Fourth Grade Multiplication and Division of Multi-Digit Numbers - - PDF document

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Fourth Grade

Multiplication and Division of Multi-Digit Numbers

2015-11-23 www.njctl.org

Slide 3 / 176 Table of Contents

Click on a topic to go to that section.

• Multiply by Multiples of 10, 100 and 1,000
• Multiplication by Two Digit Numbers
• Use Rounding to Estimate Products
• Division with and without Remainders
• Basics of Division & Estimating Quotients
• Multiplying Whole Numbers up to 4 Digits by One-Digit
• Quotients with Zeros
• Find Whole Number Quotients and Remainders with


 
 
 
 
 up to Four-Digit Dividends and One-Digit Divisors

Slide 4 / 176 Links to PARCC sample questions

Non-Calculator #2 Non-Calculator #4 Non-Calculator #6 Non-Calculator #3 End of Year Performance Based Assessment Non-Calculator #7 Non-Calculator #11 Non-Calculator #14 Non-Calculator #21 Non-Calculator #24 Non-Calculator #16 Non-Calculator #8 Non-Calculator #11 Non-Calculator #17

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Multiplication by Multiples of 10, 100, 1000

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Slide 6 / 176 Multiplication Review

Multiplication is repeated addition of same-sized groups. For example, 4 x 5 could be shown in the following ways: (Make 4 groups of 5) (Count by 5, 4 times.) 5 + 5 + 5 + 5 = 20 = 20 s Use the set model . Use skip counting .

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Use an array . Use the area model . (4 groups of 5 s) (a 4 x 5 graph) = 20 s = 20 s

Multiplication Review Slide 8 / 176 Multiplying by 10

Let's multiply 7 x 10 using the area model. On the graph below, draw a rectangle that is 7 units by 10 units. Shade in your rectangle. Count the number of squares that are shaded. You're counting 7 groups of 10, so 7 x 10 = ______. When you find the area of any rectangle, you multiply the length (l) by the width (w). The formula looks like this: A = l x w Teacher Notes

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Use the area model to find each product. 10 x 3 = _____ 14 x 10 = _____ What do you notice about each of these problems? Can you come up with a "rule" or a short-cut to find the product of any number and 10?

Multiplying by 10 Slide 10 / 176

Patterns of Zeros When you multiply by 10, 100, 1000, there is a pattern you can use. You just discovered that multiplying a whole number by 10 adds one zero to the end. Based on that, what do you think will happen if you multiply a number by 100 or by 1000? Try These: 230 x 10 42 x 100 100 x 10 2,300 4,200 1,000 7 x 1000 501 x 100 330 x 1000 7,000 50,100 330,000

click ______ click ______ click ______ click ______ click ______ click ______

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1 Find the product. 673 x 10 =

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2 Find the product. 673 x 100 =

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3 Find the product. 7103 x 10

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4 Find the product. 5421 x 100 =

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5 Find the product. 1,000 x 59 =

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6 Find the product. 50 x 100,000 =

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7 A football field is 100 yards long and 50 yards wide. What is the area of the field?

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8 Each student in 4th grade is planning on reading 60 books this school year. There are 100 students in the 4th

• grade. How many books will they read?

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9 There are 10 boys on the basketball team. If each boy sells $219.00 worth of candy for the candy sale, how much money will the team raise?

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10 There are 4 wheels on each training wheel bike. There are 5 kids in each group and there are 10 groups. How many wheels are there in all?

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11 The number 234 is multiplied by 10. Select the correct word from each group. The numberal 2 in the resulting product is in the _____ place, and the value of this digit is _____.

A ones B tens C hundreds D thousands

E 2 F 20 G 200 H 2,000

From PARCC sample test

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12 Mr. Soto's bicycle weighs 30 pounds. His car weighs 90 times as much as his bicycle. What is the weight, in pounds, of Mr. Soto's car?

From PARCC sample test

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Use Rounding to Estimate Products

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Slide 24 / 176 Use Rounding to Estimate Products

Why do we estimate? Estimating (rounding) numbers helps us to see if the product makes number sense. It is an important skill to develop good judgment about how precise an estimate is or whether your answer is possible or reasonable in various circumstances. This skill can be helpful if you don't need to find the exact answer.

