express this as an integer.
  X    Determine the size of Harold’s debt if he owes $10.
  X    Determine how far – 10 is from zero on a number line.
  X    10 degrees is how many degrees above zero?

Exercise 12.
Julia used absolute value to find the distance between 0 and 6 on a number line. She then wrote a similar
statement to represent the distance between 0 and – 6. Below is her work. Is it correct? Explain.
Answer:
|6| = 6 and |- 6| = – 6
No. The distance is 6 units whether you go from 0 to 6 or 0 to – 6. So, the absolute value 0f – 6 should also be 6, but Julia said it was – 6.

Exercise 13.
Use absolute value to represent the amount, in dollars, of a $238. 25 profit.
Answer:
|1238. 25| = 238.25

Exercise 14.
Judy lost 15 pounds. Use absolute value to represent the number of pounds Judy lost.
Answer:
|- 15| = 15

Exercise 15.
In math class, Carl and Angela are debating about Integers and absolute value. Carl said two integers can have the same absolute value, and Angela said one integer can have two absolute values. Who is right? Defend your answer.
Answer:
Carl is right. An integer and Its opposite are the same distance from zero. So, they have the same absolute values because absolute value is the distance between the number and zero.

Exercise 16.
Jamie told his math teacher: “Give me any absolute value, and I can tell you two numbers that have that absolute value.” Is Jamie correct? For any given absolute value, will there always be two numbers that have that absolute value?
Answer:
No, Jamie is not correct because zero is its own opposite. Only one number has an absolute value oJO, and that would be O.

Exercise 17.
Use a number line to show why a number and its opposite have the same absolute value.
Answer:
A number and its opposite are the same distance from zero but on opposite sides. An example is 5 and – 5. These numbers are both 5 units from zero. Their distance is the same, so they have the same absolute value, 5.

Exercise 18.
A bank teller assisted two customers with transactions. One customer made a $25 withdrawal from a savings account. The other customer made a $15 deposit. Use absolute value to show the size of each transaction. Which transaction involved more money?
Answer:
|- 25| = 25 and |15| = 15. The $25 withdrawal involved more money.

Exercise 19.
Which is farther from zero: – 7\(\frac{3}{4}\) or 7\(\frac{1}{2}\)? Use absolute value to defend your answer.
Answer:
The number that is farther from 0 is – 7\(\frac{3}{4}\). This is because = |-7\(\frac{3}{4}\)| and |7\(\frac{1}{2}\)| = 7\(\frac{1}{2}\). Absolute value is a number’s distance from zero. I compared the absolute value of each number to determine which was farther from zero. The absolute value of – 7\(\frac{3}{4}\) is 7\(\frac{3}{4}\). The absolute value of 7 is 7\(\frac{1}{2}\). We know that 7\(\frac{3}{4}\) is greater than 7\(\frac{1}{2}\). Therefore, – 7\(\frac{3}{4}\) is farther from zero than 7\(\frac{1}{2}\).
Therefore, – 7\(\frac{3}{4}\) is farther from zero than 7\(\frac{1}{2}\).

Eureka Math Grade 6 Module 3 Lesson 11 Problem Set Answer Key

For each of the following two quantities in Problems 1 – 4, which has the greater magnitude? (Use absolute value to defend your answers.)

Question 1.
33 dollars and – 52 dollars
Answer:
|- 52| = 52 |33| = 33                                       52 > 33, so – 52 dollars has the greater magnitude.

Question 2.
– 14 feet and 23 feet
Answer:
|- 14| = 14 |23| = 23                                      14 < 23, so 23 feet has the greater magnitude.

Question 3.
– 24.6 pounds and – 24.58 pounds
Answer:
|- 24.6| = 24.6                                |- 24. 58| = 24.58
24.6 > 24.58, so – 24.6 pounds has the greater magnitude.

Question 4.
– 11\(\frac{1}{4}\) degrees and 11 degrees
Answer:
|-11\(\frac{1}{4}\)| = 11\(\frac{1}{4}\)                              |11| = 11
11\(\frac{1}{4}\) > 11, so – 11\(\frac{1}{4}\) degrees has the greater magnitude.

