# Texas Go Math Grade 4 Lesson 7.8 Answer Key Multiply 3-Digit and 4-Digit Numbers with Regrouping

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## Texas Go Math Grade 4 Lesson 7.8 Answer Key Multiply 3-Digit and 4-Digit Numbers with Regrouping

Essential Question

How can you use regrouping to multiply?

Unlock the problem

Alley Spring, in Missouri, produces an average of 567 million gallons of water per week. How many gallons of water do the springs produce in 3 weeks?

Multiply. 3 × 567
Estimate. 3 × ____________ = ____________

So, Alley Spring produces ____________ gallons of water in 3 weeks.

Explanation:

Example

Use an estimate or an exact answer.

The table shows the prices of three vacation packages. Jake, his parents, and his sister want to choose a package.

(A) About how much would Package C cost Jake’s family?

So, Package C would cost lake’s family about ____________ .
Jake’s family chooses package C.

Explanation:
Here, Jake’s family chooses package C.

Math Talk

Mathematical Processes
Explain how you know you can use an estimate

(B) Jake’s family wants to compare the total costs of Packages A and C. Which plan costs more? How much more does it cost?

Package A

Package C

Subtract to compare the total costs of the packages.

By comparing total costs of package A and package C that is $3,836 –$2,366 = $1,470. So, Package ____________ would cost ____________ more than Package ____________. Answer: So, Package A would cost$1,470 more than Package C.

Math Talk

Mathematical Processes
Explain why you need an exact answer.

Share and Show

Question 1.
Tell what is happening in Step 1 of the problem.

In step 1 we have multiplied 4 with 6.

Estimate. Then find the product.

Question 2.
Estimate: _____________

The actual product is 2,412.
The estimated product is 2,400.

Explanation:
The product of 603 and 4 is 2,412. So the estimated product will be 600×4 = 2,400.

Question 3.
Estimate: _____________

Question 4.
Estimate: _____________

The actual product is 41,630.
The estimated product is 41,300.

Explanation:
The product of 8,326 and 5 is 41,630. So the estimated product will be 8,300×5 = 41,300.

Math Talk

Mathematical Processes
Explain how you can use estimation to find how many digits the product 4 × 1861 will have.
Here, the product of 4 × 1861 is 7,444. And the estimated product will be 4 × 1900 = 7,600.

Problem Solving

Question 5.
Look at the table. About how many more people visited the park in 2007 than ¡n 2000?
The number of people who visited the park in 2007 than in 2000 is 2,90,295.

Explanation:
In the table, we can see that the number of people who visited the park in 2007 is 1,160,031 and the number of people who visited the park in 2000 is 869,736. So the number of people who visited the park in 2007 than in 2000 is 1,160,031 – 869,736 = 2,90,295.

Question 6.

H.O.T Use Diagrams Philadelphia, Pennsylvania, is 2,147 miles from Salt Lake City, Utah, and 2,868 miles from Portland, Oregon. What is the difference in the round-trip distances between Philadelphia and each of the other two cities? Explain whether you need an estimate or an exact answer.

Question 7.
H.O.T. Sense or Nonsense? Multi-Step Joe says that the product of a 4-digit number and a 1-digit number is always a 4-digit number. Does Joe’s statement make sense? Explain.

Question 8.
Tissue paper comes in packages of 6 sheets. Ms. Rodriguez buys 225 packages of tissue paper. How many sheets of tissue paper does she buy?
(A) 1,220
(B) 1,250
(C) 1,320
(D) 1,350
D.

Explanation:
Given that tissue paper comes in packages of 6 sheets and Ms. Rodriguez bought 225 packages of tissue paper. So the number of sheets of tissue paper does she bought was 6×225 = 1,350.

Question 9.
Dan has 1,398 sports cards. Mason has 3 times as many sports cards as Dan. How many sports cards does Mason have?
(A) 4,194
(B) 3,974
(C) 1,401
(D) 466

A.

Explanation:
Given that Dan has 1,398 sports cards and Mason has 3 times as many sports cards as Dan. So the number of sports cards does Mason has is 1,398×3 = 4,194.

Question 10.
Multi-Step Kayla’s family wants to rent a boat for 4 days. The table shows the cost of boats for 1 day. How much more will Kayla’s family pay to rent a ski boat for 4 days than to rent a sailboat for 4 days?