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Slide 25 / 176 Use Rounding to Estimate Products

How to Round Numbers: Decide which is the last digit to keep (the place you are rounding to). Leave it the same if the next digit is less than 5 (this is called rounding down). Increase it by 1 if the next digit is 5 or more (this is called rounding up).

Slide 26 / 176 Estimate Products

Round each number to the nearest ten.

• 1. Round each number to the nearest ten.
• 2. Multiply the whole numbers.
• 3. Count the number of zeros in the estimation and add the same

number of zeros to the product.

77 80 x 28 x 30 2400

click

Slide 27 / 176 Estimate Products

Round each factor to its greatest place. 14 X 189 (It's helpful to write the problem vertically.) 189 189 rounds to 200 X 14 14 rounds to x 10 2000 Let's try one more! 227 X 1,068 1,068 rounds to 1,000 227 rounds to x 200 200,000

click click

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

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14 You want to buy a 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

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15 A hospital ordered 79 boxes of cotton swabs. There are 42 cotton swabs in each box. About how many swabs were ordered in all? A 40 B 400 C 4000

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16 Estimate the product. 527 x 62 =

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17 Estimate the product 452 x 81 =

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Multiplying Whole Numbers up to 4 Digits by One-Digit

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Multiply 12 x 5 by using Repeated Addition Starting with zero, add 12 five times . 0+12=12 12+12=24 24+12=36 36+12=48 48+12=60

Slide Slide Slide Slide

Repeated Addition Slide 35 / 176

List the first 8 multiples of 15. Using your list, find 15 x 3. Now find 15 x 7.

Counting Multiples Slide 36 / 176 Multiplying Using a Model (Array)

Find 3 x 15 Arrange of 3 rows of 15 stars . Using stars to represent ones, how many stars do you count? This number is a multiple of 3.

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You can use the area model to multiply numbers. To multiply 9 x 3, draw a rectangle with a side length of 9 and a width of 3. When you know your multiplication facts, there is no need to count

• squares. You can just multiply the length and the width to find the

area (product). Let's multiply 7 x 6. 9 3 9 x 3 = __ squares 7 6 7 x 6 = ____

Multiply Using the Area Model Slide 38 / 176

You can also use the area model to multiply a larger (2, 3, 4+ digit) number by a one-digit number. Here's an example... 78 x 5 When you first look at this problem, it may seem

• difficult. But, don't

worry! You can break it down into smaller parts that are easy to multiply! Now, multiply each part! To find the total area, find the sum of the two smaller parts. 5 70 8 5 70 8

70 x 5 = 350

5 x 8 = 40

350 + 40 390 So, 78 x 5 = 390

B r e a k d

• w

n 7 8 i n t

• 7

+ 8 !

Multiply Using the Area Model

click to reveal

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Let's try a few more problems! 37 x 9 9 30 x 9 = 270 7 x 9 = 63 30 7 270 + 63 = 333 So, 37 x 9 = 333

Area Model

click to reveal

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Let's try a few more problems! 124 x 6 100 20 4 6 100 x 6 = 600 20 x 6 = 120 4 x 6 = 24 600 + 120 + 24 = 744 So, 124 x 6 = 744

Area Model

click to reveal

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18 Use the area model to find the product of 42 x 3.

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19 Using the area model, find the product of 88 x 5.

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20 Use the area model to multiply 263 x 4.

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21 Find the product. 509 x 8 =

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We just reviewed the following strategies...

• 1. Repeated Addition
• 2. Counting Multiples
• 3. Drawing an Array
• 4. Using the Area Model.

These are all very good ways to help you understand the meaning of multiplication. But now, you will learn to multiply using the Standard Algorithm.

Multiplication Strategies Slide 46 / 176

Find 24 x 2

• 1. Write the numbers in columns.
• 2. Multiply the ones' digit by 2.
• 3. Multiply the tens' digit by 2.

x

Tens Ones

2 4 2

Multiplication Using the Standard Algorithm

Answer

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Let's try a few more examples... 32 x 3 21 x 4

413 x 2

x x x

Tens Ones Tens Ones

Hundreds

Tens Ones

Multiplication Using the Standard Algorithm

Answer

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Now let's multiply 16 x 4.

• 1. Multiply the ones.
• a. When you multiply 4 x 6, you will not get a
• ne-digit number.
• b. 4 x 6 = 24
• c. 24 =

2 tens + 4 ones .

