1. New Jersey Center for Teaching and Learning
Progressive Mathematics Initiative
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2. Division of Multi-Digit Numbers
4th Grade
Multiplication &
Division of Multi-Digit Numbers

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4. Table of Contents Click on a topic to go to that section.
·Multiplication by Multiples of 10, 100 and 1,000
·Use Rounding to Estimate Products
·Multiplication Review
·Multiplication of Two Digit Numbers
·Multiplication of a whole number by up to 4 digits by 1 digit
·Division with and without remainders
·Use rounding to estimate quotients
·Find whole numbers quotients and remainders with up to four-digit
dividends and one-digit divisors
·Quotients with zeros

5. Multiplication by Multiples of 10, 100, 1000
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table of contents

6. Multiplying by 10 Multiply 524 X 10 Solution
You need to have a thousands' column.
Step 1 Multiply each top number by 0.
Each answer is 0
Multiplying by 10
Thousands
Hundreds
Tens
Ones 5 2 4 X 1

7. Step 2 Add a zero in the ones' columns
in the second row. This lines up
the columns correctly.
Thousands
Hundreds
Tens
Ones 5 2 4 X 1
Step 3 Multiply the top row
by 1. 1 X 4 now goes
in the tens' column
(4 X 1 ten = 40), and
so on.
Step 4 Add down
ANSWER 524 X 10 = 5,240

8. Using a Place-Value Chart
Do 3724 X 100 with a place-value chart. What column in the chart contains the 3 before multiplying? after multiplying?
Hundred- Thousands
Thousands
Thousands
Hundreds
Tens
Ones 3 7 2 4
Solution
Before multiplying, the 3 is in the thousands' place, as shown. After multiplying, the 3 is in the hundred-thousands' place. That is because adding 2 zeros "moves" the number over 2 places to the left.
Hundred- Thousands
Thousands
Thousands
Hundreds
Tens
Ones 3 7 2 4

9. Patterns of Zeros When you multiply by 10, 100, 1000, there is a
pattern you can use. Look at 524 X 10 = What do you notice? If you said that multiplying a whole number by 10 adds one
zero to the end, you are right. You can multiply by 10 using this pattern.
Try This Use a pattern
X X X 10
Click
Click
Click

10. 1
673
X 10

11. 2
673
X 100

12. 3
7103
X 10

13. 4
5421
X 100

14. 5
1000 x 59 =

15. 6
18 x 1000 =

16. 7
500
X 10

17. 8
A football field is 100 yards long and 50 yards wide. What is the entire area of the field? (A= L x W)

18. 9
Each student in 4th grade is planning on reading 50 books this school year. There are 100 students in the 4th grade. How many total books will they read?

19. 10
The Sea Hawks are practicing their relay passes. If there are 9 people in the relay and 100 feet between them, how far does the ball travel when it reaches the last player? Think about the number of passes it takes to make it to the end of the relay?

20. 11
There are 10 boys on the basketball team.
If each boy sells $ for the candy sale, how much money will the team raise?

21. 12
There are 4 wheels on each of these training wheel bikes. There are 5 boys in each group and there are 10 groups. How many wheels are there in all?

22. Use Rounding to Estimate Products
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table of contents

23. Use Rounding to Estimate Products
Estimating (rounding) helps to see if the product makes number sense.
It is an important skill to develop good judgment about how precise an
estimate is possible or reasonable in various circumstances. This skill can be helpful if you don't need an exact answer.
Estimate the product of
X 28
We still follow the rounding rules:
if the digit is between the number remains the same
if the digit is between the rounding place value goes
up by one

24. Estimating to the nearest tens:
Estimation
X X 30
Since 8 X 3 = 24. Count the number of zeros in the estimation and add the same number to the product.
2,400 is the estimate

25. Estimate X 189
Round each factor rounds to
X to its greatest place rounds to X 10
2,000
2,000 is the estimate
Estimate X 1,068
1, Round each factor ,068 rounds to 1,000
X to its greatest place rounds to X 200
200,000
200,000 is the estimate

26. 13
You want to buy an video game system that costs $ If you save $40.00 per month, it will take you ten months to purchase the X-Box?
A True
B False

27. 14
Estimate the product of
47 x 430 = A
20,000 B
2,000 C
16,000

28. 15
A hospital ordered 79 boxes of cotton swabs. There are 52 cotton swabs in each box. About how many cotton swabs were ordered in all? Choose the better estimate. A 40 B
400 C
4000

29. 16
Estimate the product of
527 x 62 =

30. 17
The basketball team is ordering sweatshirts. They cost $23 each and the team needs to order 17. Estimate what the total cost would be to order them.

