We included **H****MH Into Math Grade 7 Answer Key**** PDF** **Module 3 Lesson 2 Add or Subtract a Negative Integer on a Number Line **to make students experts in learning maths.

## HMH Into Math Grade 7 Module 3 Lesson 2 Answer Key Add or Subtract a Negative Integer on a Number Line

I Can add or subtract negative integers on a number line.

**Spark Your Learning**

The scores of three contestants on a game show are shown. The final question is worth 50 points. A correct answer adds 50 points to a contestant’s score. An incorrect answer deducts 50 points.

Show the possible final scores for each contestant. What circumstances are necessary for each contestant to win?

**Turn and Talk** How can you add a number to each score to show a loss?

**Build Understanding**

1. The table shows the scores of three contestants on a game show.

A. Latrell spins a wheel to find out how many points he adds to his score. The wheel stops on “-5 points.” Use the number line to add —5 points to Latrell’s score. Then complete the equation.

8 + (-5) = ____

Answer:

8 + (-5)

8 – 5 = 3

B. Mayumi spins the wheel next. The wheel stops on “—11 points.” Use the number line to add —11 points to her score. Complete the equation.

6 + (-11) = ____

Answer:

6 + (-11)

6 – 11 = -5

C. How do Latrell’s and Mayumi’s final scores compare to their starting scores? Explain why this is reasonable.

__________________________

__________________________

__________________________

Answer:

Latrell’s score is 3 points

Mayumi’s final score is -5 points

D. Because Scott started with the lowest score, he plays a penalty round. In the penalty round, the wheel determines the number of points that are subtracted from a player’s score. The result of Scott’s spin is shown. Use the number line to find Scott’s score. Then complete the equation.

3 – (-7) = ____

Answer:

3 – (-7)

3 + 7 = 10

**Turn and Talk** Is it possible to subtract a loss from a positive number and result in a negative number? Why or why not

2. The table shows the scores of three contestants on a game show.

A. Natalie spins a wheel to find out how many points she adds to her score. The wheel stops on “—6 points.” Use the number line to add —6 points to Natalie’s score. Then complete the equation.

-2 + (-6) = ____

Answer:

-2 + (-6)

-2 – 6 = -8

B. Gina and Tyler both started with the lowest score, so they each play a penalty round. In the penalty round, the wheel determines the number of points that are subtracted from a player’s score. The result

of Gina’s spin is shown. Use the number line to find Gina’s score, and complete the equation.

-6 – (-9) = ____

Answer:

-6 – (-9)

-6 + 9 = 3 points

C. Explain which direction to move on the number line when you subtract a negative integer.

__________________________

__________________________

__________________________

__________________________

Answer:

You have to move to the left on the number line when you subtract a negative integer.

D. The result of Tyler’s spin is shown. Use the number line to find Tyler’s score, and complete the equation.

-6 – (-2) = ___

Answer:

-6 – (-2)

-6 + 2 = -4 points

**Turn and Talk** Is it possible to add a loss to a negative number and result in a positive number? Why or why not?

3. Jackson and Flora both have bank accounts, and they use credit cards. Use the number line to determine if they can pay off the credit card bill.

A. Jackson has $20 in his account. He uses a credit card to spend $30 on a coat and $10 on a movie. Jackson then deposits $50 into his account. How much will Jackson have left after he pays the credit card bill?

20 + ___ + ___ + ____ = _____

Can Jackson pay his credit card bill? Explain.

Answer:

Given,

Jackson has $20 in his account.

He uses a credit card to spend $30 on a coat and $10 on a movie.

30 + 10 = $40

His balance will be 20 – 40 = -$20

Jackson then deposits $50 into his account

-20 + 50 = $30

B. Flora starts with $10 in her account. She uses a credit card to spend $20 on a gift and $40 on some shoes, and then she returns a $30 appliance for a refund to be applied to her card. Use the number line to show these transactions.

10 – ___ – ___ – ___ = ____

Can Flora pay her credit card bill? Explain.

_________________

Answer:

Given,

Flora starts with $10 in her account.

She uses a credit card to spend $20 on a gift and $40 on some shoes, and then she returns a $30 appliance for a refund to be applied to her card.

10 – 20 – 40 – (-30)

10 – 60 + 30 = -20

**Check Understanding**

Question 1.

Jessica starts at an elevation of 40 feet and descends 60 feet. Use the number line to find Jessica’s current elevation. Then complete the equation.

