We included **H****MH Into Math Grade 7 Answer Key**** PDF** **Module 4 Lesson 1 Compute Sums of Integers **to make students experts in learning maths.

## HMH Into Math Grade 7 Module 4 Lesson 1 Answer Key Compute Sums of Integers

I Can identify integer addition problems. I feel confident that I can write and evaluate expressions to solve real-world integer addition problems.

**Spark Your Learning**

A submarine was stationed 700 feet below sea level. It ascends 250 feet every hour. If the submarine continues to ascend at the same rate, when will the submarine be at the surface?

Answer:

Given that,

A submarine was stationed 700 feet below sea level.

It ascends 250 feet every hour.

The addition expression is 700 + 250 = 950 feet.

The submarine be at the surface is at 950 feet.

**Turn and Talk** How can you express the depth as an integer to show that the submarine is below water?

**Build Understanding**

1. A submarine descends to 800 feet below sea level. Then it descends another 200 feet. What is the submarine’s final elevation? First use a number line to find out. Then use absolute value to solve the same problem without a number line.

A. Write an addition expression, and use the number line to determine the final elevation of the submarine.

Answer:

Given that,

A submarine descends to 800 feet below sea level

It descends another 200 feet.

The addition expression is (-800) + (-200) = -1000.

B. Recall that the absolute value of a number is the number’s distance from 0 on the number line. For example, the absolute value of -4 is 4 because -4 is 4 units from 0.

Because the number line arrows both go the same direction, you can find the submarine’s final distance from 0 by adding the absolute values of the numbers.

|-800| + |-200| = ___ + ___ = ____

Answer:

The submarine’s final distance from 0 by adding the absolute values of the numbers.

|-800| + |-200| = 800 + 200 = 1000.

C. How does the sum of the absolute values compare to the sum of —800 and -200?

_____________________

D. How can you use the sum of absolute values in Part B to find the final elevation—that is, to find the sum of —800 and —200?

_____________________

_____________________

E. Find -100 + (-300) by first adding the absolute values. Use the number line above to check your answer.

|-100| + |-300| = ___ + ___ = ___, so -100 + (-300) = ___

|-100| + |-300| = 100 + 300 = 400

So, -100 + (-300)

F. Complete the rule for adding integers with the same signs: ___ the absolute values of the numbers and use the of the addends.

Answer: Add the absolute values of both numbers and use the sign of the addends.

**Turn and Talk** Use a number line to explain why adding two integers with the same sign will always result in a sum that has the same sign as the addends.

2. The temperature in the morning in Sioux City, Iowa, is shown. By the afternoon, the temperature had risen 25 °F. What was the temperature in the afternoon? First use a number line to find out. Then use absolute value to solve the same problem without a number line.

A. Write an addition expression and use the number line to determine the temperature in the afternoon.

The temperature in the afternoon is ____ °F.

Answer:

Given that,

The temperature in the morning in Sioux City is -5°F

By the afternoon, the temperature had risen 25 °F.

The temperature in the afternoon is -5 + 25 = 20 °F

The temperature in the afternoon is 20 °F

B. Use absolute value to find the distance of the final temperature from 0. Because the first number moves you left on the number line and the second number moves you right, subtract the lesser absolute value from the greater absolute value. How does the result compare to the sum in Part A?

_____________________

_____________________

C. On another day, the temperature was 30 °F but a severe ice storm caused a temperature drop of 35 °F. Write an addition expression and use the number line to determine the temperature after the ice storm.

The temperature after the ice storm was ___ °F.

Answer:

The temperature was 30 °F.

But a severe ice storm caused a temperature drop of 35 °F.

The addition expression is 30 + (-35) = -5

The temperature after the ice storm was -5 °F.

D. Consider the absolute values of the numbers. Use absolute value to find the distance of the final temperature from 0. Because the first number moves you right on the number line and the second number moves you left, subtract the lesser absolute value from the greater absolute value. How does the result compare to the sum in Part C?

E. Complete the rule for adding integers with different signs: ____ the lesser absolute value from the greater absolute value and use the sign of the addend with the _____ absolute value.