31. 18
Estimate the product of
839 x 25 =

32. Multiplication Review
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table of contents

33. Multiplying by Repeated Addition
Show that 12 X 5 = 60 by repeated addition
Solution
Add 12 five times
0+12= = = = =60
click
click
click
click

34. Use repeated addition to find 5 X 20
Try This Now
Use repeated addition to find 5 X 20
= 20
click
= 40
click
= 60
click
= 80
click
= 100

35. Counting Multiples
List 8 multiples of 15. Then find 15 X 5
Solution
15, 30, 45, 60, 75, 90, 105, 120
15 X 5 = 75
Teacher Instructions: Skip count by 15's. The product is the 5th multiple.

36. Multiplying Using a Model
Find 3 x 15
Arrange of 3 rows of 15 stars .
Using stars to represent ones, you count 45 stars.
45 is a multiple of 3.

37. The previous examples give strategies to use:
1. Repeated Addition
2. Counting Multiples
3. Drawing an Array
We can also use:
The Standard Algorithm

38. Multiplying without Regrouping - Standard Algorithm
Find 24 X 2
Steps
1. Write the numbers in columns.
TENS ONES
Multiply the ones' digit by 2.
x Multiply the tens' digit by 2.
4. Write the results below the line.
ANSWER 24 x 2 = 48
CLICK

39. Multiplying without Regrouping - Standard Algorithm
Find 32 x 3
Steps
1. Write the numbers in columns.
TENS ONES
Multiply the ones' digit by 3.
x Multiply the tens' digit by 3.
4. Write the results below the line.
ANSWER 32 X 3 = 96
CLICK

40. Multiplying without Regrouping - Standard Algorithm
Find 42 x 2
Steps
1. Write the numbers in columns.
TENS ONES
Multiply the ones' digit by 2.
x Multiply the tens' digit by 2.
4. Write the results below the line.
ANSWER 84
CLICK

41. 19 32
X 2

42. 20 X

43. 21 X

44. 22
Jenna is going to paint her bedroom pink. She needs three gallons of paint and each
gallon costs $18. How much will the paint cost for Jenna to paint her bedroom?

45. Multiplying Multidigit Numbers with Regrouping
Find the value of 16 X 4
Step-By-Step
Step 1: Rewrite the problem to make it easier to solve 16
X 4
Step 2: Multiply the ones
6 X 4 = 24 ones
Regroup 24 ones as 2 tens 4 ones. Write the 4 under the ones and the 2 above the tens. 2 4

46. Step 3: Multiply the tens.
4 X 1 = 4 tens
Add the 2 tens you regrouped
4 + 2 = 6 tens 2 16
X 4 64

47. Multiplying Multidigit Numbers with Regrouping
Find the value of 87 X 6
Step-By-Step
Step 1: Rewrite the problem to make it easier to solve 87
X 6
Step 2: Multiply the ones
6 X 7 = 42 ones
Regroup 42 ones as 4 tens 2 ones. Write the 2 under the ones and
the 4 above the tens
X 6 2

48. Step 3: Multiply the tens.
6 X 8 = 48 tens
Add the 4 tens you regrouped
= 52 tens 4 87
X 6
522

49. 23
Which shows the correct
product for 47 x 4 = ____ ? A
188 B
168 C
158

50. 24
Which shows the correct product for 99 x 9 = ____ ? A
811 B
881 C
891

51. 25 52 X

52. 26 47
x 3

53. 27 88 X

54. 28 26 X

55. 29 X

56. 30
The ice cream shop has a special on cones with 3 scoops. If they sell 72 cones one night, how many scoops of ice cream is that?

57. Multiplication of 2 Digit Numbers
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table of contents

58. Click for Interactive Web Site
National Library of Virtual Manipulatives
Move to
change
numbers.
Select
Common

59. 31
Find the product. Use the diagram from the National Library of Virtual Manipulatives for help.
29 x 19 = _____
click
click

60. 32
Find the product. Use the diagram from the National Library of Virtual Manipulatives for help.
15 x 24 = _____
click
click

61. 33
Find the product. Use the diagram from the National Library of Virtual Manipulatives for help.
26 x 13 = _____
click
click

62. 34
74 x 56 = ____

63. 35
The classroom has 27 boxes of crayons with 24 crayons in each of them. What is the total number of crayons in the classroom?

