We included **H****MH Into Math Grade 7 Answer Key**** PDF** **Module 3 Lesson 1 Add or Subtract a Positive Integer on a Number Line **to make students experts in learning maths.

## HMH Into Math Grade 7 Module 3 Lesson 1 Answer Key Add or Subtract a Positive Integer on a Number Line

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

**Spark Your Learning**

John has an account balance of $20. He receives his weekly paycheck for work at his part-time job in the amount of $110. He can’t find a bike he wants, so he buys some comic books for $40. Then John finds his dream bike priced as shown. If he buys the bike now, what will his account balance be?

Answer:

Given that,

John has an account balance of $20.

For the part time job he gets $110

He buys some comic books for $40.

The cost of the bike is $80.

The total balance is $20 + $110 = $130.

After buying the comic books the balance is $130 – $40 = $90

After buying the bike the balance is $90 – $80 = $10

The balance is $10.

**Turn and Talk** What happens when you subtract a greater positive number from a lesser positive number?

Answer: when we subtract a greater positive number from the lesser positive number then we get the positive number.

**Build Understanding**

1. Use the thermometer as a number line to answer the following questions.

A. On Monday morning, it was 35 °F outside. Plot this on the thermometer.

Answer:

Given that,

Plot 35 °F on the temperature.

B. By afternoon, the temperature rose 20 degrees. What distance will you move on the thermometer? ____ In which direction will you move? ____

Answer:

Given that,

Monday morning the temperature is 35 °F

The temperature rises 20 degrees on Monday afternoon.

The distance will you move on the thermometer is 55 degrees. You can move in upward direction.

C. Show the change in temperature on the thermometer. What was the temperature Monday afternoon? ____________

Answer:

After a change in temperature on the thermometer.

The temperature on Monday afternoon was 55 degrees.

D. Tuesday’s high temperature was 25 °F. The temperature dropped by 30 °F overnight. What direction on the number line is this? _____

Show this on the number line. 20 °F

What is the resulting temperature? ____________

Answer:

Tuesday’s high temperature was 25 °F.

The temperature dropped by 30 °F overnight.

The direction on the number line is downwards.

The resulting temperature is -5

E. Explain why Tuesday’s temperature drop resulted in a negative temperature.

__________________

__________________

Answer:

The Tuesday evening the temperature is reduced. So, the temperature is negative.

**Turn and Talk** Is it possible to start with a positive temperature and then have a rise in temperature which leads to a negative temperature? Explain.

Answer:

Start with a positive temperature and then have a rise in temperature in positive only.

When the temperature is positive and then a decrease in temperature only leads to the negative temperature.

2. Use a number line to answer the following questions. Thursday

A. Thursday’s low temperature was —5 °F and rose 20 degrees by mid-afternoon. Show this on a number

line. At what point do you start on the number line? _______

What distance do you move?____

In which direction do you move?____

Show this on the number line. What is the temperature

Thursday afternoon? _____

Given that,

Thursday’s low temperature is – 5 °F

The temperature rises to 20 degrees by mid-afternoon.

The distance moved is 20 degrees from -5 degrees.

I moved in the upward direction.

The temperature on Thursday afternoon is 15 degrees.

B. Friday’s low temperature is —10 °F. During the day, the temperature rises by 5 degrees. Show the movement on the number line for Friday and give the result. ______

Answer:

Given that,

Friday’s low temperature is -10 °F.

The temperature rises by 5 degrees.

Therefore the temperature is -10 + 5 = -5 degrees.

The movement on the number line for Friday is upwards.

The result is -5 degrees.

C. Sunday’s high temperature is —10 °F. During the day, the temperature drops 2 degrees. What is the temperature Sunday afternoon? ____

Answer:

Given that,

Sunday’s high temperature is -10 °F.

The temperature drops 2 degrees.

Therefore the temperature on Sunday afternoon is -10 – (-2) = -8.

The temperature on Sunday afternoon is = -8.