Answer:

Subtract the lesser absolute value from the greater absolute value and use the sign of the addend with the greater absolute value.

**Step It Out**

Adding integers with the same signs: Add the absolute values of both numbers and use the sign of the addends.

Adding integers with different signs: Subtract the lesser absolute value from the greater absolute value and use the sign of the addend with the greater absolute value.

3. The football team lost 10 yards on one play and gained 7 yards on the next play. What integer represents the overall change in position?

A. Write an addition expression for the overall change in position.

______________

Answer:

Given that,

The football team lost 10 yards on one play.

The football team gained 7 yards on the next play.

The addition expression for the overall change in position is -10 + 7 = -3 yards.

B. Complete the sentence: The addends in Part A have (the same / different) signs, so the absolute values will be (added / subtracted).

Answer:

The addends in Part A have the different signs, so the absolute values will be subtracted.

C. Subtract the lesser absolute value from the greater absolute value.

______________________________

Answer:

The lesser absolute value is 7.

The greater absolute value is 10.

The subtraction of the lesser absolute value from the greater absolute value is 7 – 10 = -3.

D. Complete the sentences: The addend with the greater absolute value is (positive / negative) so the sign of the solution will be (positive / negative). The overall change in position is ___ yards.

Answer:

The addend with the greater absolute value is positive so the sign of the solution will benegative. The overall change in position is -3 yards.

E. Explain why your answer is reasonable.

______________________________

F. Later, the team lost 5 yards and then lost another 3 yards. Write an addition expression for the overall change in position.

______________________________

Answer:

Given that,

The team lost 5 yards.

The team lost another 3 yards.

The addition expression is -5 + (-3) = -8.

G. Explain how to evaluate the expression in Part F using absolute value. Then find this overall change in position.

______________________________

**Check Understanding**

Question 1.

The morning temperature is -15 °F. By the afternoon, the temperature rises by 20 °F. Write an addition expression for the afternoon temperature, and then find the temperature in the afternoon.

______________________________

Answer:

Given,

The morning temperature is -15 °F. By the afternoon, the temperature rises by 20 °F.

-15 + 20 = 5°F

Thus the temperature is 5°F in the afternoon.

Question 2.

During a game, Dennis lost 50 points in the first round and then lost 75 more points in the second round. Write an addition expression for the change in Dennis’s score after two rounds, and then find the change.

______________________________

Answer:

Given,

During a game, Dennis lost 50 points in the first round and then lost 75 more points in the second round.

-50 – 75 = -(50 + 75) = -125 points

**On Your Own**

Question 3.

Belle’s dad lends her $10. Then Belle borrows another $15 from him. Write and evaluate an expression that shows the change in the amount of money Belle’s dad has.

______________________________

Answer:

Given,

Belle’s dad lends her $10.

Then Belle borrows another $15 from him.

-10 – 15 = -25

Therefore the change in the amount of money Belle’s dad has is -$25.

Question 4.

The changes in the elevation of a plane while it was flying are shown below. Write and evaluate an expression that shows the plane’s change in elevation compared to its altitude before the first descent.

________________________

Answer:

The changes in the elevation of a plane while it was flying are shown below.

Altitude 1 = 1500 feet

Altitude 2 = 900 feet

1500 – 900 = 600 feet

Thus the plane’s change in elevation compared to its altitude before the first descent is 600 feet.

Question 5.

Phillip added 15 pencils to his collection. He then gave 30 pencils to a friend. Write and evaluate an expression that shows Phillip’s net gain or loss.

Answer:

Given,

Phillip added 15 pencils to his collection.

He then gave 30 pencils to a friend.

15 – 30 = -15

So, Phillip loss 15 pencils.

Question 6.

The temperature started at -20 °F, then rose by 12 °F. Write and evaluate an expression for the current temperature.

Answer:

Given,

The temperature started at -20 °F, then rose by 12 °F.

-20 + 12 = -8°F.

Question 7.

**Financial Literacy** A customer withdrew $100 from a bank account. The customer then deposited $33 the next day. Write and evaluate an expression to show the net effect of these transactions.

Answer:

Given,

A customer withdrew $100 from a bank account. The customer then deposited $33 the next day.

