We included **H****MH Into Math Grade 7 Answer Key**** PDF** **Module 3 Lesson 3 Use a Number Line to Add and Subtract Rational Numbers **to make students experts in learning maths.

## HMH Into Math Grade 7 Module 3 Lesson 3 Answer Key Use a Number Line to Add and Subtract Rational Numbers

I Can use a number line to add or subtract rational numbers.

**Spark Your Learning**

When a person owes money on a credit card, the credit card holder can think of it as a negative balance.

Devin has a balance of —$9.50 on a credit card. Which two items can he purchase without his balance going below —$15.00? Find all the pairs of items Devin can purchase.

Answer:

Given,

Devin has a balance of —$9.50 on a credit card.

Cost of Dinner rolls = $0.50

Cost of Pizza dough = $3.00

Cost of Cinnamon bread = $4.50

To find:

Which two items can he purchase without his balance going below —$15.00?

-9.50 – (4.50) – (0.50)

-$9.50 – $4.50 – $0.50 = $14.50

**Turn and Talk** If the cinnamon bread was on sale for $2.00, could he purchase all three items? Explain.

Answer: Yes

Explanation:

Given,

Devin has a balance of —$9.50 on a credit card.

Cost of Dinner rolls = $0.50

Cost of Pizza dough = $3.00

Cost of Cinnamon bread = $2.00

-9.50 – 0.50 – 3.00 – 2 = -$15.00

**Build Understanding**

1. An underwater camera is dropped from a helicopter flying over the water as shown. The camera has an elevation change of —8 feet. Where is the camera now in relation to the surface of the water?

A. The number line represents distance from sea level.

What do positive numbers represent? ________

What do negative numbers represent? ______

What does 0 represent? _____

B. On the number line, draw an arrow representing the camera’s change in elevation. Where is the camera after the change in elevation of -8 feet from the helicopter?

4\(\frac{1}{2}\) + (-8) = ____

Answer:

4\(\frac{1}{2}\) + (-8)

4\(\frac{1}{2}\) – 8 = -3\(\frac{1}{2}\) feet

C. Later, the camera is at -5\(\frac{1}{2}\) feet and has an elevation change of +3 feet. What is the camera’s final elevation in relation to the surface?

On the number line a line would start at ___ and go ___ 3 units. Draw an arrow representing the camera’s change in elevation.

-5\(\frac{1}{2}\) + 3 = ____

Answer:

-5\(\frac{1}{2}\) + 3 = -2\(\frac{1}{2}\) feet

D. Now the camera is at -5\(\frac{1}{2}\) feet again, and it sinks 2\(\frac{1}{2}\) feet. What is the camera’s final elevation in relation to the surface? Use the number line to show your work.

-5\(\frac{1}{2}\) + (-2\(\frac{1}{2}\)) = ____

Answer:

Now the camera is at -5\(\frac{1}{2}\) feet again, and it sinks 2\(\frac{1}{2}\) feet.

-5\(\frac{1}{2}\) + (-2\(\frac{1}{2}\))

-5\(\frac{1}{2}\) -2 \(\frac{1}{2}\) = -8 feet

**Turn and Talk** If the camera is at —2.5 feet and undergoes a change of elevation of 0 feet, where will the camera be then? Will it be at the surface of the water?

**Step It Out**

2. Carmela is playing with a ball.

A. The ball is on a platform 2.3 meters above the ground; then the ball falls to the ground. Use a number line to represent the change in height of the ball.

Begin at ___ to represent the height of the ball on the platform; then show the decrease in height.

Answer:

Given,

The ball is on a platform 2.3 meters above the ground; then the ball falls to the ground.

2.3 – 2.3 = 0

B. Complete the equation to represent the situation in Part A.

2.3 – ____ = ____

2.3 – 2.3 = 0

C. The ball fell into a pit 1.5 feet below ground level. Carmela grabs the ball and puts it back on ground level.

Begin at ___ to represent the height of the ball in the pit; then show the increase in height.

Answer:

Begin at 0 to represent the height of the ball in the pit; then show the increase in height.

D. Complete the equation to represent the situation in Part C.

-1.5 + ___ = ___

Answer:

-1.5 + 1.5 = 0

E. Carmela stands on the ground and kicks the ball 4.5 meters up into the air. It falls down and goes into another pit that is 3.5 meters deep.