• d. Write

4 in the ones' column and carry the # # 2 to the tens' column. This is called # # "regrouping".

• 2. Multiply 4 to the number in the tens column and

# # then add the 2 tens you regrouped. ( 4 x 1 + 2 = 6)

Tens Ones

1 6 4 4

Tens Ones

1 6 4 6 4

2 +2

x x

Standard Algorithm

Answer

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• 1. Multiply 6 x 7.
• 2. 6 x 7 = 42 (4 tens + 2 ones)
• 3. Write the 2 in the ones' column

and regroup the 4 to the tens' column.

• 4. Multiply 6 x 8 and then add the 4.

6 x 8 + 4 = 52

• 5. Write the 5 in the hundreds'

column and the 2 in the tens' column.

x

Hundreds Tens Ones

8 7 6

Standard Algorithm

Let's try another problem 87 x 6. Answer

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Do you remember the steps? 47 x 4 458 x 3

Thousands Hundreds Tens Ones Thousands Hundreds Tens Ones

x x Standard Algorithm

Answer

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Here are two REALLY tricky problems!

4219 x 3

5290 x 8

x

Ten-Thousands Thousands Hundreds Tens Ones

x

Ten-Thousands Thousands Hundreds Tens Ones

Don't forget to re-group!

Standard Algorithm

Answer

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Can find these products without using a table? 47 x 3 265 x 2 1367 x 4

Products Slide 53 / 176

22 When you multiply 561 x 9, there is nothing to regroup from the ones column to the tens column. True False

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23 When you multiply 372 x 8, there is nothing to regroup from the ones column to the tens column. True False

SLIDE 10

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

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25 The Cold Cow ice cream shop has a special on cones with three scoops. If they sell 72 cones in one night, how many scoops of ice cream did they serve?

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26 Find the product. 616 x 7 =

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27 Find the product. 2572 x 5 =

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28 Find the product 7 x 9344.

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29 Enter your answer in the box. 3,649 x 6 =

From PARCC sample test

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30 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?

Students type their answers here

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31 A movie theater has two rooms. Room A has 9 rows of seats with 21 seats in each row. Room B has three times as many seats as Room A. How many seats are there in both rooms?

Students type their answers here

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32 The middle school art teacher has 9 cases of crayons with 52 boxes in each case. The elementary school art teacher has 6 cases of crayons with 104 boxes in each case. How many total boxes of crayons do both teachers have?

Students type their answers here

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

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34 The Science Academy School has 1,204

• students. If 849
• f them buy school lunch five days each week, how many

lunches are purchased each week?

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35 A garden contains only bean plants and tomato plants. There are 5 rows of bean plants and 6 rows of tomato

• plants. Each row of bean plants has 13 plants. Each row
• f tomato plants has 16 plants.

What is the total number of plants in the garden?

From PARCC sample test

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36 The table shows the number of yards Ed ran in each of the first three football games of the season. After the first three games of the season, Rico had exactly 3 times the total number of running yards that Ed had. How many more total running yards did Rico have than Ed after the first three games of the season? Show your work using equations.

From PARCC sample test

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Multiplication by 2 Digit Numbers

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We are now ready to move onto multiplying larger numbers. Let's use the area model to find the product of 20 x 57. Because one of the factors is a multiple of 10, which is an easy number to multiply, we only need to break up "57". What is 20 x 50?

What is 20 x 7?

The sum of your products is equal to 20 x 57. So, the product of 20 x 57 = ? 20 50 7

2 Digit Numbers - Area Model Slide 70 / 176

Most problems will not have factors that are so easy to multiply! You will have to break up both factors! Let's use the area model to multiply 15 x 24. We'll need to break up both the "15" and the "24". How do you think these factors

should be broken up to make solving this

problem as easy as possible?

2 Digit Numbers - Area Model Slide 71 / 176

The model we'll make for this problem will look a little different. We'll need two sections on each side since both factors were broken up. 20 4 10 5 Multiply the factors in each of the four sections and then find the sum. This will be the product of 15 x 24.

2 Digit Numbers - Area Model Slide 72 / 176

Let's try another example... 26 x 13 How will you set up this problem? Think about it carefully and use the model below to find the product.

