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4th Grade Multiplication & Division of Multi-Digit Numbers

www.njctl.org 2013-03-21

Slide 2 / 156 Table of Contents

Click on a topic to go to that section. · Multiply by multiples of 10, 100 and 1,000 · Multiply two digit numbers · Quotients with zeros · Use rounding to estimate products · Multiply 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 · Multiplication Review

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Multiplication by Multiples of 10, 100, 1000

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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 X 1

0 0 Multiplying by 10

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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

0 0 + 5

2 4

5

2 4

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

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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 Ten- Thousand s Thousand s Hundred s 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- Thousand s Ten- Thousand s Thousand s Hundreds Tens Ones 3 7 2 4

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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
• 2. 4281 X 10 3. 100 X 10

2300 42810 1000

CLICK CLICK CLICK

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1 673 X 10

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2 673 X 100

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3 7103 X 10

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4 5421 X 100

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5 1000 x 59 =

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6 18 x 1000 =

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7 500 X 10

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8 A football field is 100 yards long and 50 yards wide. What is the entire area of the field? (A= L x W) Slide 16 / 156

9 Each student in 4th grade is planning

• n reading 50 books this school year.

There are 100 students in the 4th grade. How many total books will they read?

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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?

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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?

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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?

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Use Rounding to Estimate Products

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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

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Estimating to the nearest tens: Estimation 77 80 X 28 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

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• Estimate. 14 X 189

189 Round each factor 189 rounds to 200 X 14 to its greatest place. 14 rounds to X 10 2,000 2,000 is the estimate

• Estimate. 227 X 1,068

1,068 Round each factor 1,068 rounds to 1,000 X 227 to its greatest place 227 rounds to X 200 200,000 200,000 is the estimate

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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? True False

Slide 25 / 156 14 Estimate the product of 47 x 430 = A 20,000 B 2,000 C 16,000 Slide 26 / 156 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

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16 Estimate the product of 527 x 62 = Slide 28 / 156 17 The basketball team is

• rdering sweatshirts. They

cost $23 each and the team needs to order 17. Estimate what the total cost would be to order them. Slide 29 / 156 18 Estimate the product of 839 x 25 = Slide 30 / 156

Multiplication Review

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Multiplying by Repeated Addition Show that 12 X 5 = 60 by repeated addition Solution Add 12 five times 0+12=12 12+12=24 24+12=36 36+12=48 48+12=60

click click click click

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Try This Now

Use repeated addition to find 5 X 20 0 + 20 = 20 20 + 20 = 40 40 + 20 = 60 80 + 20 = 100 60 + 20 = 80

click click click click

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List 8 multiples of 15. Then find 15 X 5 Solution 15, 30, 45, 60, 75, 90, 105, 120 15 X 5 = 75 Pull Pull

Counting Multiples

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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.

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The previous examples give strategies to use:

• 1. Repeated Addition
• 2. Counting Multiples
• 3. Drawing an Array

We can also use: The Standard Algorithm

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Multiplying without Regrouping - Standard Algorithm Find 24 X 2 Steps

• 1. Write the numbers in columns.

TENS ONES 2 4 2. Multiply the ones' digit by 2. x 2 3. Multiply the tens' digit by 2. 4 8

• 4. Write the results below the line.

ANSWER 24 x 2 = 48

CLICK

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Multiplying without Regrouping - Standard Algorithm Find 32 x 3 Steps

• 1. Write the numbers in columns.

TENS ONES 3 2 2. Multiply the ones' digit by 3. x 3 3. Multiply the tens' digit by 3.

• 4. Write the results below the line.

ANSWER 32 X 3 = 96

CLICK

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Multiplying without Regrouping - Standard Algorithm Find 42 x 2 Steps

• 1. Write the numbers in columns.

TENS ONES 4 2 2. Multiply the ones' digit by 2. x 2 3. Multiply the tens' digit by 2.

• 4. Write the results below the line.

ANSWER 84

CLICK

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19

32

X 2 Slide 40 / 156 20

31 X 3

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42

X 3

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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? Slide 43 / 156

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

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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

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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 8 7 X 6 2

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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

Slide 47 / 156 23 Which shows the correct product for 47 x 4 = ____ ? A 188 B 168 C 158 Slide 48 / 156

24 Which shows the correct product for 99 x 9 = ____ ? A 811 B 881 C 891 Slide 49 / 156 25

52

X 6

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47 x 3

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27

88

X 5

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26

X 4

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19

X 8 Slide 54 / 156

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?