Use the number line to show the changes in height of the ball. Begin at ___ to represent the height of the ball on the ground, and show the increase followed by the decrease.

Answer:

Given,

Carmela stands on the ground and kicks the ball 4.5 meters up into the air.

It falls down and goes into another pit that is 3.5 meters deep.

Begin at -4.5 meters to represent the height of the ball on the ground, and show the increase followed by the decrease.

F. Complete the equation to represent the situation in Part E.

___ + 4.5 – ___ = -3.5

Answer:

-4.5 + 4.5 – 3.5 = -3.5

G. Using the number line model in Parts C and D as an example, explain the Addition Property of Opposites which states that the sum of a number and its opposite equals zero. Another name for opposite is additive inverse.

___________________

___________________

___________________

**Turn and Talk** How can you interpret the model in Parts A and B as show that the sum of a number and its opposite is 0?

3. Describe each situation in words.

A Margarita has $50 in her bank account. What transaction would result in an account balance of $0?

________________________

Answer:

Margarita has $50 in her bank account.

50 + 0 – 50 = 0

By adding -50 to the account we can say that the account balance will be $0.

B. The temperature is 15 °F. What change in temperature would result in the temperature being 0 °F?

________________________

Answer:

The temperature is 15 °F.

15°F + (-15°F) = 0°F

C. A kite is 25 feet in the air. What needs to happen to the kite in order for it to be at ground level?

________________________

Answer:

A kite is 25 feet in the air.

25ft – 25ft = 0

D. Describe a situation in which opposite quantities combine to make 0.

________________________

________________________

Answer:

The distance the plane travels increases, but eventually, the displacement is 0.

**On Your Own**

Question 1.

From an elevation of 2.5 feet above sea level, a bird dives 4 feet to catch a fish. How far below the surface is the fish?

A. Draw an arrow to represent this situation on the number line shown.

Answer:

B. Complete the equation to represent the situation.

2.5 – 4 = ___

Answer:

2.5 – 4 = -1.5

Question 2.

Pietro used a number line to subtract –\(\frac{1}{8}\) – (-\(\frac{1}{4}\)). The figure shows the arrow he drew to represent the subtraction. Is he getting the right result? Explain.

Answer:

Given,

Pietro used a number line to subtract –\(\frac{1}{8}\) – (-\(\frac{1}{4}\)).

–\(\frac{1}{8}\) + \(\frac{1}{4}\) = \(\frac{1}{8}\)

Question 3.

The overnight low temperature is -7 °F. By morning, the temperature increases by 15 degrees. Draw an arrow on the thermometer to represent this situation and find the morning temperature.

Answer:

Given,

The overnight low temperature is -7 °F.

By morning, the temperature increases by 15 degrees.

-7 + 15 = 8°F

Question 4.

Mr. Anderson has a credit card balance of -$80.23 at the end of the month. Use Mr. Anderson’s credit card balance to describe a situation in which opposite quantities combine to make 0.

Answer:

Given,

Mr. Anderson has a credit card balance of -$80.23 at the end of the month.

x – 80.23 = 0

x = 80.23

**On Your Own**

**Use Tools Use the thermometer to help solve Problems 5-8.**

Question 5.

In the morning, the temperature is —5 °F. The temperature increases by 13 °F, then decreases by 5 °F. Write an equation to represent the situation.

Answer:

Given,

The temperature is —5 °F.

The temperature increases by 13 °F, then decrease by 5 °F.

T = -5°F + 13°F – 5°F

Question 6.

The high temperature for the day is 28 °F. The record high for the day was 54 °F. What is the difference in temperatures?

Answer:

Given,

The high temperature for the day is 28 °F.

The record high for the day was 54 °F.

54°F – 28°F = 26°F

Question 7.

The high temperature for the day is 28 °F. The record low for the day was — 12 °F. What is the difference in temperatures?

Answer:

The high temperature for the day is 28 °F.

The record low for the day was — 12 °F.

28°F – (-12°F)

28°F + 12°F = 40°F

Question 8.

This morning the temperature was —5 °F. How much must the temperature change to reach 0 °F?