D. Explain why the temperatures on Friday and Sunday afternoons are both negative, even though one is the result of an increase in temperature and one is the result of a decrease in temperature.

__________________

__________________

__________________

__________________

Answer:

The temperatures on Friday and Sunday started negative. So, after decreasing or increasing the change in the negative temperature it will results from the negative temperatures.

**Turn and Talk** How can you predict whether the sum of a positive and a negative number will be positive or negative by comparing the two numbers?

Answer:

The sum of positive numbers is 2 + 3 = 5

The sum of negative numbers is -2 + (-3) = -5

The sum of positive numbers is positive and the sum of negative numbers is negative.

3. Jane wants to buy a new tablet that costs $100. She keeps a record of the money she earns and spends as shown. Will Jane have enough money to buy the tablet on Sunday? Follow the steps using the number line below.

A. Jane’s starting balance is ____. Plot the amount on the number line.

Answer:

B. Jane earns ____ babysitting. Draw an arrow from the starting amount to represent the amount Jane earns by babysitting. How much money does Jane have now? ______

Answer:

Hane earns on babysitting is $25.

Jane have now is $60 + $25 = $85

C. Jane received ___ for a weekly allowance. Draw another arrow from the end of the arrow from Step B to represent Jane’s allowance.

How much money does Jane have now? ____

Answer:

Jane received $20 for the weekly allowance

The Jane have now is $85 + $20 = $105

D. Jane spent ___ at the football game. Draw another arrow to represent the amount Jane spent at the football game. How much money does Jane have now? ____

Answer:

Jane spent $10 at the football game.

Hane have now is $105 – $10 = $95

E. The tablet costs ___. Draw an arrow to represent the amount Jane would spend on the tablet. Does she have enough money? Explain.

Answer:

The table cost is $95.

The cost of a new tablet is $100.

There Jane has not enough money to buy a tablet.

**Check Understanding**

Question 1.

A business has $10,000 in its bank account. In order to build an addition onto its office, it takes out a loan for $30,000. What is its new account balance once the loan is deposited?

Answer:

Given that,

A business has $10,000 in its bank account.

In addition, he took a loan of $30,000.

The total amount in the bank is $10,000 + $30,000 = $40,000.

Question 2.

If the amount required to build the addition is actually $45,000, will the business in Problem 1 have enough to do it? Explain.

Answer:

Given that,

A business has $10,000 in its bank account.

In addition, he has taken a loan of $30,000.

The total amount in the bank is $10,000 + $30,000 = $40,000.

But the amount required to build the addition is actually $45,000.

Therefore $45000 – $40,000 = $5000

The Business has no enough money to build.

**On Your Own**

**Use the number line for Problems 3 and 4.**

Question 3.

It is first down in the football game, your team has the ball at your 25-yard marker, and the play is a successful run for 6 yards. Where does the ball end up? Where is the ball relative to where it started?

Answer:

Given that,

The team has the ball at your 25-yard marker.

The play is a successful run for 6 yards.

The ball is started at 25 yards

25 yards + 6 yards = 31 yards.

The ball ends up with 31 yards.

Question 4.

On second down, your quarterback drops back to pass but is sacked for a 10-yard loss. Where does the ball end up?

Answer:

Given that,

The team has the ball at your 25-yard marker.

The team lost 10 yards.

The ball is started at 25 yards.

The game ends at 25 -10 = 15.

The ball ends up with 15 yards.

Question 5.

**Reason** Review the actions covered in Problems 3 and 4. Over these two plays, has your team gained or lost total ground? How much? Explain.

Answer:

In the two plays the first team with 31 yards

The second ream with 15 yards.

The first team is gained and the second team is lost.

Question 6.

What is the sum of 18 and 20?

Answer:

sum of 18 and 20

18 + 20 = 38

Question 7.

What is the result of subtracting 35 from 25?

Answer:

subtracting 35 from 25

25 – 35 = -10

Question 8.

