# Into Math Grade 7 Module 4 Lesson 2 Answer Key Compute Differences of Integers

We included HMH Into Math Grade 7 Answer Key PDF Module 4 Lesson 2 Compute Differences of Integers to make students experts in learning maths.

## HMH Into Math Grade 7 Module 4 Lesson 2 Answer Key Compute Differences of Integers

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

Evan and Laura are playing a video game. Their scores are shown. By how many points is Laura winning the game? Show your thinking.  Given that,
The Evan score is = -30
The Laura score is = 80
The subtraction expression is = 80 – (-30) = 110.
Laura won the game with 110 points.

Turn and Talk Write an addition expression that could be used to solve the problem. Does order matter in this problem? Why or why not?

Build Understanding

1. The temperature in the afternoon was 20 °F, and it went down by 30 °F by the evening.
A. Write a subtraction expression, and use the number line to determine what the temperature was by evening. By evening the temperature was ____ °F.
Given that,
The temperature in the afternoon was 20 °F.
It went down by 30 °F by the evening.
The subtraction expression is 20°F – 30 °F = -10 °F By the evening the temperature was -10 °F.

B. What is the sign of the number you subtracted? What direction did you move on the number line? __________
I subtracted the positive sign of the number. I moved on the number line in left side of the direction.

C. The thermometer shows the temperature on a Monday evening. The following evening it was expected to drop 10 °F. Write a subtraction expression, and use a number line to determine what the expected temperature was on Tuesday evening.  By Tuesday evening the expected temperature was ____ °F.
Given that,
The thermometer shows the temperature on a Monday evening is -5 °F
At the evening it was expected to drop 10 °F.
The subtraction expression is -5 °F -10 °F = -15 °F. By Tuesday evening the expected temperature was -15 °F.

D. What is the sign of the number you subtracted? What direction did you move on the number line? ______________
I subtracted the positive sign of the number. I moved to the number line on the left side of the direction.

E. Look at your number line movement for subtracting a positive number, and complete the equivalent addition expression for each subtraction expression.
20 – 30 = 20 + (____) -5 – 10 = -5 + (____)
The equivalent expression is 20 – 30 = 20 + (-15) -5 – 10 = -5 + (-5)

F. Complete the conjecture: To subtract a positive integer, ____ its ____
To subtract a positive integer on the number line it moves the opposite direction of its adding integers.

Turn and Talk Why do subtracting 30 and adding -30 give the same result? Is the same true for every integer? Explain.
Answer: The subtracting 30 and adding -30 give the same result. And it is same for all the integers.

2. Jenny borrows $20 from Bill. Jenny is now in debt to Bill. Her debt can be represented as -20 dollars. Bill tells Jenny to ignore$12 of that loan. A. Write a subtraction expression that describes Jenny’s debt as a negative number. Use the number line to determine the amount of money Jenny still owes Bill. Given that,
Jenny borrows $20 from Bill. Jenny is now in debt to Bill. Her debt can be represented as -20 dollars. Bill tells Jenny to ignore$12 of that loan.
The subtraction expression is -20 – (-12) = -8. B. What is the sign of the number you subtracted? What direction did you move on the number line? ________________
I subtracted the negative sign of the number. I moved on the number line in right side of the direction.

C. Perry has $10. Perry also borrows$3 from Lily, and Lily tells him not to pay her back. This situation can be represented by the expression 10 – (-3). Use the number line to find to find the value of this expression and determine Perry’s net amount of money. Perry’s net amount of money is ____ dollars.
Given that,
Perry has $10. Perry also borrows$3 from Lily.
Perry has total money is $13. Lily tells him not to pay her back. The subtraction expression is 10 – (-3) = 13. Perry’s net amount of money is$13.

D. What is the sign of the number you subtracted? What direction did you move on the number line? ______________
I subtracted the negative sign of the number. I moved to the number line on the right side of the direction.

E. Look at your number line movement for subtracting a negative number, and complete the equivalent addition expression for each subtraction expression.
-20 – (-12) = -20 + ___ 10 – (-3) = 10 + ___
-20 – (-12) = – 20 + 7 = 10 – (-3) = 10 + 3.

F. Complete the conjecture: To subtract a negative integer, ___ its ____.
To subtract a negative integer is simply an addition of negative and positive numbers.