Answer:

Given,

This morning the temperature was —5 °F.

-5 °F + 5 °F = 0°F.

Question 9.

**Reason** Evan added (-2\(\frac{1}{2}\)) + 4 and got 6\(\frac{1}{2}\). Draw arrows on the number line to represent the problem. Then explain Evan’s error.

Answer:

(-2\(\frac{1}{2}\)) + 4 = 1\(\frac{1}{2}\)

Question 10.

The number line shows the elevation of the bottom of a harbor and the elevation of a fish swimming close to the surface.

A. What change in elevation is necessary for the fish to reach bottom?

___________________

Answer: -1.5 meters

B. Once the fish reaches the bottom, what change in elevation will bring it back up to the surface?

___________________

Answer:

-10.5 – (-1.5)

-10.5 + 1.5 = -9 meters

Question 11.

**Financial Literacy** Stock in Boomer Branding, Inc. started the week at $26.50 per share. During the week, the following changes in the share price were registered:

A. Show the changes on the number line.

Answer:

B. What was the price per share at the end of the week?

Answer:

C. **Open Ended** Describe a situation using stocks in which opposite quantities combine to make 0.

Answer:

**For Problems 12-15, find rational numbers to complete each equation. Use the number line to help.**

Question 12.

___ + (- ___) = -8.75

Answer:

1.25 + (-10) = -8.75

Question 13.

____ – ___ = -1\(\frac{3}{4}\)

Answer:

-2 – (-\(\frac{1}{4}\))

-2 + \(\frac{1}{4}\) = -1\(\frac{3}{4}\)

Question 14.

(- ___) + (- ___) = -9.25

Answer:

-4.25 + (-5.00) = -9.25

Question 15.

____ + ____ = 0

Answer:

15.75 + (-15.75) = 0

Question 16.

A bank account has a balance of $135. What transaction would result in an account balance of $0? ________

Answer:

Given,

A bank account has a balance of $135.

$135 – $135 = $0

So, the account balance will be 0 when you withdraw $135.

Question 17.

The temperature is —7 °F. What change in temperature would result in the temperature being 0 °F? ___________________

Answer:

Given,

The temperature is —7 °F.

To find:

What change in temperature would result in the temperature being 0 °F?

-7 °F + 7 °F = 0°F

**I’m in a Learning Mindset!**

How can I help my peers describe situations in which opposites combine to make 0?

___________________

Answer:

For example, a hydrogen atom has 0 charges because its two constituents are oppositely charged.

**Lesson 3.3 More practice/Homework**

Question 1.

Caleb rode his bike for 3\(\frac{1}{2}\) miles in the morning. Then he rode his bike another 2\(\frac{1}{2}\) miles in the afternoon. How many miles did Caleb ride all together? Draw an arrow on the number line to show how to find the answer. Then write the answer below.

Answer:

Given,

Caleb rode his bike for 3\(\frac{1}{2}\) miles in the morning.

Then he rode his bike another 2\(\frac{1}{2}\) miles in the afternoon.

3\(\frac{1}{2}\) + 2\(\frac{1}{2}\) = \(\frac{7}{2}\) + \(\frac{5}{2}\) = \(\frac{12}{2}\) = 6 miles

Question 2.

**Critique Reasoning** Jasmine evaluated the expression 10 – (-3) and says it is equal to 7. Is she right? If not, what was her mistake?

Answer:

10 – (-3) = 10 + 3 = 13

So, Jasmine is wrong.

Question 3.

On a number line, what other number is the same distance from —2.8 as —7.2 is?

________________________

Answer:

-2.8 – (-7.2) = -2.8 + 7.2 = 4.4

-7.2 is 4.4 units away from -2.8

-2.8 + 4.4 = 1.6

So, the other number which is this same distance is -2.8 + 4.4 = 1.6

Question 4.

A number line ¡s drawn left to right with integers spaced 1 centimeter apart. An ant crawls onto the number line at +2. It then crawls 3.5 centimeters left, 4.8 centimeters right, and 7.9 centimeters left.

A. Where is the ant on the number line now? ______

Answer:

Given,

An ant crawls onto the number line at +2.

It then crawls 3.5 centimeters left, 4.8 centimeters right, and 7.9 centimeters left.

