Transcript NJCTL G4 Mlt_Dv Mltdgt

New Jersey Center for Teaching and Learning
Progressive Mathematics Initiative
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4th Grade
Multiplication &
Division of Multi-Digit Numbers
2012-08-07
www.njctl.org
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the Slide Show view. (See Slide 10 for an example.)
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
Multiplication by
Multiples of 10, 100, 1000
Click to return to the
table of contents
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
Thousands
Hundreds
Tens
Ones
5
2
4
1
0
0
0
X
0
Step 2 Add a zero in the ones' columns
in the second row. This lines up
the columns correctly.
Thousands
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
Hundreds
Tens
Ones
2
4
1
0
0
0
0
5
2
4
0
5
2
4
0
5
X
+
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?
HundredThousands
TenThousands
Thousands
3
Hundreds
7
Tens
Ones
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.
HundredThousands
3
TenThousands
Thousands
Hundreds
7
2
4
Tens
Ones
0
0
Patterns of Zeros When you multiply by 10, 100, 1000, there is a
pattern you can use. Look at 524 X 10 = 5240. 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
1. 230 X 10
Click
2300
2. 4281 X 10
Click
42810
3. 100 X 10
Click
1000
1
673
X 10
2
673
X 100
3
7103
X 10
4
5421
X 100
5
1000 x 59 =
6
18 x 1000 =
7
500
X 10
8
A football field is 100 yards long and 50 yards wide.
What is the entire area of the field? (A= L x W)
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?
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?
11
There are 10 boys on the basketball team.
If each boy sells $219.00 for the candy sale, how
much money will the team raise?
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?
Use Rounding to
Estimate Products
Click to return to the
table of contents
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
77
X 28
We still follow the rounding rules:
if the digit is between 0 - 4 the number remains the same
if the digit is between 5 - 9 the rounding place value goes
up by one
Estimating to the nearest tens:
77
X 28
Estimation
80
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
Estimate.
189
X 14
14 X 189
Round each factor
to its greatest place.
189 rounds to
200
14 rounds to X 10
2,000
2,000 is the estimate
Estimate. 227 X 1,068
1,068
X 227
Round each factor
to its greatest place
200,000 is the estimate
1,068 rounds to 1,000
227 rounds to X 200
200,000
13
You want to buy an video game system that costs
$399.95. If you save $40.00 per month, it will take
you ten months to purchase the X-Box?
A
True
B
False
14
Estimate the product of
47 x 430 =
A
B
20,000
2,000
C
16,000
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
16
Estimate the product of
527 x 62 =
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.
18
Estimate the product of
839 x 25 =
Multiplication Review
Click to return to the
table of contents
Multiplying by Repeated Addition
Show that 12 X 5 = 60 by repeated addition
Solution
Add 12 five times
0+12=12
click
12+12=24
click
24+12=36
click
36+12=48
click
48+12=60
Try This Now
Use repeated addition to find 5 X 20
0 + 20 = 20
20 +click
20 = 40
40 + 20
= 60
click
60 +click
20 = 80
80 + 20
= 100
click
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
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.
The previous examples give strategies to use:
1. Repeated Addition
2. Counting Multiples
3. Drawing an Array
We can also use:
The Standard Algorithm
Multiplying without Regrouping - Standard Algorithm
Find 24 X 2
Steps
1. Write the numbers in columns.
TENS
2
x
4
ONES
4
2
8
2. Multiply the ones' digit by 2.
3. Multiply the tens' digit by 2.
4. Write the results below the line.
ANSWERCLICK
24 x 2 = 48
Multiplying without Regrouping - Standard Algorithm
Find 32 x 3
Steps
1. Write the numbers in columns.
TENS
3
x
ONES
2
3
2. Multiply the ones' digit by 3.
3. Multiply the tens' digit by 3.
4. Write the results below the line.
ANSWER
32 X 3 = 96
CLICK
Multiplying without Regrouping - Standard Algorithm
Find 42 x 2
Steps
1. Write the numbers in columns.
TENS
4
x
ONES
2
2
2. Multiply the ones' digit by 2.
3. Multiply the tens' digit by 2.
4. Write the results below the line.
CLICK 84
ANSWER
19
32
X 2
20
31
X
3
21
42
X
3
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?
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
16
X 4
4
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
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.