2 Digit Numbers - Area Model

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37 Use the area model to find the product. 29 x 19 =

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38 Use the area model to find the product

• f 74 x 56.

Write your answer in standard form.

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39 The classroom has 27 boxes of crayons with 24 crayons in each box. What is the total amount of crayons in the classroom? Use an area model to solve the problem, and write your answer in standard form.

Slide 76 / 176 Click for Interactive Web Site

National Library of Virtual Manipulatives Move to change numbers. Select Common

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Now, let's multiply 54 x 23 using the Standard Algorithm .

• 1. First, we have to multiply 54

by 3 ones. 54 x 3 = 162

• 2. Next, we have to multiply

54 by 2 tens. 54 x 20 = 1080

• 3. The last step is to add the

two products. 162 + 1080 = 1242

T h i s i s w h a t t h e p r

• b

l e m l

• k

s l i k e u s i n g t h e S t a n d a r d A l g

• r

i t h m .

Standard Algorithm

54 x 23 54 x 3 162 54 x 23 54 x 20 1080 54 x 23 162 + 1080 1242

1

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Now, let's multiply 124 x 43 using the Standard Algorithm .

• 1. First, we have to multiply 124

by 3 ones. 124 x 3 = 372

• 2. Next, we have to multiply

124 by 4 tens. 124 x 40 = 4960

• 3. The last step is to add the

two products. 372 + 4960 = 5332

Standard Algorithm

124 x 43 124 x 3 372 124 x 43 124 x 40 4960 124 x 43 372 + 4960 5332

1 1

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Can you find the product of 138 x 23? Think about the steps we used in the examples. Don't forget to regroup and place zeros as needed.

138 x 23

Standard Algorithm Slide 80 / 176

Let's try one more problem... 422 x 18

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40 Find the product. 243 x 12

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41 Find the product. 723 x 47

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42 Find the product. 64 x 48 =

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43 Find the product. 501 x 13 =

SLIDE 15

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44 Mr. Kowolski ordered 35 boxes of granola bars. Each box contained 24 granola bars. What is the total number of granola bars Mr. Kowolski

• rdered?

From PARCC sample test

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45 The store ordered small posters and large posters to promote their opening. Twelve times as many small posters were ordered as large posters. If there were 48 large posters, how many more small posters were ordered than large posters?

Students type their answers here

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46 Thirty four people each did one hundred forty-nine sit ups. What is their combined total number of sit ups?

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

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Click to return to the table of contents

Basics of Division and Estimating Quotients

Slide 90 / 176 645 3 215 Division... the Basics!

There are three parts to a division problem. This is the Quotient... the answer to a division problem. This is the Divisor... the number you are dividing by This is the Dividend... the number to be divided.

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What does it mean if two numbers are divisible? Let's come up with a list of numbers that are divisible...

Division Slide 92 / 176

When you divide, it helps to know Rules of Divisibility. How do you know that a number is divisible by 10? How do you know that a number is divisible by 5? How do you know that a number is divisible by 2?

The number ends with zero. The number ends with zero or five. The number ends with 0,2,4,6,or 8 (even #).

click click click

Division Slide 93 / 176

Now that we've reviewed some of the simple rules, let's try a tricky one! Think about this... The following numbers are all divisible by 3:

9 183 204 1002 150 70,000,002

What do you notice about these numbers? Can you describe a rule that can be used to determine if a number is divisible by 3?

Division Slide 94 / 176

Divisible by 2 Divisible by 3 Divisible by 10

152 250 360 126 105 247 316 83 170 4623 81 54 15210

Use what you learned about the Rules of Divisibility to place each number into the Venn Diagram.

Slide 95 / 176 Estimating Quotients

When estimating quotients, it's helpful to use numbers that are divisible . Let's estimate the quotient of 46 ÷ 6. Ask yourself...how could I rewrite this problem using numbers that are divisible? Change the problem to 48 ÷ 6 . The quotient is 8! Numbers that are divisible are called Compatible Numbers because they "get along" very well!

click to reveal

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Let's rewrite each of the following problems using compatible numbers. 52 ÷ 5 31 ÷ 6 103 ÷ 4 73 ÷ 8 Consider the problem 147 ÷ 13. Do you think there is more than

• ne way to use compatible numbers to estimate the quotient? Explain

your answer. 50 ÷ 5 30 ÷ 6 100 ÷ 4 72 ÷ 8

click click

Compatible Numbers

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Now, let's try a few word problems... Molly has $21 and wants to buy a new nail polish that is $4 per

• bottle. About how many bottles can she buy?