For Problems 5-7, answer true or false. If false, explain why.

Question 5.
The absolute value of a negative number will always be a positive number.
Answer:
True

Question 6.
The absolute value of any number will always be a positive number.
Answer:
False. Zero is the exception since the absolute value of zero is zero, and zero is not positive.

Question 7.
Positive numbers will always have a higher absolute value than negative numbers.
Answer:
False. A number and its opposite have the same absolute value.

Question 8.
Write a word problem whose solution is |20| = 20.
Answer:
Answers will vary. Kelli flew a kite 20 feet above the ground. Determine the distance between the kite and the ground.

Question 9.
Write a word problem whose solution is |- 70| = 70.
Answer:
Answers will vary. Paul dug a hole in his yard 70 inches deep to prepare for an in-ground swimming pool. Determine the distance between the ground and the bottom of the hole that Paul dug.

Question 10.
Look at the bank account transactions listed below, and determine which has the greatest impact on the account balance. Explain.
a. A withdrawal of $60
b. A deposit of $55
c. A withdrawal of $58.50
Answer:
|- 60| = 60                         |55| = 55                           |- 58.50| = 58.50
60 > 58. 50 > 55, so a withdrawal of $60 has the greatest impact on the account balance.

Eureka Math Grade 6 Module 3 Lesson 11 Exit Ticket Answer Key

Jessie and his family drove up to a picnic area on a mountain. In the morning, they followed a trail that led to the mountain summit, which was 2,000 feet above the picnic area. They then returned to the picnic area for lunch. After lunch, they hiked on a trail that led to the mountain overlook, which was 3, 500 feet below the picnic area.

a. Locate and label the elevation of the mountain summit and mountain overlook on a vertical number line. The picnic area represents zero. Write a rational number to represent each location.
Answer:
Picnic area:   0 
Mountain summit:   2,000  
Mountain overlook:   3,500  

b. Use absolute value to represent the distance on the number line of each location from the picnic area.
Answer:
Distance from the picnic area to the mountain summit    |2,000| =   2,000   
Distance from the picnic area to the mountain overlook:    |- 3,500| =   3,500   

c. What is the distance between the elevations of the summit and overlook? Use absolute value and your number line from part (a) to explain your answer.
Answer:
Summit to picnic area and picnic area to overlook: 2,000 + 3,500 = 5,500
There are 2,000 units from zero to 2,000 on the number line.
There are 3,500 units from zero to – 3, 500 on the number line.
Altogether, that equals 5, 500 units, which represents the distance on the number line between the two elevations. Therefore, the difference in elevations is 5,500 feet.

Eureka Math Grade 6 Module 3 Lesson 11 Opening Exercise Answer Key

Answer:
After two minutes:
→ What are some examples you found (pairs of numbers that are the same distance from zero)?
\(\frac{1}{2}\) and \(\frac{1}{2}\), 8.01 and – 8.01, – 7 and 7.
→ What is the relationship between each pair of numbers?
They are opposites.
→ How does each pair of numbers relate to zero?
Both numbers in each pair are the same distance from zero.

Engage NY Eureka Math 6th Grade Module 3 Lesson 10 Answer Key

Eureka Math Grade 6 Module 3 Lesson 10 Example Answer Key

Example 1.
Writing Inequality Statements Involving Rational Numbers
Write one inequality statement to show the relationship among the following shoe sizes: 10\(\frac{1}{2}\), 8, and 9.
a. From least to greatest:
Answer:
8 < 9 < 10\(\frac{1}{2}\)

b. From greatest to least:
Answer:
10\(\frac{1}{2}\) > 9 > 8

Example 2.
Interpreting Data and Writing Inequality Statements
Mary is comparing the rainfall totals for May, June, and July. The data Is reflected in the table below. Fill in the blanks below to create inequality statements that compare the changes in Total Rainfall for each month (the right-most column of the table).

