Name 6.86.8Divide Divide

Four-Digit Four-Digit Numbers Numbers

by Two-Digit by Two-Digit NumbersNumbers

Learning Target:Learning Target: Divide four-digit numbers by Divide four-digit numbers by two-digit numbers.two-digit numbers.Success Criteria:Success Criteria: • I can use estimation to place the first digit in a quotient.• I can use estimation to place the first digit in a quotient.• I can use place value to divide.• I can use place value to divide.• I can use estimation or multiplication to check my answer.• I can use estimation or multiplication to check my answer.

Explore and Grow

Chapter 6 ⎜ Lesson 8 279

All of the division problems have no remainders. Which problems have two-digit quotients? Which problems have three-digit quotients? How do you know without calculating?

Reasoning Can a four-digit whole number divided by a two-digit whole number have a whole number quotient with four digits?Explain your reasoning.

1,890 ÷ 18 8,200 ÷ 40 4,774 ÷ 62

6,138 ÷ 33 1,050 ÷ 25 1,995 ÷ 21

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Think and Grow: Understand Multiplicative ComparisonThink and Grow: Divide Four-Digit Numbers by Two-Digit Numbers

280

Example Find 3,290 ÷ 31.

131 ) ‾ 3,290 32 hundreds ÷ 31 − 3 1 1 hundred × 31 1 32 hundreds − 31 hundreds

There is 1 hundred left over.

So, 3,290 ÷ 31 = R . Reasonable? R is close to . ✓

Estimate

Use the estimate to place the first digit in the quotient.

31 ) ‾ 3,290 The first digit is in the place.

Divide the hundreds.

Divide the tens.

Regroup 1 hundred as 10 tens and combine with 9 tens.19 tens cannot be shared among 31 groups without regrouping.So, place a zero in the quotient.

Divide the ones.

106 R 431 ) ‾ 3,290 − 3 1 19 − 0 190 190 ones ÷ 31 − 186 6 ones × 31 4 190 ones − 186 ones

There are 4 ones left over.

Regroup 19 tens as 190 ones.

Remember, you can use multiplication

to check your answer too.

Divide. Then check your answer.

1. 1. 28 ) ‾ 1,148

2.2. 13 ) ‾ 1,596

Show and GrowShow and GrowSSShhhhhhhoowwwwwwww aannnddddddd GGGGGrrrrrroowwwwwSSSSSSSShhhhhhhhoooooooowwwwwwww aaaaaaannnnnnnndddddddd GGGGGGGGrrrrrrrroooooooowwwwwwwwShow and GrowShow and Grow

1031 ) ‾ 3,290 − 3 1 19 − 0 0 tens × 31 19 19 tens − 0 tens

There are 19 tens left over.

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281Chapter 6 ⎜ Lesson 8

Name

Apply and Grow: Practice

Divide. Then check your answer.

10. 10. Reasoning Your friend finds 6,408 ÷ 51 and gets an answer of 124 R 84. Explain your friend’s mistake.

11. 11. Writing Explain why you can use multiplication to check your answer to a division problem.

3. 3. 16 ) ‾ 9,640

9. 9. A rectangular section of the flame trench on Launch Pad 39A at NASA’s Kennedy Space Center was damaged during the launch of the space shuttle Discovery. The area of the section damaged was 1,500 square feet. The section was 75 feet long. How wide was the section?

6. 6. 2,784 ÷ 72 =

4. 4. 26 ) ‾ 5,460

7. 7. 8,047 ÷ 83 =

5. 5. 37 ) ‾ 3,885

8. 8. 9,504 ÷ 96 =

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Think and Grow: Modeling Real Life

282

Show and GrowShow and GrowSSShhhhhhhoowwwwwwww aannnndddddddd GGGGrrrrrrroowwwwwwwSSSSSSSShhhhhhhhoooooooowwwwwwww aaaaaaaannnnnnnndddddddd GGGGGGGGrrrrrrrroooooooowwwwwwwwShow and GrowShow and Grow12. 12. A librarian has 1,048 books to

shelve. Each shelf can hold 32 books. The librarian fills each shelf before moving to another shelf. How many books are on the last shelf?

14. 14. DIG DEEPER A recreation director prepares the course of a 3-mile race by posting a motivational sign every85 yards along the course. How many signs does the director use? Explain.

13. 13. A banker receives 2,215 nickels. A standard roll of nickels contains 40 nickels. How many standard rolls of nickels can the banker make?

Interpret the quotient and the remainder.

The quotient is . So, the biologist explores 75 kilometers of the reef each week

for weeks.

The remainder is . There are kilometers left.

So, the biologist explores kilometers of the reef the last week.

R 75 ) ‾ 2,300 − 50 −

2,300 ÷ 75 = R

Example The Great Barrier Reef is 2,300 kilometers long. A marine biologist studies the entire reef. He can explore no more than 75 kilometers of the reef each week. How many kilometers of the reef does the biologist explore the last week?

Divide the total length by the length he can explore each week to find how many weeks he explores the reef.

Remember,1 mile = 1,760 yards.

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Name Homework & Practice 6.86.8

Learning Target:Learning Target: Divide four-digit numbers Divide four-digit numbers by two-digit numbers.by two-digit numbers.

283Chapter 6 ⎜ Lesson 8

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16 16 20

tens

1,600 ÷ 80 = 20Example Find 1,264 ÷ 79. Estimate

179 ) ‾ 1,264 − 79 47

Divide the tens. Divide the ones.

Divide. Then check your answer.

1. 1. 13 ) ‾ 5,343

4. 4. 3,300 ÷ 15 =

2. 2. 23 ) ‾ 3,296

5. 5. 4,592 ÷ 82 =

3. 3. 48 ) ‾ 1,414

6. 6. 8,751 ÷ 64 =

Use the estimate to place the first digit in the quotient.

79 ) ‾ 1,264 The first digit is in the place.

1679 ) ‾ 1,264

− 79 474

− 4740

So, 1,264 ÷ 79 = . Reasonable? is close to .

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284

9. 9. Which One Doesn’t Belong? Which expression does not have a two-digit quotient?

1,955 ÷ 85 6,701 ÷ 36

1,699 ÷ 54 2,754 ÷ 71

11. 11. Modeling Real Life A recycling company has 2,609 pounds of materials to sort. For efficiency, it divides all of the materials into boxes that each hold 20 pounds of materials. How many pounds of materials are in the last box?

10. 10. Is your friend correct? Explain. Show how to check your friend’s answer two different ways.

12. 12. Modeling Real Life An art museum has 1,025 paintings to divide equally among 20 rooms. How many more paintings does it need so that every room has the same number of paintings?

7. 7. A hot-air balloon travels 2,016 miles in 96 hours. The balloon travels the same number of miles each hour. How many miles does the balloon travel in 1 hour?

8. 8. The area of the rectangle is 1,875 square feet. What is the widthof the rectangle?

Review & RefreshFind the difference. Then check your answer.

w ft

75 ft

14. 14. 3.63 − 0.48 = 13. 13. 145.92 − 15.78 =

70 R30 61 ) ‾ 4,300 − 427 30 − 0 30

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