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Multiplication of 2 Digit Numbers

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Click for Interactive Web Site

National Library of Virtual Manipulatives

Move to change numbers. Select Common

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31 Find the product. Use the diagram from the National Library of Virtual Manipulatives for help.

29 x 19 = _____

click click

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32 Find the product. Use the diagram from the National Library of Virtual Manipulatives for help.

15 x 24 = _____

click click

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33 Find the product. Use the diagram from the National Library of Virtual Manipulatives for help.

26 x 13 = _____

click click

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34 74 x 56 = ____ Slide 61 / 156 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? Slide 62 / 156 Multiplying By Two-Digit Numbers

124 X 32 8

Multiply the one's column Ask: Do I need to regroup?

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124 X 32 48

Multiply the ten's column Ask: Do I need to regroup?

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124 X 32 248

Multiply the hundred's column. Ask: Do I need to regroup?

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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

• ur calculations over by one place value.

Put a zero because you are really multiplying by 30.

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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

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124 X 32 248 + _3720

Last we multiply the 3 times 1 and get 3. Now you add the two sub-totals to get the final product.

3968

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Let's look at two related, but simpler, "1 by 2" problems for review.

124 X 2 248 124 X 30 3720

1

Pull Pull

for teacher instructions

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Multiplying Two-Digit Numbers More Practice

2 138 X 23 4

Multiply the one's column. Ask: Do I need to regroup?

Multiply the Ten's column. Ask: Do I need to regroup?

1 2 138 X 23 14

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Multiply the hundred's column. Ask: Do I need to regroup?

1 2 138 X 23 414 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.

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1

138 X 23 414

Multiply the ten's column and add the one. Last multiply the hundred's column.

+ 2760 3174

click

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36 242 x 12 Slide 73 / 156 37 501 X 13 Slide 74 / 156 38 723 X 47 Slide 75 / 156

39 Thirty-four people each did

• ne hundred forty-nine sit ups.

What is the combined total number of sits ups they did? Slide 76 / 156 40 On Saturday Mike did one hundred twenty-six push-ups in five minutes. How many push-ups would Mike do in

• ne hour?

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Multiplication of a Whole Number by up to 4 Digits

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Multiplying 3 Digit Numbers by 1 Digit Find 3 X 458

2 458 X 3 3 X 8 = 24 4 Multiply the ones. Write 4 in the ones place. Write the 2

• ver the tens column.

1 2 458 X 3

3 X 5 = 15

74 15 + 2 = 17 Multiply the tens by 3. Add the 2

• ver the tens column to that product.

Write 7 in the tens place. Write 1

• ver the hundreds column.

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1 2 458 X 3 1,374

3 X 4 = 12

12+ 1 = 13 Multiply the hundreds by 3. Add the 1

• ver the hundreds column to that
• product. Write the 3 in the hundreds
• place. Write the 1 in the thousands

place. 458 X 3 1,374

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42 When you multiply 561 x 9 there is nothing to carry from the ones column into the tens column. A TRUE B FALSE Slide 82 / 156 43 616 x 7 = Slide 83 / 156 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? Slide 84 / 156

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? Slide 85 / 156

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

• ccur in the product.

4219 X 3

7 6 5 2 1

5290 X 8

2 2 3 4

3428 X 2

8 5 6 6

Slide 86 / 156 46 1367 x 3 = ____ Slide 87 / 156

47 2572 x 5 = ____ Slide 88 / 156 48 7 x 9344 = ____ Slide 89 / 156 49 6255 x 2 = ____ Slide 90 / 156

50 3072 x 4 = ____ Slide 91 / 156 51 A family flies 1,765 miles to their favorite vacation destination three times a year. How many round trip miles do they travel? Slide 92 / 156 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? Slide 93 / 156

53 The Science Academy school has 1,204 students. If 849 of them purchase school lunch

• n each of the five school days

in a week, how many lunches will be served? Slide 94 / 156

Division with and without Remainders

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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 5 20 dividend

4 quotient

20 ÷ 5 = 4 20

__

5 = 4

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54 Identify the dividend of the problem: 96 divided by 8. Slide 97 / 156 55 Now find the quotient of 96 divided by 8. Slide 98 / 156

divisible by 2

divisible by 3

divisible by 10 54 170

None of the Above

501 152

360 47 126 81 2,541 15,210 97 316 250

Review of divisibilty rules

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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.