-100 + 33 = -67 net

**For Problems 8—13, find each sum.**

Question 8.

-7 + 10

______________

Answer:

-7 + 10

10 – 7 = 3

So, the answer is 3.

Question 9.

-42 + (-6)

______________

Answer:

-42 + (-6)

-42 – 6 = -48

So, the answer is -48.

Question 10.

-5 + (-2)

______________

Answer:

-5 + (-2)

-5 – 2 = -7

So, the answer is -7.

Question 11.

-21 + (-5)

______________

Answer:

-21 + (-5)

-21 – 5 = -26

So, the answer is -26.

Question 12.

18 + (-13)

______________

Answer:

18 + (-13)

18 – 13 = 5

So, the answer is 5.

Question 13.

-15 + 6

______________

Answer:

-15 + 6

6 – 15 = -9

So, the answer is -9.

Question 14.

**Reason** Blake’s journey through the elevators of his building is shown. Write and evaluate an expression that shows the change in Blake’s location compared to his starting point.

________________________

________________________

Answer:

-11 + 5 = -6 floors

Question 15.

Seth earned $76 and spent $42. Write and evaluate an addition expression that shows how much money Seth has left from the amount that he earned.

_____________________

Answer:

Given,

Seth earned $76 and spent $42.

76 + (-42)

76 – 42 = $34

Question 16.

A scuba diver started at sea level and dove 100 feet. The diver then rose 25 feet. Write and evaluate an expression that shows the diver’s current elevation relative to sea level.

_____________________

Answer:

Given,

A scuba diver started at sea level and dove 100 feet.

The diver then rose 25 feet.

-100 + 25 = -75 feet

Question 17.

The football team gained 10 yards but then lost 17. Write and evaluate an addition expression showing the team’s net yardage.

_____________________

Answer:

Given,

The football team gained 10 yards but then lost 17.

10 – 17 = -7 yards

Thus the expression shows that they lost 7 yards.

**For Problems 18-23, find each sum.**

Question 18.

-14 + 0

_____________________

Answer: -14

Question 19.

4 + (-50)

_____________________

Answer:

4 + (-50)

-50 + 4 = -46

So, the answer is -46.

Question 20.

-12 + (-63)

_____________________

Answer:

-12 + (-63)

+ × – = –

-12 – 63 = -75

So, the answer is -75.

Question 21.

22 + (-7)

_____________________

Answer:

22 + (-7)

22 – 7 = 15

So, the answer is 15.

Question 22.

36 + (-36)

_____________________

Answer:

36 + (-36)

36 – 36 = 0

So, the answer is 0.

Question 23.

-28 + 14

_____________________

Answer:

-28 + 14 = -14

So, the answer is -14.

Question 24.

**Financial Literacy** A bank account had a balance of $1,100. Then the customer withdrew $450. Write and evaluate an addition expression showing the new account balance.

Answer:

Given,

A bank account had a balance of $1,100.

Then the customer withdrew $450.

1100 – 450 = $650

Thus the new account balance is $650.

**I’m in a Learning Mindset!**

What questions can I ask my teacher or others to help me understand integer addition?

_____________________

**Lesson 4.1 More Practice/Homework**

**Compute Sums of Integers**

Question 1.

**Use Structure** Joni climbed 230 feet up a hill and then rappelled down 300 feet into a valley.

A. Write an addition expression to represent the situation.

_____________________

Answer:

Given,

Joni climbed 230 feet up a hill and then rappelled down 300 feet into a valley.

230 + (-300)

B. Evaluate the expression to determine how far Joni was from where she started.

_____________________

Answer:

Joni climbed = 230 feet

Rappelled down = 300 feet

230 – 300 = -70 feet

Question 2.

The temperature at 8:00 a.m. on a winter day was -2 °F. By noon, the temperature had increased by 28 °F. Should you add or subtract the absolute values to find the temperature at noon? Write and evaluate an absolute value expression to find the temperature at noon.

_____________________

Answer:

Given,

The temperature at 8:00 a.m. on a winter day was -2 °F.

By noon, the temperature had increased by 28 °F.