64. Multiplying By Two-Digit Numbers
Multiply the one's column
Ask: Do I need to regroup?
124 X 8

65. Multiply the ten's column
Ask: Do I need to regroup?
124
X 32 48

66. Multiply the hundred's column.
Ask: Do I need to regroup?
124
X 32
248

67. 124 X 32 248 Now we will multiply the 3 which is
in the tens position, therefore we
will place a zero in the ones to move
our calculations over by one place value.
124
X 32
248
Put a zero because you are really multiplying by 30.

68. 124 X__32 248 720 Now we will multiply the 3 so first
we get 12. We put the 2 down and
carry the one. Then multiply 3 times 2
you get 6 plus the carried one gives 7. 1
124
X__32
248
720

69. Last we multiply the 3 times 1 and get 3
Last we multiply the 3 times 1 and get 3. Now you add the two sub-totals to get the final product.
124
X 32
248
+_3720
3968

70. 124 124 X 2 X 30 248 3720 Let's look at two related, but simpler,
"1 by 2" problems for review. 1
124
X 2
248
124
X 30
3720

71. Multiplying Two-Digit Numbers
More Practice 2
138
X 23 4
Multiply the one's column.
Ask: Do I need to regroup?
1 2
138
X 23 14
Multiply the Ten's column.
Ask: Do I need to regroup?

72. 138 X 23 414 1 138 X 23 414 60 Multiply the hundred's column.
1 2
138
X 23
414
Multiply the hundred's column.
Ask: Do I need to regroup? 1
138
X 23
414 60
Multiply the one's column.
Ask: Do I need to regroup?
Multiply the ten's column and
add the one. Last multiply
the hundred's column.
Put a zero because you are really multiplying by 20.

73. 1 138 X 23 414 + 2760 3174 Multiply the ten's column
and add the one. Last multiply
the hundred's column. 1
138
X 23
414
+ 2760
3174
click

74. 36
242
x 12

75. 37
501
X 13

76. 38
723
X 47

77. 39
Thirty-four people each did one hundred forty-nine sit ups. What is the combined total number of sits ups they did?

78. 40
On Saturday Mike did one hundred twenty-six push-ups in five minutes. How many push-ups would Mike do in one hour?

79. Multiplication of a Whole Number by up to 4 Digits by 1 Digit
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table of contents

80. Multiplying 3 Digit Numbers by 1 Digit
Find 3 X 458 2
458
X X 8 = 24 4
Multiply the ones. Write 4 in the ones place. Write the 2 over the tens column.
1 2
458
X X 5 = 15
= 17
Multiply the tens by 3. Add the 2 over the tens column to that product. Write 7 in the tens place. Write 1 over the hundreds column.

81. 1 2
458
X 3
1,374
Multiply the hundreds by 3. Add the 1 over the hundreds column to that product. Write the 3 in the hundreds place. Write the 1 in the thousands place.
3 X 4 = 12
12+ 1 = 13
458 X
1,374

82. 41
263 X 4 =

83. 42
When you multiply 561 x 9 there is nothing to carry from the ones column into the tens column. A
TRUE B
FALSE

84. 43
616 x 7 =

85. 44
There are 432 students in a school. Each student has 8 classes per day. How many classes do all of the students have each day?

86. 45
On a Friday night, 417 tickets were sold at the movie theater. Each ticket cost $9. How much money did the theater collect through ticket sales?

87. Mentally analyze each problem
Mentally analyze each problem. Look at the digits in the box to the right of each problem. Try to place these digits in the bottom box in the order you think they will occur in the product.
4219
X 3
5290
X 8 7 6 5 2 1 2 3 4
3428
X 2 8 5 6

88. 46
1367 x 3 = ____

89. 47
2572 x 5 = ____

90. 48
7 x 9344 = ____

91. 49
6255 x 2 = ____

92. 50
3072 x 4 = ____

93. 51
A family flies 1,765 miles to their favorite vacation destination three times a year. How many round trip miles do they travel?

94. 52
The student council sold carnations for Valentine's day for $3 a piece. They got the carnations donated and sold 409 of them. How much money did they make?

95. 53
The Science Academy school has 1,204 students. If 849 of them purchase school lunch on each of the five school days in a week, how many lunches will be served?