2 – 3.5 = -1.5

-1.5 + 4.8 = 3.3

3.3 – 7.9 = -4.6

So, the ant is at -4.6 on the number line.

B. How far is it from its original position? _____

Answer:

Distance between initial and final location is

2 – (-4.6) = 6.6 cm

C. What is the total distance the ant crawled along the number line?

Answer:

Total distance the ant covered is 3.5 + 4.8 + 7.9 = 16.2 cm

D. **Open Ended** Describe a situation in which the ant crawls in a way that results in opposite quantities combining to make 0.

Answer: The situation will be the ant is at +2 and walks 3.5 cm right then 4.8 cm left then 7.9 cm right.

Use Tools For Problems 5 and 6, draw arrows on the number line to show the operations indicated and fill in the answer.

Question 5.

0.5 + (-1.5) – (-5.5) = ____

Answer:

0.5 + (-1.5) – (-5.5)

0.5 – 1.5 + 5.5 = 4.5

Question 6.

-1\(\frac{1}{2}\) – (+\(\frac{3}{2}\)) – (-\(\frac{5}{8}\)) = _____

Answer:

-1\(\frac{1}{2}\) – (+\(\frac{3}{2}\)) – (-\(\frac{5}{8}\))

-1\(\frac{1}{2}\) – \(\frac{3}{2}\) + \(\frac{5}{8}\)

–\(\frac{3}{2}\) – \(\frac{3}{2}\) + \(\frac{5}{8}\)

–\(\frac{6}{2}\) + \(\frac{5}{8}\)

LCD of 2 and 8 is 8.

–\(\frac{6}{2}\) + \(\frac{5}{8}\) = –\(\frac{24}{8}\) + \(\frac{5}{8}\) = –\(\frac{19}{8}\) = -2\(\frac{3}{8}\)

**Test Prep**

Question 7.

If the temperature was 0 °C and then there was a temperature change of +5 °C, what temperature change would return the temperature to 0 °C?

A. -10 °C

B. -5°C

C. 0 °C

D. 5°C

Answer:

If the temperature was 0 °C and then there was a temperature change of +5 °C

0 + 5 = 5

We need to subtract by 5 to return the temperature to 0 °C

5 – 5 = 0°C

Thus Option C is the correct answer.

Question 8.

Find the sum.

–\(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{5}{8}\)

A. \(\frac{1}{8}\)

B. \(\frac{3}{8}\)

C. \(\frac{5}{8}\)

D. \(\frac{7}{8}\)

Answer:

–\(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{5}{8}\) = (-1 + 1 + 5)/8 = \(\frac{5}{8}\)

Thus option C is the correct answer.

Question 9.

Which set of operations corresponds to the arrows shown on the number line?

A. -15 – (+20) + (-10)

B. -15 + (+20) – (-10)

C. -15 – (+20) – (+10)

D. -15 – (-20) + (-10)

Answer:

D. -15 – (-20) + (-10)

From the above number line we can see that

-15 – (-20) + (-10)

-15 + 20 – 10 = 5 – 10 = -5

Thus option D is the correct answer.

**Spiral Review**

Question 10.

A map is drawn using a scale of 1 centimeter to 25 kilometers. What actual distance is represented by a map length of 3.2 centimeters?

Answer:

Given,

A map is drawn using a scale of 1 centimeter to 25 kilometers.

1 cm = 25 km

3.2 cm = x

x = 25 × 3.2

x = 80 km

Hence 3.2 cm on the map represents 80 kilometers of actual distance.

Question 11.

Find the percent change from 200 to 192.

Answer:

(200 – 192)200 = 8/200 = 1/25

1/25 × 4/4 = 4/100 = 4%

Question 12.

You make an initial deposit of $2,500 in an account that offers 6% simple interest per year. How much will be in the account after 4 years?

Answer:

Given,

You make an initial deposit of $2,500 in an account that offers 6% simple interest per year.

P = 2500

T = 4

R = 6%

P(1 + Rt)

2500 (1 + 4 × 6%)

2500 (1 + 24%)

2500 (1 + 0.24)

2500 × 1.24 = 3100

Therefore there will be $3100 in the account after 4 years.