Turn and Talk In Part E, explain how the movements on the number line show that the expressions are equivalent.

Step It Out

To subtract an integer, add its opposite.

3. Complete the equivalent addition expression for each subtraction expression. Then evaluate.
A. 6 – 6 = 6 + ___ ; ____
B. 5 – (-4) = 5 + ____ ; ____
C. -8 – 7 = -8 + ___ ; ____
D. -4 – (-9) = – 4 + ___ ; ____
E. Complete each statement.

After rewriting subtraction as addition, a statement that adds two negative numbers results in a ____ number.
After rewriting subtraction as addition, a statement that adds two positive numbers results in a ____ number.
After rewriting subtraction as addition, a statement that adds opposites results in _____.
A. 6 – 6 = 6 + (-6); 0
B. 5 – (-4) = 5 + 4; 9
C. -8 – 7 = -8 + (-7); -15
D. -4 – (-9) = – 4 + 9; 5
After rewriting subtraction as addition, a statement that adds two negative numbers results in a negative number.
After rewriting subtraction as addition, a statement that adds two positive numbers results in a positive number.
After rewriting subtraction as addition, a statement that adds opposites results in zero.

Check Understanding

Question 1.
Elise had a credit card balance of -$120. She made a payment of$70 this month. Write and evaluate a subtraction expression to find her new credit card balance.
___________________
___________________
Given,
Elise had a credit card balance of -$120. She made a payment of$70 this month.
That means we have to subtract 70 from 120
70 – 120 = -50

Question 2.
The temperature on a Monday evening was 8 °F. Tuesday evening it was expected to drop 12 °F. Write and evaluate a subtraction expression to find the expected temperature on Tuesday evening.
___________________
Given,
The temperature on a Monday evening was 8 °F. Tuesday evening it was expected to drop 12 °F.
8 – 12 = -4°F
Thus it would be -4°F on Tuesday temperature.

Question 3.
Complete the equivalent addition expression for each subtraction expression. Then evaluate.
A. 23 – 4 = 23 + ___ ; ____
23 + (-4) = 19 (since the greatest value has the negative sign)

B. 7 – (-15) = 7 + ___ ; ____
7 – (-15)
7 + 15 = 22

C. -15 – 4 = -15 + ___ ; ___
-15 – 4
-15 + (-4) = -19 (When both the signs are negative then we have to add the numbers.)

Question 4.
How do you subtract an integer from another integer without using a number line? Give an example.
The integer subtraction is governed by following the simple rules that the subtraction is normal as the natural numbers but the sign of a bigger number comes in the final result.
Example: -47 is to be subtracted from + 50 then, result = 50-47 = 3.

Question 5.
The temperature is 2 °F and drops to -15 °F overnight. Write and evaluate a subtraction expression to determine the change in temperature.
_____________________
Given,
The temperature is 2 °F and drops to -15 °F overnight.
2 – (-15)
2 + 15 = 17 °F
17°F is the change in temperature.

Question 6.
A submarine descended 500 feet below sea level. It then descended another 275 feet. Write and evaluate a subtraction expression to determine the new position of the submarine relative to sea level.
_____________________
Given,
A submarine descended 500 feet below sea level.
It then descended another 275 feet.
-(500 + 275) = -775 feet.