Write one inequality to order the Changes in Total Rainfall:
From least to greatest:   – 1.4 < 0.3 < 0.5   
From greatest to least:   0.5 >0.3 > -1.4     

In this case, does the greatest number indicate the greatest change in rainfall? Explain.
Answer:
No. In this situation, the greatest change is for the month of May since the average total rainfall went down from last year by 1.4 inches, but the greatest number in the inequality statement is 0. 5.

Eureka Math Grade 6 Module 3 Lesson 10 Exercise Answer Key

Exercise 1.
Graph your answer from the Opening Exercise part (a) on the number line below.
Answer:

Exercise 2.
Also, graph the points associated with 4 and 5 on the number line.
Answer:

Exercise 3.
Explain in words how the location of the three numbers on the number line supports the inequality statements you wrote in the Opening Exercise parts (b) and (c).
Answer:
The numbers are ordered from least to greatest when I look at the number line from left to right. So, 4 is less than 4. 75, and 4.75 is less than 5.

Exercise 4.
Write one inequality statement that shows the relationship among all three numbers.

Answer:
4 < 4.75 < 5

Exercise 5.
Mark’s favorite football team lost yards on two back-to-back plays. They lost 3 yards on the first play. They lost 1 yard on the second play. Write an inequality statement using integers to compare the forward progress made on each play.
Answer:
– 3 < – 1

Exercise 6.
Sierra had to pay the school for two textbooks that she lost. One textbook cost $55, and the other cost $75. Her mother wrote two separate checks, one for each expense. Write two integers that represent the change to her mother’s checking account balance. Then, write an inequality statement that shows the relationship between these two numbers.
Answer:
– 55 and – 75; – 55 > – 75

Exercise 7.
Jason ordered the numbers – 70, – 18, and – 18. 5 from least to greatest by writing the following statement: – 18 < – 18.5 < – 70. Is this a true statement? Explain.
Answer:
No, it is not a true statement because 18 < 18. 5 < 70, so the opposites of these numbers are in the opposite order. The order should be – 70 < – 18.5 < 18.

Exercise 8.
Write a real-world situation that is represented by the following inequality: – 19 < 40. Explain the position of the numbers on a number line.
Answer:
The coldest temperature in January was – 19 degrees Fahrenheit, and the warmest temperature was 40 degrees Fahrenheit. Since the point associated with 40 is above zero on a vertical number line and – 19 is below zero, we know that 40 is greater than – 19. This means that 40 degrees Fahrenheit is warmer than – 19 degrees Fahrenheit.

Exercise 9.
A Closer Look at the Sprint
Look at the following two examples from the Sprint.

a. Fill in the numbers In the correct order.
– 1< – <\(\frac{1}{4}\) < 0 and 0 > – \(\frac{1}{4}\) > – 1

b. Explain how the position of the numbers on the number line supports the inequality statements you created.
Answer:
– 1 is the farthest left on the number line, so it is the least value. 0 is farthest right, so it is the greatest value, and – \(\frac{1}{4}\) is in between.

c. Create a new pair of greater than and less than inequality statements using three other rational numbers.
Answer:
Answers will vary. 8 > 0. 5 > – 1.8 and – 1.8 < 0.5 < 8

Eureka Math Grade 6 Module 3 Lesson 10 Problem Set Answer Key

For each of the relationships described below, write an Inequality that relates the rational numbers.

Question 1.
Seven feet below sea level Is farther below sea level than 4\(\frac{1}{2}\) feet below sea level.
Answer:
– 7 < – 4\(\frac{1}{2}\)

Question 2.
Sixteen degrees Celsius is warmer than zero degrees Celsius.
Answer:
16 > 0

Question 3.
Three and one-half yards of fabric Is less than five and one-half yards of fabric.
Answer:
3\(\frac{1}{2}\) < 5\(\frac{1}{2}\)

Question 4.
A loss of $500 in the stock market is worse than a gain of $200 in the stock market.
Answer:
– 500 < 200

Question 5.
A test score of 64 is worse than a test score of 65, and a test score of 65 is worse than a test score of 67\(\frac{1}{2}\)
Answer:
64 < 65 < 67\(\frac{1}{2}\)

Question 6.
In December, the total snowfall was 13. 2 inches, which is more than the total snowfall in October and November, which was 3.7 inches and 6. 15 inches, respectively.
Answer:
13.2 > 6.15 > 3.7

For each of the following, use the information given by the inequality to describe the relative position of the numbers on a horizontal number line.

