Into Math Grade 7 Module 6 Lesson 3 Answer Key Solve Multi-step Problems with Rational Numbers in Context

We included HMH Into Math Grade 7 Answer Key PDF Module 6 Lesson 3 Solve Multi-step Problems with Rational Numbers in Context to make students experts in learning maths.

HMH Into Math Grade 7 Module 6 Lesson 3 Answer Key Solve Multi-step Problems with Rational Numbers in Context

I Can solve multi-step problems that involve rational numbers in different forms and multiple operations.

Step It Out

1. Jordan uses the recipe shown to make yogurt putty. He buys a bag of cornstarch for $3.89 that contains 128 servings that are each \(\frac{1}{8}\) cup.
HMH Into Math Grade 7 Module 6 Lesson 3 Answer Key Solve Multi-step Problems with Rational Numbers in Context 1
What is the maximum number of batches of putty Jordan can make with the cornstarch? How much does the cornstarch for each batch cost?
A. How many cups of cornstarch are in the bag?
____ servings × ___ cup per serving = ___ cups
Answer:
128 servings × \(\frac{1}{8}\) = 16 cups

Explanation:
There are 16 cups of cornstarch in the bag.
B. How many batches of putty can Jordan make? Use decimals for the cups of cornstarch per batch. Round your answer to the nearest tenth.
HMH Into Math Grade 7 Module 6 Lesson 3 Answer Key Solve Multi-step Problems with Rational Numbers in Context 2
Answer:
= 16 ÷ 2 \(\frac{1}{4}\)
= 16 × \(\frac{2}{9}\)
= 16 × 0.22
= 3.55
= 4 batches (rounded to nearest tenth)

C. What is the maximum whole number of batches Jordan can make with the cornstarch? Explain.
_____________________
_____________________
_____________________
Answer:
The maximum whole number of batches Jordan can make with the cornstarch is 4.

D. How much does the cornstarch for each batch cost?
$____ ÷ ___ ≈ ____, which is approximately
$ ___ per batch.
Answer:
The cornstarch for each batch cost is $31 per batch.
= $3.89 ÷ \(\frac{1}{8}\)
= $3.89 × 8
= $31 per batch

Turn and Tàlk How can you use estimation to check that your answer for the cost per batch is reasonable?

2. Charise collects antique salt and pepper shakers. The value of her cactus salt and pepper shakers is shown. The value of these salt and pepper shakers is expected to change by an average of -2\(\frac{2}{5}\)% per year. What is the value of the salt and pepper shakers projected to be in two years?
HMH Into Math Grade 7 Module 6 Lesson 3 Answer Key Solve Multi-step Problems with Rational Numbers in Context 3
Answer:
$53.61

Explanation:
Given,
The rate of change = -2\(\frac{2}{5}\)%
= -2.4%
Growth factor = 1 + growth rate
Growth factor = 1 – 2.4%
= 1 – 0.024 = 0.976
Every year Charise cactus salt and pepper shakers will have their value increased.
After 2 years their value will be
$56.28 × 0.976 × 0.976 = $56.28 × 0.9525
$53.61
A. Explain why it is useful to convert the percent to a decimal.
_____________________
_____________________
Answer:
It is simpler to calculate the values and visualize and compare them. Therefore it is useful to convert the percent to a decimal.
B. Convert the mixed-number percent to a decimal percent. Then divide the resulting value in the percent by 100.
-2\(\frac{2}{5}\)% = ____% = ____
Answer:
-2.4% = -2.4
Given,
-2\(\frac{2}{5}\)%
Now we need to convert them to a decimal percent
\(\frac{12}{5}\)%
-2.4%
Now divide the result by 100
–\(\frac{2.4}{100}\)%
–\(\frac{2.4}{100}\) × 100
= -2.4

C. Find the value of the salt and pepper shakers after the first year.
56.28 × (___) = ____
56.28 + (___) = ____
To the nearest cent, the value after the first year is $ ____
Answer:
The value after the first year is $111.209.
56.28 × 0.976 = 54.92
56.28 + 54.92 = 111.209

D. You can use substitution to rewrite the two expressions in Part C as a single expression: 56.28 + [56.28 × (-0.024)]. Use properties of operations to write this expression as a product of two factors, and show that it has the same value as the final answer to Part C.
Answer:
Given expression:
56.28 + [56.28 × (-0.024)] = -54.92
Now use properties of operations
56.28 + 56. 28 × (-0.024) = -54.92

E. Find the value of the salt and pepper shakers after the second year. Round your answer to the nearest cent. Show your work.