40 + (-60) = ____

Answer:

Given,

Jessica starts at an elevation of 40 feet and descends 60 feet.

40 + (-60)

40 – 60 = -20 feet

Question 2.

The temperature is —4 °F, and later the temperature is —1 °F. Use the number line to find the change in temperature. Then complete the equation.

Answer:

Given,

The temperature is —4 °F, and later the temperature is —1 °F.

-1 – (-4)

-1 + 4 = 3°F

**On Your Own**

Question 3.

Denny has a balance of $7 on his transit card. Each train ride debits $3, which is the same as adding -$3 to the card. Use the number line to add -$3 to Denny’s balance, and complete the equation.

$ 7 + (-$3) = ____

Answer:

Given,

Denny has a balance of $7 on his transit card.

Each train ride debits $3, which is the same as adding -$3 to the card.

7 + (-3) = 4

**Three friends are playing a board game. The table shows their current scores. Each player draws two cards. The first card says “add” or “subtract.” The second card says a number of points. Use a number line and complete the equation to find each player’s final score.**

Question 4.

Andrew’s cards say “add” and “—4 points.”

Answer:

-4 + (-4)

-4 – 4 = -8

Question 5.

Saleema’s cards say “subtract” and “—7 points.”

Answer:

-3 – (-7)

-3 + 7 – 4

Question 6.

Cassie’s cards say “subtract” and “—8 points.”

Answer:

-9 – (-8)

-9 + 8 = -1

Question 7.

Tomas and a friend are hiking in Death Valley National Park in California. They start at an elevation of -10 meters. During the hike, they ascend 30 meters, descend 40 meters, and then descend another 20 meters. Use the number line and complete the equation to find their final elevation.

-10 + ___ + ___ + ___ = ____

Final elevation: ____

Answer:

Given,

Tomas and a friend are hiking in Death Valley National Park in California.

They start at an elevation of -10 meters.

During the hike, they ascend 30 meters, descend 40 meters, and then descend another 20 meters.

-10 + 30 + (-40) + (-20)

20 – 40 – 20 = -40

Final elevation: -40 meters

Question 8.

The temperature at midnight is —7 °F. Before noon, the temperature decreases by 2 °F, then increases by 5 °F, then increases by 4 °F. Use the number line and complete the equation to find the temperature at noon.

—7 °F — ___ + ___ + ____ = ___ Temperature at noon: ____

Answer:

Given,

The temperature at midnight is —7 °F.

Before noon, the temperature decreases by 2 °F, then increases by 5 °F, then increases by 4 °F.

-7 – 2 + 5 + 4

-9 + 9 = 0°F

Question 9.

**Critique Reasoning** Leah said that when you add two negative integers the result must be negative. Do you agree or disagree? Use a number line to help explain your answer.

Answer:

Yes, when you add two negative integers the result must be negative.

Example:

-200 – 200 = -400

Question 10.

**Open Ended** Write a story problem for the number line shown. Provide the answer to the problem.

Answer:

Question 11.

**STEM** The freezing point of seawater is —2 °C. The freezing point of nitric acid is —42 °C. How much greater is the freezing point of seawater than the freezing point of nitric acid?

Answer:

Given,

The freezing point of seawater is —2 °C.

The freezing point of nitric acid is —42 °C.

-2 – (-42)

-2 + 42 = 40 °C.

**For Problems 12-17, use a number line to add or subtract.**

Question 12.

7 – (-3) = ____

Answer:

7 – (-3)

– × – = +

7 + 3 = 10

So, the answer is 10.

Question 13.

-20 + (-30) = ____

Answer:

-20 + (-30)

+ × – = –

-20 – 30 = -50

So, the answer is -50.

Question 14.

-1 + (-6) = ___

Answer:

-1 + (-6)

+ × – = –

-1 – 6 = -7

So, the answer is -7

Question 15.

5 – (-4) = ____

Answer:

5 – (-4)

– × – = +

5 + 4 = 9

So, the answer is 9

Question 16.

-8 – (-5) = ____

Answer:

-8 – (-5)

– × – = +

-8 + 5 = -3

So, the answer is -3.

Question 17.

5 + (-5) = ____

Answer:

5 + (-5)

+ × – = –

5 – 5 = 0

So, the answer is 0.

**I’m in a Learning Mindset!**

What is challenging about subtracting negative integers? Can I work through it on my own, or do I need help?

**Lesson 3.2 More Practice/Homework**

Question 1.