96. Division with and without Remainders
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table of contents

97. Division terms to remember....
·The number to be divided into is known as the dividend
·The number which divides the other number is known
as the divisor
·The answer to a division problem is called the quotient
divisor dividend
4 quotient 20 __ 5
= 4
20 ÷ 5 = 4

98. 54
Identify the dividend of the problem:
96 divided by 8.

99. 55
Now find the quotient of
96 divided by 8.

100. Review of divisibilty rules
250
divisible by 2
152
divisible
by 3
360
126
501 47
316 97
170
divisible
by 10
2,541
None of the Above 81 54
15,210

101. Division with and without remainders
When we are dividing, we are breaking apart into equal groups
EXAMPLE 1
Find 55 5
Step 1 Place the first
digit in the tens
place. Divide the
tens. 1
- 5
5 X 1 = 5
5 - 5 = 0
Compare 0 < 5

102. Step 2 Bring down the
ones
Step 3
Divide the ones 1 11
5 55
- 5 05
Bring down
the 5
5 55
- 5 05
X 5 = 5
= 0
Compare 0 < 5
ANSWER The quotient is 11
Always check your answer 11 X 5 = 55

103. Repeated Subtraction You can also check your work in Example 1 by using repeated subtraction.
Verify that = 0
How many times do you subtract 11? ____ So, 55  5 = 11

104. Here is another way to look at 55 divided by 5
Take 55 pennies and put them into 11 equal groups

105. Try this: Find the quotient
click
click
 3 =  2 = 42

106. 56
8 96

107. 57

108. 58
3 78

109. 59
Liam bought boxes of popcorn to share with his 5 friends. If Liam spent $15, How much was each box? A
$5.00 B
$4.00 C
$3.00

110. Sometimes when we break apart a whole number into groups there is an amount left over.
For example: 7
9)65
-63
2 We say there are 2 left over because you can not make a group of 9 out of 2.

111. For example: 7
9)65
-63 2
65 ÷ 9 = 7 R 2
R means the remainder

112. ? Finish solving this problem and put the remainder in for the answer.60
Finish solving this problem and put the remainder in for the answer. 3
6) ÷ 6 = 3 R ____
-__ ?

113. 61
Finish solving this problem and put the remainder in for the answer. 9
5) ÷ 5 = 9 R ____
-__ ?

114. 62
Finish solving this problem and put the remainder in for the answer. 6
7) ÷ 7 = 6 R ____
-__ ?

115. ? Finish solving this problem and put the remainder in for the answer.63
Finish solving this problem and put the remainder in for the answer. 7
4) ÷ 4 = 7 R ____
-__ ?

116. 64
Finish solving this problem and put the remainder in for the answer. 8
8) ÷ 8 = 8 R ____
-__ ?

117. Interpreting the Remainder
In word problems, we need to interpret the what the remainder means.
For example: Kara has 38 strawberries. She wants to share them with 4 people. 9
4) 38
-36
2 4 people will each get strawberries and there will be left over.

118. What does the remainder below mean?
Manny is packing away the baseballs. He has 41 baseballs and 6 fit in a box. How many boxes does he need? 6
6) 41
-36
5 The remainder means he would have 5 baseballs that would not fit in the 6 boxes. He
would need 7 boxes to fit all
the baseballs.

119. 65
If you have 53 basketballs to transport from New Mexico to New Jersey and 8 basketballs are in each box, how many boxes will you need to ship all of the basketballs? A 5 B 6
53 ÷ 8 = 6 R 5 C 8 D 9

120. 66
A class is taking a trip to the middle school to see a play. They are going to travel by van. Each van will hold 6 students and 26 students will be going. How many vans will they need? A 7 B 6
26 ÷ 6 = 4 R 2 C 4 D 2

121. 67
Justina wants to share her pretzels with her friends. She has 47 pretzels to share between 6 people. How many pretzels will each person get? A 5 B 6
47 ÷ 6 = 7 R 5 C 7 D 8
Teacher Instructions: Be careful This answer will be letter C, 7.

122. 68
Ramel is cutting yarn for a project. Each piece needs to be 5 inches long. He has 39 inches of yarn. How many 5 inch pieces will he have? A 7 B 6
39 ÷ 5 = 7 R 4 C 5 D 4
Teacher Instructions: Be careful, this answer will be letter A, 7.