Turn and Talk A student said that you can solve this problem by finding 2\(\frac{2}{5}\)% of $56.28 and then subtracting this amount twice from $56.28. Does this method work? Why or why not?
Answer:
Yes, the method works.

Explanation:
2\(\frac{2}{5}\)% of $56.28
\(\frac{12}{5}\)% of $56.28
(12 × 56.28) ÷ 5
675.36 ÷ 5
135.072 – (2 × 56.28) = 135.072 – 113.16 = 21.912

3. Suppose the aquarium shown developed a leak at the bottom corner and lost water at an average rate of 6\(\frac{3}{4}\) fluid ounces per minute. How many hours, to the nearest tenth, would it take for the aquarium to be empty?
HMH Into Math Grade 7 Module 6 Lesson 3 Answer Key Solve Multi-step Problems with Rational Numbers in Context 4
A. Multiply by equivalent forms of 1 to convert gallons to fluid ounces.
HMH Into Math Grade 7 Module 6 Lesson 3 Answer Key Solve Multi-step Problems with Rational Numbers in Context 5
B. Find the number of minutes, to the nearest tenth, that it takes for the aquarium to empty.
___ ÷ 6\(\frac{3}{4}\) = 2,560 ÷ ____ ≈ ___ minutes
C. What remaining work do you need to do to solve the problem? Solve the problem and show your work.
_____________________
_____________________

D. Explain how you can check your answer for reasonableness.
_____________________
_____________________

Check Understanding

Question 1.
A block of clay contains twenty 4-ounce portions of clay. A ceramics teacher wants to use the block to make as many spheres of clay as possible, each weighing \(\frac{2}{5}\) pound. How many spheres can the class make?
Answer:
The class can make 12.5 spheres.

Explanation:
Given,
A block of clay has 20 4 – ounce portions
= 20 × 4
= 80 ÷ 16
= 5
Spheres of clay each weighing = \(\frac{2}{5}\)
5 ÷ \(\frac{2}{5}\)
5 × \(\frac{5}{2}\)
\(\frac{25}{2}\) = 12.5

Question 2.
A laptop computer costs $356.75 when it is new. The value of the computer is expected to change by -11\(\frac{3}{4}\)% per year. What is the expected value, to the nearest cent, of the computer after 3 years? Is the answer reasonable? Explain.
Answer:
$245.19

Explanation:
Given,
The laptop costs = $356.75
Value of the computer is expected to change by -11\(\frac{3}{4}\)%
value of change after 3 years
The price = 356.75 × (1 – 11.75%) × (1 – 11.75%) × (1 – 11.75%)
= 356.75 × 0.8825 × 0.8825 × 0.8825
= $245.19

On Your Own

Question 3.
Luis is hiking at a park. He sees the sign shown and decides to hike to Wandering Twin Lake. Luis knows that he can hike at an average rate of \(\frac{1}{3}\) mile in 6 minutes.
HMH Into Math Grade 7 Module 6 Lesson 3 Answer Key Solve Multi-step Problems with Rational Numbers in Context 6

A. How many hours will it take Luis to reach Wandering Twin Lake?
_____________________
Answer:
1.47 hours.

Explanation:
Luis takes 6 minutes to hike at an average rate of \(\frac{1}{3}\).
Wandering twin lake is 4.9 miles away it takes to get to the place is
4.9 × 18
88.2 minutes
In hours this is 88.2 ÷ 60
= 1.47 hours

B. Explain how you know your answer is reasonable.
_____________________
Answer:

Question 4.
Financial Literacy Mr. Liling bought 10 shares of stock in QJZ Software at the beginning of 2016 for $198.58 per share. The table shows how the value of the stock changed during 2016 and during 2017.
A. What was the total value of Mr. Liling’s shares, rounded to the nearest cent, at the end of 2016?
_____________________
Answer:
The total value at the end of 2016 is 188.85.