Brad has 8 points during a trivia game. He answers a question incorrectly and —12 points are added to his score. Use the number line to add —12 points to Brad’s score, and complete the equation to show his final score.

8 + (-12) = ____

Answer:

Given,

Brad has 8 points during a trivia game.

He answers a question incorrectly and —12 points are added to his score.

8 + (-12) = -4 points

Question 2.

**Math on the Spot** A dolphin is swimming 3 feet below sea level. It dives down 9 feet to catch some fish. Then the dolphin swims 4 feet up toward the surface with its catch. What is the dolphin’s final elevation relative to sea level?

Answer:

Given,

A dolphin is swimming 3 feet below sea level.

It dives down 9 feet to catch some fish.

-3 – 9 = -12

12 feet below sea level.

Then the dolphin swims 4 feet up toward the surface with its catch.

-12 + 4 = -8

8 feet below sea level.

Question 3.

**Use Tools** Dario was scuba diving at an elevation of -20 feet, and then descended 20 feet more. After the descent, what was his elevation in relation to the other diver shown?

(-20 – ___) – ____ = ____

Relative elevation: _____

Answer:

(-20 – 20) – 30 = -40 – 30 = -70 feet

Relative elevation: -70 ft

Question 4.

Latisha has $40 in her checking account. She makes a withdrawal of $20 and then writes a check for $40. Then she deposits $30. Use the number line and complete the equation to find her final balance.

$40 + ___ + ___ + ___ = ___

Final balance: ____

Answer:

Given,

Latisha has $40 in her checking account.

She makes a withdrawal of $20 and then writes a check for $40.

Then she deposits $30.

40 + (-20) + (-40) + 30 = $10

**For Problems 5-10, use a number line to add or subtract.**

Question 5.

2 – (-4) = ____

Answer:

2 – (-4)

– × – = +

2 + 4 = 6

So, the answer is 6.

Question 6.

-2 + (-7) = ___

Answer:

-2 + (-7)

+ × – = –

-2 – 7 = -9

So, the answer is -9

Question 7.

-10 + (-60) = ___

Answer:

-10 + (-60)

+ × – = –

-10 – 60 = -70

So, the answer is -70.

Question 8.

3 – (-1) = ___

Answer:

3 – (-1)

3 + 1 = 4

So, the answer is 4.

Question 9.

-7 – (-7) = ___

Answer:

-7 – (-7)

-7 + 7 = 0

So, the answer is 0.

Question 10.

2 + (-9) = ____

Answer:

2 + (-9)

+ × – = –

2 – 9 = -7

So, the answer is -7

**Test Prep**

Question 11.

Elena wants to use a number line to find the difference 5 – (-7). Which is the best description of how she should do this?

A. Start at -7 and move 5 units right.

B Start at —7 and move 5 units left.

C Start at 5 and move 7 units right.

D Start at 5 and move 7 units left.

Answer:

Given,

Elena wants to use a number line to find the difference 5 – (-7).

The starting point is 5 and it moves 7 units to the right on the number line.

5 + 7 = 12

So, option C is the correct answer.

Question 12.

Which sum or difference can you evaluate using the number line model shown?

A. -3 – (-2)

B -3 – 2

C. -1 + 3

D. -1 – (-3)

Answer:

The point is on -3 it is moving 2 points to the right side on the number line.

-3 – (-2)

-3 + 2 = -1

So, option A is the correct answer.

Question 13.

Aaron is playing a board game and has a score of 20 points. He spins a spinner to see how many points will be added to his score. The spinner lands on “—50 points.” Find Aaron’s final score. Show your work.

Answer:

Given,

Aaron is playing a board game and has a score of 20 points.

The spinner lands on “—50 points.”

20 + (-50)

20 – 50 = -30 points

Question 14.

Which sum or difference is equal to 0?

A. -7 – 7

B. 4 – (-4)

C. -1 +(-1)

D. 6 + (-6)

Answer:

**Spiral Review**

Question 15.

At a restaurant, Brianna and Naomi each order an appetizer for $6.50 and an entree for $9.75. They decide to leave a 20% tip based on the total bill before tax. What is the total value of the tip they will leave?

Answer:

Question 16.

Colton has a $6 credit balance on his credit card. He uses the credit card to pay $9 for lunch. Use the number line to subtract $9 from Colton’s credit balance, and complete the equation.

$6 – $9 = ____

Answer:

Given,

Colton has a $6 credit balance on his credit card.

He uses the credit card to pay $9 for lunch.

$6 – $9 = -$3