4
87
X 6
2
Step 3: Multiply the tens.
6 X 8 = 48 tens
Add the 4 tens you regrouped
48 + 4 = 52 tens
4
87
X 6
522
23
Which shows the correct
product for 47 x 4 = ____ ?
A
188
B
168
C
158
24
Which shows the correct product for
99 x 9 = ____ ?
A
811
B
C
881
891
25
X
52
6
26
47
x 3
27
X
88
5
28
X
26
4
29
X
19
8
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?
Multiplication of
2 Digit Numbers
Click to return to the
table of contents
Click for Interactive Web Site
National Library of Virtual Manipulatives
Move to
change
numbers.
Select
Common
31
Find the product. Use the diagram from the National
Library of Virtual Manipulatives for help.
29 x 19 = _____
click
click
32
Find the product. Use the diagram from the National
Library of Virtual Manipulatives for help.
15 x 24 = _____
click
click
33
Find the product. Use the diagram from the
National Library of Virtual Manipulatives for help.
26 x 13 = _____
click
click
34
74 x 56 = ____
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?
Multiplying By Two-Digit Numbers
Multiply the one's column
Ask: Do I need to regroup?
124
X 32
8
Multiply the ten's column
Ask: Do I need to regroup?
124
X 32
48
Multiply the hundred's column.
Ask: Do I need to regroup?
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
0
Put a zero because you are
really multiplying by 30.
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
Last we multiply the 3 times 1 and
get 3. Now you add the two subtotals to get the final product.
124
X 32
248
+_3720
3968
Let's look at two related, but simpler,
"1 by 2" problems for review.
1
124
X 2
248
124
X 30
3720
2
138
X 23
4
12
138
X 23
14
Multiplying Two-Digit Numbers
More Practice
Multiply the one's column.
Ask: Do I need to regroup?
Multiply the Ten's column.
Ask: Do I need to regroup?
12
138
X 23
414
1
138
X 23
414
60
Multiply the hundred's column.
Ask: Do I need to regroup?
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.
1
138
X 23
414
+ 2760
3174
click
Multiply the ten's column
and add the one. Last multiply
the hundred's column.
36
242
x 12
37
501
X 13
38
723
X 47
39
Thirty-four people each did one hundred fortynine sit ups. What is the combined total
number of sits ups they did?
40
On Saturday Mike did one hundred twenty-six
push-ups in five minutes. How many push-ups
would Mike do in one hour?
Multiplication of a Whole Number
by up to 4 Digits by 1 Digit
Click to return to the
table of contents
Multiplying 3 Digit Numbers by 1 Digit
Find 3 X 458
2
458
X 3
4
3 X 8 = 24
12
458
X 3
74
3 X 5 = 15
15 + 2 = 17
Multiply the ones. Write 4
in the ones place. Write the
2 over the tens column.
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.
12
458
X 3
1,374
3 X 4 = 12
12+ 1 = 13
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.
41
263 X 4 =
42
When you multiply 561 x 9 there is nothing to carry
from the ones column into the tens column.
A
TRUE
B
FALSE
43
616 x 7 =
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?
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?
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 7
X 3 6
5
2
1
5290 2
X 8 2
3
4
0
3428 8
X 2 5
6
6
46
1367 x 3 = ____
47
2572 x 5 = ____
48
7 x 9344 = ____
49
6255 x 2 = ____
50
3072 x 4 = ____
51
A family flies 1,765 miles to their favorite vacation
destination three times a year. How many round trip
miles do they travel?
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?
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?
Division with and without
Remainders
Click to return to the
table of contents
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
4 quotient
divisor 5
20 ÷ 5 = 4
20 dividend
20
__
= 4
5
54
Identify the dividend of the problem:
96 divided by 8.
55
Now find the quotient of
96 divided by 8.
Review of divisibilty rules
250
divisible by 2
152
360 126
501 47
316
97
2,541
15,210
divisible
by 3
170
divisible
by 10
81
54
None of
the Above
Division with and without remainders
When we are dividing, we are breaking apart into equal groups
EXAMPLE 1
Find 55
Step 1 Place the first
digit in the tens
place. Divide the
tens.