What is the result of subtracting 35 from 40?

Answer:

subtracting 35 from 40

40 – 35 = 5

**Use the thermometers provided for Problems 9—11.**

Question 9.

Your home feels cold to you at 60 °F. You turn up the heat in order to raise the temperature by 15 degrees. What will the resulting temperature be?

Answer:

Given,

Your home feels cold to you at 60 °F.

You turn up the heat in order to raise the temperature by 15 degrees.

60 + 15 = 75 degrees

The resulting temperature will be 75°F.

Question 10.

You have a beaker of water that is currently at 70 °F. You add some ice to lower the temperature by 15 degrees. What temperature do you want the water to go down to?

Answer:

Given,

You have a beaker of water that is currently at 70 °F.

You add some ice to lower the temperature by 15 degrees.

70 – 15 = 55 degrees

Question 11.

John has $50 in his bank account. He gets his usual allowance of $20 and mows two lawns, earning $10 each. He puts that money in the bank. Then John spends $45 on a video game. How much money does he have after that purchase?

Answer:

Given,

John has $50 in his bank account. He gets his usual allowance of $20 and mows two lawns, earning $10 each.

50 + 20 + 10 + 10 = $90

Then John spends $45 on a video game.

90 – 45 = $45

Thus $45 left after that purchase.

**Use the number line for Problems 12—15.**

Question 12.

What is the result of 20 plus 30 minus 60?

Answer:

(20 + 30) – 60

50 – 60 = -10

So, the result is -10.

Question 13.

What is the result of -10 plus 30?

Answer:

-10 plus 30

-10 + 30 = 20

So, the result is 20.

Question 14.

What is the result of 70 minus 50 plus 20?

Answer:

70 minus 50 plus 20

(70 – 50) + 20

20 + 20 = 40

So, the result is 40.

Question 15.

What is the result of 20 minus 50?

Answer:

20 minus 50

20 – 50 = -30

So, the result is -30.

**I’m in a Learning Mindset!**

How effective was the number line as a tool for subtracting positive integers?

**Lesson 3.1 More practice/Homework**

**Add or Subtract a Positive Integer on a Number Line**

Question 1.

Ms. Howard buys a car for $500 and adds a music system that costs $200. Then she adds a pair of seat covers for the price shown. How much has Ms. Howard spent on the car so far?

Answer:

Given,

Ms. Howard buys a car for $500 and adds a music system that costs $200.

500 + 200 = $700

The price of seat cover is $50

2 × 50 = 100

$700 + $100 = $800

Thus Ms. Howard spent $800 on the car.

Question 2.

At the beginning of the week, Tideland Manufacturing had an inventory of 60,000 screws. This week they received a shipment of 30,000 more screws. Then they used 50,000 screws to make their Tideland mowers. How many screws do they have left in inventory?

Answer:

Given,

Tideland Manufacturing had an inventory of 60,000 screws. This week they received a shipment of 30,000 more screws.

60,000 + 30,000 = 90,000 screws

Then they used 50,000 screws to make their Tideland mowers.

90,000 – 50,000 = 40,000 screws

Therefore 40,000 screws have left in inventory.

Question 3.

**STEM** A chemical reaction is endothermic if it absorbs heat from its surroundings. It is exothermic if it gives off heat to its surroundings. In her chemistry class, Lily is given a salt (ammonium nitrate) and a beaker of water at 60 °F. She dissolves the salt in the water and sees that the temperature of the solution is now 50 °F. Did the temperature of the solution increase or decrease? By how many degrees? What kind of reaction has occurred? Explain.

Answer:

In her chemistry class, Lily is given a salt (ammonium nitrate) and a beaker of water at 60 °F.

She dissolves the salt in the water and sees that the temperature of the solution is now 50 °F.

60 °F – 50 °F = 10°F

Thus the temperature is decreased by 10°F.

Thus endothermic reaction has occurred.

Question 4.