Question 7.
Eddy has $45. He needs a new bike tire that costs$70. Write and evaluate a subtraction expression to determine how much more Eddie needs in order to get the bike tire.
_____________________
Given,
Eddy has $45. He needs a new bike tire that costs$70.
$70 –$45 = $25 Question 8. Reason An oil rig drill digs at a constant rate each day. The progress on Monday and Tuesday is shown. Write and evaluate a subtraction expression to determine the total change in depth of the dig by the end of Tuesday. Explain why your answer is reasonable. Answer: An oil rig drill digs at a constant rate each day. The progress on Monday and Tuesday is shown. -(200 + 200) = -400 Thus, the total change in depth of the dig by the end of Tuesday is 400 feet. For Problems 9-14, write each subtraction expression as an equivalent addition expression and evaluate it. Question 9. -12 – (-10) __________ Answer: -12 – (-10) -12 + 10 = -2 (since the greatest value has the negative sign) Question 10. 25 – 67 __________ Answer: 25 – 67 -(67 – 25) = -42 25 – 67 = -42 (since the greatest value has the negative sign) Question 11. 0 – (-13) __________ Answer: 0 – (-13) – × – = + 0 + 13 = 13 Question 12. -2 – (-10) __________ Answer: -2 – (-10) – × – = + -2 + 10 = 8 Question 13. -15 – 12 __________ Answer: -15 – 12 – (15 + 12) = -27 (since the greatest value has the negative sign) Question 14. 22 – 37 __________ Answer: 22 – 37 -(37 – 22) = -15 (since the greatest value has the negative sign) Question 15. Reason Cheyenne is playing a board game. Her score was -175 at the start of her turn, and at the end of her turn her score was -325. What was the change in Cheyenne’s score from the start of her turn to the end of her turn? How did you determine your answer? Answer: Given, Cheyenne is playing a board game. Her score was -175 at the start of her turn, and at the end of her turn her score was -325. -325 – (-175) -325 + 175 = -150 Question 16. The West High football team gained 7 yards but then lost 15 yards. Write and evaluate a subtraction expression to determine the overall change in yardage. Answer: Given, The West High football team gained 7 yards but then lost 15 yards. Overall change in Yardage = 7 – 15 = -8 Thus the west high football team loses 8 yards. Question 17. Financial Literacy Amy had a$10 monthly fee for music streaming due when she received her paycheck. After paying for the music streaming service, she had $65 remaining from her paycheck. Write and evaluate a subtraction expression to determine the original value of Amy’s paycheck. Answer: Given, Amy had a$10 monthly fee for music streaming due when she received her paycheck.
After paying for the music streaming service, she had $65 remaining from her paycheck. x – 10 = 65 x = 65 + 10 x =$75
10 + 65 = $75 75 – 10 =$65

Question 18.
At the beginning of the game, April had a score of —150 points. April played for another 20 minutes, and her final score was —355. Write and evaluate a subtraction expression to determine the change of her score from the beginning of the game to the end of the game. Given,
At the beginning of the game, April had a score of —150 points.
April played for another 20 minutes, and her final score was —355.
End point – beginning point
355 – 150 = 205 point
Thus the change in the score is 205 points.

For Problems 19-26, write each subtraction expression as an equivalent addition expression and evaluate it.

Question 19.
41 – 41
__________
Any number subtracted with the same number will be 0.
41 – 41 = 0

Question 20.
36 – 48
__________
36 – 48
-(48 – 36) = -12
The greatest value has a negative sign so the answer will be negative.

Question 21.
-13 – (-10)
__________
-13 – (-10)
-13 + 10 = -3

Question 22.
-9 – (-13)
__________
-9 – (-13)
-9 + 13 = 4

Question 23.
21 – 6
__________
21 – 6
-6 + 21 = 15

Question 24.
-33 – 7
__________
-33 – 7
When both the signs are negative then we have to add the numbers.
-(33 + 7)
-(40)
-33 – 7 = -40

Question 25.
0 – (-5)
__________
0 – (-5)
– × – = +
0 + 5 = 5

Question 26.
-19 – (-19)
__________
-19 – (-19)
-19 + 19 = 0

I’m in a Learning Mindset!

How effective was the number line for subtraction problems with integers?

Lesson 4.2 More Practice/Homework

Question 1.
Sadie won her golf game with Brynn. What Is the difference in their scores? A. Write a subtraction expression to represent the situation.
___________________
Answer: 4 – (-2) = 6

B. What is the difference In the girl’s scores?
___________________
The difference between Sadie and Brynn is 6.
4 – (-2) = 6

Question 2.
Wednesday morning, the temperature was —12 °F. By the afternoon, the temperature was 23 °F. Write and evaluate a subtraction expression to determine the number of degrees of change in temperature between the morning and the afternoon.
___________________
Given,
Wednesday morning, the temperature was —12 °F. By the afternoon, the temperature was 23 °F.
Δ °F = 23°F – (-12°F)
= 23°F + 12°F
= 35°F

Question 3.
Open Ended Write a word problem that includes subtracting a negative number from a positive number.
___________________
On Monday morning, the temperature was -8 °F. By the afternoon, the temperature was 21 °F. Write and evaluate a subtraction expression to determine the number of degrees of change in temperature between the morning and the afternoon.
Solution:
Δ °F = 21°F – (-8°F)
= 21°F + 8°F
= 29°F

Math on the Spot For Problems 4-6, find each difference.