Scott wants to save $52. If he charges $5 for each lawn he rakes, about how many lawns does he need to rake?

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48 Tickets for the rides at the boardwalk cost $3 per ride. About how many rides can you go on if you have $32 to spend on tickets?

Students type their answers here

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49 Nine friends want to share 38 slices of pizza. About how many slices will each person get?

Students type their answers here

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50 Mrs. Ruffle can make 7 fancy bows in an hour. If she needs to make 68, about how many hours will it take?

Students type their answers here

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51 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?

Students type their answers here

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52 Mr. Sugar, the pastry chef, can decorate 4 cakes in one

• hour. If 42 cakes need to be decorated, about how many

hours will it take?

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Click to return to the table of contents

Division With and Without Remainders

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Now that we've learned how to estimate quotients, it's time to f ind exact answers! When you divide, you are breaking a number apart into equal groups . The problem 15 ÷ 3 means that you are making 3 equal groups

• ut of 15 total items .

Each equal group contains 5 items, so 15 ÷ 3 = 5

Division with Remainders Slide 105 / 176

How will knowing your multiplication facts really well help you to divide numbers? Multiplying is the opposite (inverse) of dividing, so you're just multiplying backwards! Find each quotient (You may want to draw a picture and circle equal groups!) 16 ÷ 4 24 ÷ 8 30 ÷ 6 63 ÷ 9 4 3 5 7

click to reveal click click click click

Division with Remainders Slide 106 / 176

You will not be able to solve every division problem mentally. A problem like 56 ÷ 4 is more difficult to solve, but knowing your multiplication facts will help you to find this quotient, too! To make this problem easier to solve, we can use the same Area Model that we used for multiplication. How can you divide 56 into two numbers that are each divisible by 4? ( ? + ? = 56) 4 ? ? 56

Area Model Slide 107 / 176

4 40 16 56 ? ? You can break 56 into 40 + 16 and then divide each part by 4. Ask yourself... What is 40 ÷ 4? What is 16 ÷ 4? (or 4 x n = 40?) (or 4 x n = 16?) The quotient of 56 ÷ 4 is equal to the sum of the two partial quotients.

Area Model Slide 108 / 176

Let's try another example. Use the area model to find the quotient of 78 ÷ 3. How can you break up 78? Remember... you want the numbers to be divisible by 3. 3

Area Model

SLIDE 19

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53 Use the area model to find the quotient. 96 ÷ 8 =

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54 Use the area model to find the quotient. 69 ÷ 3 =

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55 Use the area model to find the quotient. 98 ÷ 7 =

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Sometimes, you'll have a problem with numbers that do not divide evenly. The leftover number is called the remainder . For example, 17 ÷ 6. This means we are making groups of 6

• ut of 17 total items. Here's how that would look...

There are not enough flowers to make another equal group of 6. Since there are 2 complete groups and 5 remaining (extra) items, we say the quotient of 17 ÷ 6 is " 2 with a remainder of 5 ". This is how we write the quotient: 17 ÷ 6 = 2 R5

Remainders Slide 113 / 176

Use basic multiplication facts to find each quotient. Be sure to include the remainder!

Ask yourself...what is the largest number that will go in evenly? (It may not go over!) How many do I have left?

24 ÷ 5 19 ÷ 3 70 ÷ 8 52 ÷ 7 5 x 4 = 20 3 x 6 = 18 8 x 8 = 64 7 x 7 = 49 4 left 1 left 6 left 3 left 24 ÷ 5 = 19 ÷ 3 = 70 ÷ 8 = 52 ÷ 7 = 4 R4 6 R1 8 R6 7 R3

clic k clic k clic k clic k

Remainders Slide 114 / 176

Here's what a problem with a remainder would look like using the Area Model.

65 ÷ 9

Think about the 9 times tables. What is the largest multiple of 9 that will go in to 65? How many extras will you have?

9 x 7 = 63 65 - 63 = 2

63 is the largest multiple of 9 that will fit into 65 and there will be 2

• extra. So, 65 ÷ 9 = 7 R2

9 65 9 65 63

2

7 2 Extra!