At the beginning of the month, Joe has $180 in his bank account. He wants to buy a new gaming system for $250 in two weeks. His parents have offered to loan him money if he needs it. He gets $20 a week for an allowance. Will he have enough money at the end of two weeks to make the purchase on his own? If not, how much will he have to borrow from his parents? Explain.

Answer:

At the beginning of the month, Joe has $180 in his bank account. He wants to buy a new gaming system for $250 in two weeks.

180 – 250 = -70

He needs $70 more to buy a new gaming system.

His parents have offered to loan him money if he needs it. He gets $20 a week for an allowance.

20 × 2 = $40

180 + 40 = $220

250 – 220 = 30

Thus he needs to borrow $30 from his parents.

Question 5.

**Reason** Can you ever add two positive integers and get a negative integer? Explain.

Answer:

No, when we add two positive integers the result will be a positive integer.

Example:

2 + 3 = 5 is a positive integer.

Question 6.

**Reason** Can yoú subtract a positive integer from a positive integer and get a negative result? Explain your answer.

Answer:

Yes, we can subtract a positive integer from a positive integer and get a negative result.

5 – 7= -2

**Test Prep**

Question 7.

Marcus owes his mother $10. He babysits his little sister and earns $25. Then he cleans the garage and earns $32. After he pays his mother, how much money does Marcus have?

Answer:

Given,

He babysits his little sister and earns $25.

Then he cleans the garage and earns $32.

25 + 32 = $57

His overall earnings is $57

Marcus owes his mother $10.

57 – 10 = $47

Therefore he has $47 after he pays his mother.

Question 8.

The water in a lake is 4 feet above its usual level. Then the level of the lake drops 7 feet. If 0 represents its usual level, which number line shows the final level of the water in the lake?

Answer:

Given,

The water in a lake is 4 feet above its usual level.

Then the level of the lake drops 7 feet.

4 + (-7) = -3

So, the point should be placed on -3 on the number line.

So, option C is the correct answer.

**Circle the word that best completes the sentence.**

Question 9.

Donna subtracts a positive number from a greater positive number. The resulting difference will be (positive / negative)

Answer: Donna subtracts a positive number from a greater positive number. The resulting difference will be **positive**.

Question 10.

Devon subtracts a positive number from a lesser positive number. The resulting difference will be (positive / negative)

Answer: Devon subtracts a positive number from a lesser positive number. The resulting difference will be **negative**.

**Spiral Review**

Question 11.

Elena draws a scale drawing for a garden. The scale drawing is 3 inches by 6 inches. The garden will be 12 feet by 24 feet. What is the scale of the drawing in inches to feet?

Answer:

Elena draws a scale drawing for a garden. The scale drawing is 3 inches by 6 inches.

The garden will be 12 feet by 24 feet.

12 feet = 3 inches

1 feet = x

x × 12 = 3

x = 3/12

x = 1/4 = 0.25

The scale is of 0.25 inches per feet.

Question 12.

Raoul makes shell necklaces to sell at a craft fair. The supplies for each necklace cost $3.75. Raoul sells the necklaces for $11.25. What is the percent markup for a shell necklace?

Answer:

Given,

Raoul makes shell necklaces to sell at a craft fair.

The supplies for each necklace cost $3.75.

Raoul sells the necklaces for $11.25.

Mark up = selling price – cost price

Mark up = 11.25 – 3.75 = $7.5

The percent markup for a shell necklace = markup/ cost price × 100%

= 7.5/3.75 × 100%

2 × 100% = 200%

Thus the percent markup for a shell necklace is 200%

Question 13.

Neveah goes out to dinner at a restaurant. The bill for dinner is $57.25, and Neveah gives the server a 20% tip. What is the total cost for dinner?

Answer:

Given,

Neveah goes out to dinner at a restaurant.

The bill for dinner is $57.25, and Neveah gives the server a 20% tip.

57.25 × 20/100 = $11.45

$57.25 + $11.45 = $68.70

Thus the total cost for dinner is $68.70