Therefore, since there was an increase in temperature, we’ll add the values given and this will be:

= -2°F + 28°F

= 26°F

Therefore, the temperature at noon is 26°F.

Question 3.

**Math on the Spot** Andrea’s income from a lemonade stand was $28. Supply expenses were $9. Write and evaluate an addition expression to find Andrea’s profit or loss.

_____________________

_____________________

_____________________

Answer:

Given,

Andrea’s income from a lemonade stand was $28. Supply expenses were $9.

28 + (-9)

$28 – $9 = $19

**For Problems 4.-12, find each sum.**

Question 4.

14 + 8

______________

Answer:

14 + 8 = 22

The sum of 14 and 8 is 22.

So, the answer is 22.

Question 5.

20 + (-5)

______________

Answer:

20 + (-5)

+ × – = –

20 – 5 = 15

So, the answer is 15.

Question 6.

-19 + 2

______________

Answer:

-19 + 2 = -17

The greatest value has a negative sign so the answer will be negative.

So, the answer is -17.

Question 7.

-10 + (-34)

______________

Answer:

-10 + (-34)

-10 – 34 = -44

So, the answer is -44.

Question 8.

46 + (-3)

______________

Answer:

46 + (-3)

46 – 3 = 43

So, the answer is 43.

Question 9.

-7 + (-24)

______________

Answer:

-7 + (-24)

-7 – 24 = -31

So, the answer is -31.

Question 10.

100 + (-26)

______________

Answer:

100 + (-26)

100 – 26 = 74

So, the answer is 74.

Question 11.

-57 + 90

_________

Answer:

-57 + 90

90 – 57 = 33

So, the answer is 33.

Question 12.

75 + (-30)

_________

Answer:

75 + (-30)

75 – 30 = 45

So, the answer is 45.

Question 13.

A car factory had an inventory of 327 car radios in stock. Then the company installed the radios in 243 cars and delivered those cars. Write and evaluate an addition expression for the remaining inventory of radios.

______________________________

______________________________

Answer:

Given,

A car factory had an inventory of 327 car radios in stock.

Then the company installed the radios in 243 cars and delivered those cars.

327 + (-243)

327 – 243 = 84

**Test Prep**

Question 14.

Melissa has $37 and spends $15. Which expression represents this situation?

A. 37 + 15

B. -37 + (-15)

C. -37 + 15

D. 37+ (-15)

Answer:

Given,

Melissa has $37 and spends $15.

37 + (-15)

37 – 15 = 22

Option D is the correct answer.

Question 15.

A rock climber descends 22 feet into a small canyon. The climber then climbs up 7 feet. Which integer represents his final position relative to where he started?

A. 29 ft

B. 15 ft

C. -15ft

D. -29 ft

Answer:

Given,

A rock climber descends 22 feet into a small canyon.

The climber then climbs up 7 feet.

-22 + 7 = -15 feet

Option C is the correct answer.

Question 16.

Write and evaluate an expression for the following number line.

Answer:

-2 + 2 = 0

**Spiral Review**

Question 17.

A room is 15 feet long and 12 feet wide. A scale drawing of the room is 10 inches by 8 inches. What is the scale of inches in the drawing to inches in the actual room?

_____________________

Answer:

Given,

A room is 15 feet long and 12 feet wide.

A scale drawing of the room is 10 inches by 8 inches.

1 foot = 12 inches

Long: 15 feet = 15 × 12 = 180 inches

Wide: 12 feet = 144 inches

180/10 = 144/8 = 18

Thus the scale factor is 18.

Question 18.

During a sale, cameras were discounted 30% from their original price of $295.99. How much was each camera during the sale to the nearest cent?

_____________________

Answer:

Given,

During a sale, cameras were discounted 30% from their original price of $295.99.

295.99 (1 – 30%)

295.99(1 – 0.3)

395.99 × 0.7 = 207.19

Question 19.

A bank pays 7% interest on 3-year certificates of deposit. What is the value of a $500 certificate after one year? Give your answer to the nearest cent.

_____________________

Answer:

Given,

A bank pays 7% interest on 3-year certificates of deposit.

500 × 7%

500 × 7/100 = $35

$500 + $35 = $535