Question 4.
10 – 14
___________________
10 – 14 = -4
The greatest value has a negative sign so the answer will be negative.

Question 5.
-7 – (-5)
___________________
-7 – (-5)
– × – = +
-7 + 5 = -2
The greatest value has a negative sign so the answer will be negative.

Question 6.
-8 – 2
___________________
-8 – 2
When both the signs are negative then we have to add the numbers.
-(8 + 2) = -10

For Problems 7—15. find each difference.

Question 7.
-14 – 5
___________________
-14 – 5
When both the signs are negative then we have to add the numbers.
-(14 + 5) = -19

Question 8.
23 – (-7)
___________________
23 – (-7)
23 + 7 = 30
23 – (-7) = 30

Question 9.
-100 – 8
___________________
-100 – 8
When both the signs are negative then we have to add the numbers.
-(100 + 8) = -108

Question 10.
24 – 57
___________________
24 – 57
-(57 – 24) = -33
The greatest value has a negative sign so the answer will be negative.
24 – 57 = -33

Question 11.
65 – 65
___________________
65 – 65 = 0

Question 12.
-23 – (-5)
___________________
-23 – (-5)
-23 + 5 = -18
The greatest value has a negative sign so the answer will be negative.
-23 – (-5) = -23 + 5 = -18

Question 13.
-5 – (-11)
___________________
-5 – (-11)
-5 + 11 = 6
-5 – (-11) = 6

Question 14.
-16 – 9
___________________
-16 – 9
When both the signs are negative then we have to add the numbers.
-(16 + 9) = -25

Question 15.
24 – (-37)
___________________
24 – (-37)
24 + 37 = 61
24 – (-37) = 61

For Problems 16-17, write each subtraction expression as an equivalent addition expression and evaluate it.

Question 16.
-3 – (-5)
-3 – (-5)
-3 + 5 = 2
-3 – (-5) = 2

Question 17.
15 – 21
-(-15 + 21)
-(6) = -6
15 – 21 = -6

Test Prep

Question 18.
Maya’s bank account had $55. She wrote a check for$42. Which expression represents the situation?
A. 55 + 42
B. -42 – 55
C. 55 – 42
D. 42 – 55
Given,
Maya’s bank account had $55. She wrote a check for$42.
55 – 42 = 13
Option C is the correct answer.

Question 19.
George had a score of 25 points in a game. During the rest of the game, he lost 59 points. What score did George have at the end?
A. 34
B. -34
C. 84
D. -84
Given,
George had a score of 25 points in a game. During the rest of the game, he lost 59 points.
25 – 59 = -34
Option B is the correct answer.

Question 20.
The highest elevation in California is 14,505 feet, and the lowest elevation is —282 feet. Write and evaluate an expression to determine the distance between the lowest and highest elevations.
______________
Given,
The highest elevation in California is 14,505 feet, and the lowest elevation is —282 feet.
Distance = 14,505 – (-282)
= 14,505 + 282
= 14787 feet
Thus the distance between the lowest and highest elevations is 14,787 feet.

Question 21.
Evaluate -13 – (-17).
A. -30
B. -4
C. 4
D. 30
-13 -(-17)
-13 + 17 = 4
-13 – (-17) = 4
Thus option C is the correct answer.

Question 22.
Evaluate 23 – (-9).
23 – (-9)
– × – = +
23 + 9 = 32

Spiral Review

Question 23.
Kelsey jogs 60 feet in 6 seconds. What is this rate in miles per hour? Round to the nearest tenth.
______________
Given,
Kelsey jogs 60 feet in 6 seconds.
The rate is 60/6 = 10 mile/hour
Therefore the rate in miles per hour to the nearest tenth is 10 miles per hour.

Question 24.
Find the percent change from 75 to 24. State whether it is an increase or decrease. Round to the nearest tenth of a percent if necessary.
______________
(24 – 75)/75
= -51/75
= -17/25
= -17/25 × 4/4
= -68/100
= -68%

Question 25.
Find the percent change from 26 to 34. State whether it is an increase or decrease. Round to the nearest tenth of a percent if necessary.
______________