(A) $63 (B)$252
(C) $900 (D)$1,152

TEXAS Test Prep

Question 11.
What number is 150 more than the product of 5 and 4,892?
(A) 24,610
(B) 24,160
(C) 25,610
(D) 24,061
A.

Explanation:
The product of 5 and 4,892 is 24,460 and the number is 150 more than the product is 24,460+150 = 24,610.

### Texas Go Math Grade 4 Lesson 7.8 Homework and Practice Answer Key

Estimate. Then find the product.

Question 1.
Estimate:

The actual product is 5,322.
The estimated product is 5,400.

Explanation:
The product of 887 and 6 is 5,322 and the estimated product is 900×6 which is 5,400.

Question 2.
Estimate:

The actual product is 18,472.
The estimated product is 18,400.

Explanation:
The product of 2,309 and 8 is 18,472 and the estimated product is 2,300×6 which is 18,400.

Question 3.
Estimate

The actual product is 21,465.
The estimated product is 21,600.

Explanation:
The product of 7,155 and 3 is 21,465 and the estimated product is 7,200×3 which is 21,600.

Problem Solving

Question 4.
It is 1,748 miles from Dan’s home in Austin, Texas to his sister’s home in San Jose, California. It is 1,174 miles to his brother’s home near Minneapolis, Minnesota. How many miles more is the trip there and back to Dan’s sister’s home than the trip there and back to his brother’s home?

Question 5.
A theater seats 378 people. There are 2 shows each weekend for 4 weekends. If all of the seats are sold for all performances, how many people will see the shows? Explain whether you need an estimate or an exact answer.
The number of people who will see the show is 1,512 people.

Explanation:
Given that a theater seats 378 people and there are 2 shows each weekend for 4 weekends. So the number of people who will see the show is 378×4 which is 1,512 people.

Question 6.
Emma says that the product of a 3-digit number and a 1-digit number will be either a 3-digit number or a 4-digit number. Does Emma’s statement make sense? Explain.
Emma’s statement doesn’t make sense.

Explanation:
Here, Emma’s statement doesn’t make sense. Because if we multiply a three-digit number by 0 we will get 0 only and if we multiply 0.105 by 4 we will get 0.42.

Lesson Check

Question 7.
It takes Earth 365 days to orbit the sun. How many days does it take Earth to orbit the sun 3 times?
(A) 1,095 days
(B) 985 days
(C) 995 days
(D) 1,185 days
A.

Explanation:
Given that the earth takes 365 days to orbit the sun, so the number of days does it take Earth to orbit the sun 3 times is 365×3 which is 1,095 days.

Question 8.
Denver, Colorado is 5,280 feet above sea level. How many feet above sea level is a mountain peak that is 4 times higher above sea level?
(A) 20,820 feet
(B) 5,284 feet
(C) 21,120 feet
(D) 26,140 feet
C.

Explanation:
Given that Denver, Colorado is 5,280 feet above sea level, so the number of feet above sea level is a mountain peak that is 4 times higher above sea level is 4×5,280 which is 21,120 feet.

Question 9.
How many thousands are in the estimated 4 × 6,817?
(A) 22
(B) 14
(C) 10
(D) 28

D.

Explanation:
The product of 4 × 6,817 is 27,268. So the estimated number of thousands is 28.

Question 10.
Between which two numbers is the product of product of 9 × 452?
(A) 3,600 and 4,500
(B) 3,000 and 4,000
(C) 4,800 and 5,400
(D) 2,700 and 3,600
A.

Explanation:
The product of 9 × 452 is 4,068.

Question 11.
Multi-Step The secret code for a math competition is 382 less than 5 times 861. What is the code?
(A) 2,771
(B) 4,687
(C) 3,923
(D) 1,049
C.

Explanation:
Given that the secret code for a math competition is 382 less than 5 times 861 which is 861×5 = 4,305 – 382 = 3,923. So the secret code is 3,923.

Question 12.
Multi-Step Airplane tickets to Fairbanks, Alaska will cost $958 each. Airplane tickets to Vancouver, Canada will cost$734. How much can the four members of the Harrison family save on airfare by vacationing in Vancouver?
(A) $896 (B)$2,936
(C) $224 (D)$906
Given that Airplane tickets to Fairbanks, Alaska will cost $958 each, so for four members it will be$958×4 which is $3,832, and airplane tickets to Vancouver, Canada will cost$734. So for four members, it will be $734×4 which is$2,936. So Harrison’s family will save on airfare by vacationing in Vancouver will be $3,832-$2,936 which is \$896.