1
5 55
-5
0
5
5X1=5
5-5=0
Compare 0 < 5
Step 2 Bring down the
ones
1
5 55
-5
05
Step 3
Bring down
the 5
ANSWER The quotient is 11
Always check your answer 11 X 5 = 55
Divide the ones
11
5 55
-5
05
- 5
0
1X5=5
5- 5=0
Compare 0 < 5
Repeated Subtraction You can also check your work in Example 1 by
using repeated subtraction.
Verify that 55 - 11 - 11 - 11 -11 -11 = 0
How many times do you subtract 11? ____ So, 55  5 = 11
Here is another way to look at 55 divided by 5
Take 55 pennies and put them into 11 equal groups
Try this: Find the quotient
1. 69  3 = 23
click
2. 84  2 = 42
click
56
8 96
57
5
75
58
3 78
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
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.
For example:
7
9)65
-63
2
65 ÷ 9 = 7 R 2
R means the remainder
60
Finish solving this problem and put the remainder
in for the answer.
3
6)20
-__
?
20 ÷ 6 = 3 R ____
61
Finish solving this problem and put the remainder
in for the answer.
9
5)48
-__
?
48 ÷ 5 = 9 R ____
62
Finish solving this problem and put the remainder
in for the answer.
6
7)45
-__
?
45 ÷ 7 = 6 R ____
63
Finish solving this problem and put the remainder
in for the answer.
7
4)31
-__
?
31 ÷ 4 = 7 R ____
64
Finish solving this problem and put the remainder
in for the answer.
8
8)68
-__
?
68 ÷ 8 = 8 R ____
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 9
strawberries and there will be 2
left over.
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.
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
C
8
D
9
53 ÷ 8 = 6 R 5
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
C
4
D
2
26 ÷ 6 = 4 R 2
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
C
7
D
8
47 ÷ 6 = 7 R 5
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
C
5
D
4
39 ÷ 5 = 7 R 4
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
C
9
D
10
68 ÷ 9 = 7 R 5
Use Rounding to
Estimate Quotients
Click to return to the
table of contents
Estimation
Sometimes it is good to estimate to figure out
about how many times a number
goes into another number.
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
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?
Click
$50
$50 ÷ 5 = ____ lawns
70
Tickets for the rides at the boardwalk cost $3 per
ride. About how many rides can you go on with $32?
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.)
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?
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?
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?
Find whole numbers quotients
and remainders with up to
four-digit dividends and onedigit divisors
Click to return to the
table of contents
Division with 3 digit dividends
128
5)640
-5
14
-10
40
-40
0
Steps:
Divide
Multiply
Subtract
Bring Down
3 can not go into 2, so do 3 into 21
72
3)216
-21
06
- 6
0
Steps:
Divide
Multiply
Subtract
Bring Down
Click for web site.
Set to 3 digit dividend,
1 digit divisor, &
remainder.
Practice these:
358/2 = _____
588/7 = _____
792/6 = _____
75
485/5 = _____
76
711/9 = _____
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?
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?
79
New uniforms for the nine members of the
basketball team will cost $315. How much is one
uniform?
Division with 4 digit dividends
529
7)3703
-35
20
-14
63
-63
0
Steps:
Divide
Multiply
Subtract
Bring Down
Click for web site.
Set to 4 digit dividend,
1 digit divisor, &
remainder.
Practice these:
1748/2 = _____
7430/5 = _____
1746/3 = _____
80
1944/9 = _____
81
3664/8 = _____
82
The circus made $5,607 from ticket sales during
the first week in August. Each ticket cost $9. How
many tickets were sold?
83
The circus also made $1,004 from selling balloons
for $4 each. How many balloons were sold?
84
The circus also made $1,443 from selling popcorn
for $3 a bag. How many bags were sold?
Quotients with Zeros
Click to return to the
table of contents
Be careful, sometimes a zero
needs to be used as a place
holder when there is not enough
to make a group.
7
508
3556
-35
056
-56
0
7 can't go into 5,
so put a 0 and
bring the 6 down.
85
What is the next step in this division problem?
9
2721
3
-27
02
A
Put a 2 in the quotient
B
Put a 0 in the quotient
C
Put a 1 in the quotient
86
What is the next step in this division problem?
7
4 2832
-28
03
A
Put a 0 in the quotient
B
Put a 3 in the quotient
C
Put a 4 in the quotient
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?
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?
89
The Rodriguez family has budgeted $1540 for food
for five days. How much money can they spend
on food each day?
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