Explanation:
Given,
Mr Liling bought 10 shares
At the beginning of 2016 for $198.58 per share.
In year 2016 change in stock prize is -4\(\frac{9}{10}\) = –\(\frac{49}{10}\)%
= 100 – \(\frac{49}{10}\)%
= 100 – 4.9%
= 95.1%
The total value of Mr. Liling’s shares is $198.58 × 95.1%
= 18884.958 ÷ 100
= 188.85

HMH Into Math Grade 7 Module 6 Lesson 3 Answer Key Solve Multi-step Problems with Rational Numbers in Context 7

B. What was the total value of Mr. Liling’s shares, rounded to the nearest cent, at the end of 2017?
Answer:
The total value at the end of 2017 is 218.93.
In 2017 change in stock price is 10\(\frac{1}{4}\) = \(\frac{41}{4}\)%
= 100 + \(\frac{41}{4}\)%
= 100 + 10.25%
= 110.25%
he total value of Mr. Liling’s shares at the end of 2017 is $198.58 × 110.25%
= 21893.445%
= 218.93

C. Explain how you know your answers are reasonable.
Answer:

Question 5.
According to Denise’s recipe, each batch of granola requires 1.75 cups of shelled sunflower seeds. She has 3 bags of shelled sunflower seeds that each contain eleven \(\frac{1}{4}\)-cup servings. What is the maximum number of batches of granola that Denise can make with the sunflower seeds?
Answer:
19

Explanation:
From the given question find 11\(\frac{1}{4}\) × 3 ÷ 1.75
(\(\frac{45}{4}\) × 3) ÷ 1.75
(\(\frac{45}{4}\) × 3) ÷ (175 ÷ 100)
(\(\frac{45}{4}\) × 3) ÷ (7 ÷ 4)
(\(\frac{45}{4}\) × 3) × (4 × 7)
135 ÷ 7
19

Question 6.
In 2016, a maglev train in Japan traveled 1.1 miles in 10\(\frac{4}{5}\) seconds.

HMH Into Math Grade 7 Module 6 Lesson 3 Answer Key Solve Multi-step Problems with Rational Numbers in Context 8

A. Find the speed of the train in miles per hour.
Answer:
3.8 miles per hour

Explanation:
Given,
Distance = 1.1 miles
time taken = 10\(\frac{4}{5}\) seconds.
= \(\frac{54}{5}\) sec
Speed = Distance ÷ time
We know, 60 × 60 sec = 1 hr
1 sec = 1 ÷ (60 × 60)
\(\frac{54}{5}\) = 1 ÷ (60 × 60)
= 1 ÷ (60 × 60) × \(\frac{54}{5}\)
= 0.003 hr
Speed = 1.1 ÷ (0.003)
= 366. 67 miles per hour

B. How can you use estimation to show that your answer is reasonable?
Answer:
The estimation for the speed is 367 miles per hour. By estimating an approximate answer and it doesnot exceed the original numbers.

Question 7.
Brad is using the recipe shown to make trail mix for his hiking club. He buys two 20-ounce canisters of raisins for $4.31 each. A canister holds 17 servings of raisins. Each serving is \(\frac{1}{4}\) cup.
A. If Brad only wants to make whole batches of trail mix, what is the maximum number of batches he can make using the raisins?
Answer:

HMH Into Math Grade 7 Module 6 Lesson 3 Answer Key Solve Multi-step Problems with Rational Numbers in Context 9

B. Use your answer from Part A to find the cost of the raisins per batch of trail mix. Round your answer to the nearest cent.
Answer:

Question 8.
The percent error of a measurement tells how close the measurement is to the actual value. Dani ran four times around the track, a total distance of 1,600 meters. Her GPS watch recorded the distance as 1,592 meters.
A. To find the percent error, first find the absolute value of the difference between the distance recorded on Dani’s watch and the actual distance.
Answer:

B. Now express the difference from Part A as a percent of the actual value. This is the percent error.
Answer:

Question 9.
A student identified the volume of a solution to be 13 milliliters. The true volume was 12.5 milliliters. What is the percent error of the measurement? Use the definition of percent error in Problem 8.
Answer:

Question 10.
Gianna is taking a walking tour in her city. The entire tour is 10\(\frac{1}{10}\) kilometers long. According to an app on her phone, Gianna’s average walking rate is 1.6 meters per second.

A. What is Gianna’s average walking rate in kilometers per hour?
_____________________
Answer:

B. About how long will it take Gianna to complete the walking tour? Express your answer in hours and minutes.
_____________________
Answer:

C. Construct Arguments Explain how you know your answer is reasonable.
_____________________
Answer:

Question 11.
Open Ended A container of oatmeal costs $3.79 and contains about 17 servings of the size shown. Write a word problem involving the serving size, the number of servings per container, and the price of the oatmeal.
HMH Into Math Grade 7 Module 6 Lesson 3 Answer Key Solve Multi-step Problems with Rational Numbers in Context 10
Answer:

Question 12.
Attend to Precision A snail is moving along a path that is 4 meters long. The snail moves at an average rate of 3\(\frac{3}{10}\) inches per minute.
A. Find the length of the path to the nearest inch. (Hint: 1 in. ≈ 2.54 cm)
Answer:
The length of the path is 157 inches.

Explanation:
Given,
The length of the path = 4 meters
1 meter = 100 cm
4 m = 400 cm
also 1 in = 2.54 cm
1 cm = 1 ÷ 2.54 in
therefore 400 cm = 400 × (1 ÷ 2.54 inches)
= 157.48
= 157 (rounded to the nearest inch).

B. To the nearest minute, how long does it take the snail to reach the end of the path?
Answer:
1 minute

Explanation:
Given,
Speed = 3\(\frac{3}{10}\) inches per minute = \(\frac{33}{10}\)
Distance = 4 meters
time = Distance ÷ speed
= 4 ÷ ( \(\frac{33}{10}\))
= 4 × \(\frac{10}{33}\)
= 40 ÷ 33
= 1.2 minute
= 1 minute ( Rounded to the nearest minute)

Lesson 6.3 More Practice/Homework

Question 1.
Math on the Spot Sophia uses 3\(\frac{3}{4}\) cups of flour for each cake she makes. She has a 10-pound bag of flour that cost $8.79 and contains 152 quarter-cup servings.
A. How many cakes can Sophia make with this flour? _____________________
Answer:

B. Use your answer from Part A to find the cost of the flour for each cake. Round your answer to the nearest cent. _____________________
Answer:

Question 2.
Use Tools A bobsled team is practicing runs on a track. Their first run takes 4.85 minutes. On each of the next two runs, the team’s time changes by -5\(\frac{1}{2}\)% compared to the previous time.
A. What was the team’s time, rounded to the nearest hundredth of a minute on their final run?
_____________________
Answer:

HMH Into Math Grade 7 Module 6 Lesson 3 Answer Key Solve Multi-step Problems with Rational Numbers in Context 11

B. Explain how you can check your answer for reasonableness.
_____________________
Answer:

Question 3.
Use Tools Calvin maintains a 55-gallon artificial pond. He fills the pond with a hose at an average rate of 9\(\frac{3}{16}\) quarts per minute.
Answer:
Given,
1 gallon = 4 quarts
Calvin maintains = 55 gallon artificial pond.
Average rate = 9\(\frac{3}{16}\) quarts per minute.
= (55 × 4) ÷ 9\(\frac{3}{16}\)
= 220 ÷ \(\frac{147}{16}\)
= 220 × \(\frac{16}{147}\)
= 23.946 minutes
= 23.9 minutes.

A. How long, to the nearest tenth of a minute, does it take to fill the pond?
Answer:
23.9 minutes.

Explanation:
It took 23.9 minutes to fill the pond.

B. Explain how you can check your answer for reasonableness.
Answer:
Now we will check the reasons
= 23.9 × 9\(\frac{3}{16}\)
= (23.9 × 3) × \(\frac{16}{147}\)
= 219.6 quarts
= 219.6 ÷ 4
= 54.9
= 55 gallons

Question 4.
Use Tools Kayla bikes for 2.25 hours at an average rate of 10\(\frac{1}{2}\) miles per hour. Talisha bikes the same distance at an average rate of 12\(\frac{2}{5}\) miles per hour. How long does Talisha take to complete the ride?
Answer:
1.9 hours

Explanation:
Given,
The distance = 2.25 × 10\(\frac{1}{2}\)
= 2.25 × \(\frac{21}{2}\)
= (2.25 × 21) ÷ 2
= 47.5 ÷ 2
= 23.625
Speed = 12\(\frac{2}{5}\)
= \(\frac{62}{5}\)
time = Distance ÷ speed
= 23.625 ÷ (\(\frac{62}{5}\))
= 23.625 × \(\frac{5}{62}\)
= (23.625 × 5) ÷ 62
= 118.125 ÷ 62
= 1.9 hours.

Test Prep

Question 5.
A new mobile device has a value of $256.25. Its value changes by -22\(\frac{1}{2}\)% each year. What is the value of the phone after two years?
A. $140.93
B. $198.59
C. $153.91
D. $57.66
Answer:
The value of the phone after two years is $153.91.
Given,
New mobile device value = $256.25
Value changes by -22\(\frac{1}{2}\)% = –\(\frac{45}{2}\)%
Find the value of phine after two years
For first year
The value of change is 100 – \(\frac{45}{2}\)
\(\frac{45}{2}\) = 22.5
100 – 22.5
= 77.5%
The value of change for second year is (77.5 × 100 – \(\frac{45}{2}\))%
= (77.5 × 77.5)%
= 6006.25%
= (6006.25 ÷ 10000)× $256.25
= 0.600625 × $256.25
= $153.91

Question 6.
Khalid has 2 bags of cornmeal that each contain 25 servings. One serving is \(\frac{3}{4}\) cup. Khalid is making muffins that require 2.5 cups of cornmeal per batch. What is the maximum number of batches of muffins that Khalid can make using the cornmeal?
A. 7
B. 15
C. 18
D. 37
Answer:

Question 7.
A 2\(\frac{1}{2}\)-quart container of juice develops a leak and loses juice at an average rate of 3.3 fluid ounces per minute. Which is the best estimate of the time it takes until the container is empty?
A. 0.75 minute
B. 8 minutes
C. 24 minutes
D. 80 minutes
Answer:
0.75 minute

Explanation:
Average rate = 3.3 fluid ounces per minute
Distance = 2\(\frac{1}{2}\) = \(\frac{5}{2}\)
Speed = distance ÷ time
3.3 = \(\frac{5}{2}\) ÷ time
time = \(\frac{5}{2}\) ÷ 3.3
= 5 ÷ (3.3 × 2)
= 5 ÷ 6.6
= 0.75 minute

Question 8.
Laura jogs at an average rate of 5.6 miles per hour for 2\(\frac{1}{10}\) hours. Priya jogs the same distance but takes 1\(\frac{3}{5}\) hours. Write an expression you can use to find Priya’s average rate, using a decimal value or an operation symbol (+, —, ×, ÷ ) to fill in each box.
5.6 × HMH Into Math Grade 7 Module 6 Lesson 3 Answer Key Solve Multi-step Problems with Rational Numbers in Context 12
Answer:
5.6 × \(\frac{21}{10}\) × \(\frac{8}{5}\)

Explanation:
Given,
Average speed rate = 5.6 miles per hour
Time = 2\(\frac{1}{10}\) hours = \(\frac{21}{10}\)
Priya jogs = 1\(\frac{3}{5}\)  = \(\frac{8}{5}\)
5.6 × \(\frac{21}{10}\) × \(\frac{8}{5}\)

Spiral Review

Question 9.
Nicolas and Jerome are scuba diving. Nicolas is at an elevation of -25 feet compared to the surface of the water. Jerome is at an elevation of -32 feet. Which diver is closer to the surface of the water? How much closer is he compared to the other diver?
Answer:
Nicolas is closer to the surface as he is 7 feet closer to the surface than Jerome.

Explanation:
Therefore Nicolas is closer to the surface.
Nicolas is at an elevation of -25 feet.
Jerome is at an elevation of -32 feet.
= -25 – (-32)
= -7 feet.

Question 10.
The temperature at noon on a winter day was 2 °F. By 6 p.m., the temperature had dropped to -9 °F. Write a subtraction expression you can use to find the number of degrees the temperature dropped. Then evaluate the expression.
Answer:
The expression would be 2 – (-9).

Explanation:
We to find the number of degrees the temperature has changed by using the given equation
Starting temperature – ending temperature
Given,
Starting temperature = 2 °F
Current temperature = -9 °F
Now the equation becomes
= 2 – (-9)

Question 11.
Write an equation to represent the situation in the table.
HMH Into Math Grade 7 Module 6 Lesson 3 Answer Key Solve Multi-step Problems with Rational Numbers in Context 13
Answer:

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