Question 7.
– 0.2 < – 0.1
Answer:
– 0.2 is to the left of – 0.1, or – 0.1 is to the right of – 0.2.

Question 8.
8\(\frac{1}{4}\) > -8\(\frac{1}{4}\)
Answer:
8\(\frac{1}{4}\) is to the right of – 8\(\frac{1}{4}\) or – 8\(\frac{1}{4}\) is to the left of 8\(\frac{1}{4}\).

Question 9.
– 2 < 0 < 5
Answer:
– 2 is to the left of zero and zero is to the left of 5, or 5 is to the right of zero and zero is to the right of – 2.

Question 10.
– 99 > – 100
Answer:
– 99 is to the right of – 100, or – 100 is to the left of – 99.

Question 11.
– 7.6 <- 7\(\frac{1}{2}\) – 7
Answer:
– 7.6 is to the left of – 7\(\frac{1}{2}\) and – 7\(\frac{1}{2}\) is to the left of – 7, or – 7 is to the right of – 7\(\frac{1}{2}\) and – 7\(\frac{1}{2}\) is to the right of – 7.6.

Fill in the blanks with numbers that correctly complete each of the statements.

Question 12.
Three integers between -4 and 0
Answer:
– 3 < – 2 < – 1

Question 13.
Three rational numbers between 16 and 15
Answer:
15.3 < 15.6 < 15.7
Other answers are possible.

Question 14.
Three rational numbers between -1 and -2
Answer:
– 1.9 < – 1.55 < – 1.02
Other answers are possible.

Question 15.
Three integers between 2 and – 2
Answer:
– 1 < 0 < 1

Eureka Math Grade 6 Module 3 Lesson 10 Exit Ticket Answer Key

Question 1.
Kendra collected data for her science project. She surveyed people asking them how many hours they sleep during a typical night. The chart below shows how each person’s response compares to 8 hours (which is the answer she expected most people to say).

a. Plot and label each of the numbers in the right-most column of the table above on the number line below.

Answer:

b. List the numbers from least to greatest
Answer:
– 1.0, – \(\frac{1}{4}\), 0, 0.5, 1.5

c. Using your answer from part (b) and inequality symbols, write one statement that shows the relationship among all the numbers.
Answer:
– 1.0 < –\(\frac{1}{4}\) < 0 < 0.5 < 1.5 or 0.5 > 0.5 > 0 > –\(\frac{1}{4}\) > -1.0

Eureka Math Grade 6 Module 3 Lesson 10 Opening Exercise Answer Key

“The amount of money I have in my pocket is less than $5 but greater than $4.”
a. One possible value for the amount of money in my pocket is ___________ .
Answer:
$4.75

b. Write an inequality statement comparing the possible value of the money in my pocket to $4.
Answer:
4.00 < 4.75

c. Write an inequality statement comparing the possible value of the money in my pocket to $5.
Answer:
4.75 < 5.00

Eureka Math Grade 6 Module 3 Lesson 10 Inequality Statements Answer Key

Rational Numbers: Inequality Statements – Round 1
Directions: Work in numerical order to answer Problems 1 – 33. Arrange each set of numbers in order according to the inequality symbols.

Question 1.

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Question 2

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Question 3.

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Question 4.

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Question 5.

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Question 6.

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Question 7.

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Question 8.

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Question 9.

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Question 10.

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Question 11.

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Question 12.

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Question 13.

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Question 14

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Question 15.

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Question 16.

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Question 17.

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Question 18.

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Question 19.

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Question 20.

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Question 21.

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Question 22.

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Question 23.

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Question 24.

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Question 25.

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Question 26.

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Question 27.

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Question 28.

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Question 29.

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Question 30.

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Question 31.

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Question 32.

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Question 33.

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Rational Numbers: Inequality Statements – Round 2
Directions: Work in numerical order to answer Problems 1 – 33. Arrange each set of numbers in order according to the inequality symbols.

Answer: