## 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.