5 55 1

• 5

5 X 1 = 5 5 - 5 = 0 Compare 0 < 5

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5 55

• 5

05 Bring down the 5 1 Step 3 Step 2 Bring down the

• nes

Divide the ones 5 55

• 5

05

• 5 1 X 5 = 5

0 5 - 5 = 0 Compare 0 < 5 11 ANSWER The quotient is 11 Always check your answer 11 X 5 = 55

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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

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

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Try this: Find the quotient

• 1. 69 3 = 23 2. 84 2 = 42

click click

Slide 104 / 156 56 8 96 Slide 105 / 156

57 5 75 Slide 106 / 156 58 3 78 Slide 107 / 156

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

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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.

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For example: 7 9)65

• 63

2 65 ÷ 9 = 7 R 2 R means the remainder

Slide 110 / 156 60 Finish solving this problem and put the remainder in for the answer.

3 6)20 20 ÷ 6 = 3 R ____

• __

?

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61 Finish solving this problem and put the remainder in for the answer.

9 5)48 48 ÷ 5 = 9 R ____

• __

?

Slide 112 / 156 62 Finish solving this problem and put the remainder in for the answer.

6 7)45 45 ÷ 7 = 6 R ____

• __

?

Slide 113 / 156 63 Finish solving this problem and put the remainder in for the answer.

7 4)31 31 ÷ 4 = 7 R ____

• __

?

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64 Finish solving this problem and put the remainder in for the answer.

8 8)68 68 ÷ 8 = 8 R ____

• __

?

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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.

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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.

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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

7

D

8

53 ÷ 8 = 6 R 5

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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 6 B

5

C

4

D

2

26 ÷ 6 = 4 R 2

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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

Pull Pull

for teacher instructions

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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 8 B

7

C

5

D

4

39 ÷ 5 = 7 R 4

Pull Pull

for teacher instructions

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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

8

D

9

68 ÷ 9 = 7 R 5

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Using Rounding to Estimate Quotients

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

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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

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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

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70 Tickets for the rides at the boardwalk cost $3 per ride. About how many rides can you go on with $32? Slide 127 / 156 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.)

Slide 128 / 156 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? Slide 129 / 156

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? Slide 130 / 156 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? Slide 131 / 156

Find whole numbers quotients and remainders with up to four-digit dividends and one-digit divisors

Click to return to the table of contents

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Division with 3 digit dividends 128 5)640

• 5

14

• 10

40

• 40

Steps: Divide Multiply Subtract Bring Down

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3 can not go into 2, so do 3 into 21 72 3)216

• 21

06

• 6

Steps: Divide Multiply Subtract Bring Down

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

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Practice these: 358/2 = _____ 588/7 = _____ 792/6 = _____

Pull Pull

Slide 136 / 156 75 485/5 = _____ Slide 137 / 156 76 711/9 = _____ Slide 138 / 156

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?

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78 For field day students will be organized into teams

• f 8. If there will be 224 students participating, how

many teams will there be?

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

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Division with 4 digit dividends 529 7)3703

• 35

20

• 14

63

• 63

Steps: Divide Multiply Subtract Bring Down

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

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Practice these: 1748/2 = _____ 7430/5 = _____ 1746/3 = _____

Pull Pull

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80 1944/9 = _____ Slide 145 / 156 81 3664/8 = _____ Slide 146 / 156 82 The circus made $5,607 from ticket sales during the first week in August. Each ticket cost $9. How many tickets were sold? Slide 147 / 156

83 The circus also made $1,004 from selling balloons for $4

• each. How many balloons were

sold? Slide 148 / 156 84 The circus also made $1,443 from selling popcorn for $3 a

• bag. How many bags were sold?

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Quotients with Zeros

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Be careful, sometimes a zero needs to be used as a place holder when there is not enough to make a group.

3556

• 35

0 56

• 56

7 508

7 can't go into 5, so put a 0 and bring the 6 down.

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85 What is the next step in this division problem?

A Put a 2 in the quotient B

Put a 0 in the quotient

C

Put a 1 in the quotient

2721

• 27

02 3 9

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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

2832

• 28

03 4 7

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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? Slide 154 / 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? Slide 155 / 156 89 The Rodriguez family has budgeted $1540 for food for five days. How much money can they spend on food each day? Slide 156 / 156