123. 69
Mr. Bullock wants new shelves in his classroom. He has 68 books and wants to put 9 on a shelf. How many shelves will he need? A 5 B 7
68 ÷ 9 = 7 R 5 C 9 D 10

124. Use Rounding to Estimate Quotients
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table of contents

125. Sometimes it is good to estimate to figure out
Estimation
Sometimes it is good to estimate to figure out
about how many times a number
goes into another number.

126. For example:
Molly has $21 and wants to buy new nail polish that is $4 a bottle. About how many bottles can she buy?
Round $21 to 20.
20 ÷ 4 = 5
She can buy about 5 bottles

127. What should $52 be rounded to? $50 $50 ÷ 5 = ____ lawns
Example:
Scott wants to save $52. If he charges $5 for each lawn he rakes, about how many lawns does he need to rake?
What should $52 be rounded to?
$50
$50 ÷ 5 = ____ lawns
Click

128. 70
Tickets for the rides at the boardwalk cost $3 per ride. About how many rides can you go on with $32?

129. 71
Nine friends want to share 32 slices of pizza. About how many slices will each get?
(Hint: Round the both the 9 and 32.)

130. 72
The art teacher needs 5 inches of string for each project. If she has 39 inches of string, about how many projects can be made?

131. 73
Mrs. Blankenship can make 7 fancy bows in an hour. If she has 68 bows to make, about how many hours will it take her?

132. 74
The pastry chef can decorate 4 cakes an hour. If 42 cakes need to be decorated for Saturday's orders, about how many hours will it take?

133. Find whole numbers quotients and remainders with up to four-digit dividends and one-digit divisors
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table of contents

134. Division with 3 digit dividends
128
5)640 -5 14
-10 40
-40
Steps:
Divide
Multiply
Subtract
Bring Down

135. 3 can not go into 2, so do 3 into 2172
3)216
-21 06
- 6
Steps:
Divide
Multiply
Subtract
Bring Down

136. Click for web site.
Set to 3 digit dividend,
1 digit divisor, &
remainder.

137. Practice these: 358/2 = _____ 588/7 = _____ 792/6 = _____ Steps:
Teacher Instructions:
Steps:
Divide
Multiply
Subtract
Bring Down

138. 75
485/5 = _____

139. 76
711/9 = _____

140. 77
The toy store just received 426 new remote control planes. They are very popular, so the store manager wants to put all of them out. There are six empty shelves. How many will go on each shelf?

141. 78
For field day students will be organized into teams of 8. If there will be 224 students participating, how many teams will there be?

142. 79
New uniforms for the nine members of the basketball team will cost $315. How much is one uniform?

143. Division with 4 digit dividends
529
7)3703
-35 20
-14 63
-63
Steps:
Divide
Multiply
Subtract
Bring Down

144. Click for web site.
Set to 4 digit dividend,
1 digit divisor, &
remainder.

145. Practice these: 1748/2 = _____ 7430/5 = _____ 1746/3 = _____ Steps:
Teacher Instructions:
Steps:
Divide
Multiply
Subtract
Bring Down

146. 1944/9 = _____ 80

147. 81
3664/8 = _____

148. 82
The circus made $5,607 from ticket sales during the first week in August. Each ticket cost $9. How many tickets were sold?

149. 83
The circus also made $1,004 from selling balloons for $4 each. How many balloons were sold?

150. 84
The circus also made $1,443 from selling popcorn for $3 a bag. How many bags were sold?

151. Quotients with Zeros
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table of contents

152. 508 3556 7 -35 056 -56 Be careful, sometimes a zero
needs to be used as a place
holder when there is not enough
to make a group.
508
3556
-35
056
-56 7
7 can't go into 5, so put a 0 and bring the 6 down.

153. 9 -27 3 02 85 What is the next step in this division problem? 2721 A
Put a 2 in the quotient B
Put a 0 in the quotient C
Put a 1 in the quotient

154. 7 2832 4 -28 03 86 What is the next step in this division problem? A
Put a 0 in the quotient B
Put a 3 in the quotient C
Put a 4 in the quotient

155. 87
For vacation, the Rodriguez family wants to drive 1224 miles. If the driving is split evenly between 3 days, how many miles will be driven each day?

156. 88
While on vacation the Rodriguez family will pay $1040 for 4-day passes to an amusement park for five people. What is the cost per person?

157. 89
The Rodriguez family has budgeted $1540 for food for five days. How much money can they spend on food each day?

158. New Jersey Center for Teaching and Learning
Progressive Mathematics Initiative (PMI)
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