Area Model with Remainder

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56 Find the quotient. Be sure to include the remainder. 48 ÷ 5

Students type their answers here

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57 Find the quotient. Be sure to include the remainder. 45 ÷ 7 =

Students type their answers here

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58 Find the quotient. Be sure to include the remainder. 68 ÷ 8 =

Students type their answers here

Slide 118 / 176 Interpreting the Remainder

When solving word problems, it is important to think about what the remainder means so you can answer the question correctly! Here's an example. Kara has 38 strawberries. If she and her 3 friends share them, how many strawberries will each girl receive? 38 ÷ 4 =

Slide 119 / 176 Word Problem

Manny is packing away some baseballs. He has 41 baseballs and can fit 6 into each box. How many boxes does he need?

How does the remainder effect your answer? 41 ÷ 6

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59 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. If 26 students are going on the trip, how

many vans will they need? A 6 B 5 C 4 D 2

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60 Justine wants to share her pretzels with her friends. She has 38 pretzels to share among 5 people (including herself). How many pretzels will each person receive? A 5 B 6 C 7 D 8

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61 Ramel is cutting yarn for a project. Each piece needs to be 7 inches long and he has 50 inches of yarn. How many 7-inch pieces will he have? A 9 B 8 C 7 D 6

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62 Mr. Bullock wants new shelves in his classroom. He has 68 books and wants to put 9 on each shelf. How many shelves will he need?

Students type their answers here

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63 The Parent's Club raised money and bought 33 new balls for the classes to use at recess. If there are 8 classes, how many balls will each class get?

Students type their answers here

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64 The art teacher needs to buy new boxes to store the markers in. Each box will bold 8 markers and there are 78

• markers. How many boxes does the art teacher need to

buy?

Students type their answers here

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Whole Number Quotients and Remainders with up to Four-Digit Dividends and One-Digit Divisors

Click to return to the table of contents

SLIDE 22

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Let's try a problem with larger numbers! How about 136 ÷ 4? Even though the dividend is a three-digit number, the steps are the same! How can you break up 136? Remember... you want the numbers to be divisible by 4.

Fill in the area model below. You may break 136 up into two or more

parts. 4

Larger Number Division Slide 128 / 176

Let's look at some of your possible area models for 136 ÷ 4. You could have broken 136 up in many different ways! How could you have broken 136 into two numbers? How could you have broken 136 into three or more numbers?

Area Models Slide 129 / 176

Here's another example. Let's find the quotient of 216 ÷ 3. As we discussed before, knowing your multiplication facts will make dividing numbers much easier! Keep your basic facts in mind when breaking apart larger numbers.

Area Models Slide 130 / 176

Do you think you can try one on your own? Use the area model to find the quotient of 485 ÷ 5. Remember, there is more than one way to break up 485, so use numbers that are easy for you to divide! And, you may break 485 into as many parts as you want!

Area Models Slide 131 / 176

65 Use an area model to solve. 358 ÷ 2 =

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66 Use an area model to solve. 792 ÷ 6 =

SLIDE 23

Slide 133 / 176 The Standard Algorithm

You can also solve division problems using the standard

• algorithm. Let's go step-by-step to find the quotient of 42 ÷ 3.
• 1. Set up your problem.

42 ÷ 3

42 3

Divisor Place outside the division symbol. Dividend Place inside the division symbol.

Slide 134 / 176

42 3

• 2. Check to see if the divisor goes

into the first digit of the dividend. "Does 3 go into 4?" Yes! "How many times?" One time!

• 3. Since 3 goes into 4 one time, place a 1

in the quotient directly above the 4.

• 4. Multiply 1 x 3 and place it under the 4.
• 5. Subtract and then bring down the next

digit. 42 3 1 42 3 1

• 3

12

The Standard Algorithm Slide 135 / 176

42 3 1

• 3

12

• 6. Now divide 12 by 3.

"How many times does 3 go into 12?" 4 times!

• 7. Since 3 goes into 12 four times,

place a 4 in the quotient above the 2.

• 8. Multiply 4 by 3 and then subtract.

42 ÷ 3 = 14 42 3 1

• 3

12 4 42 3 1

• 3

12 4

• 12

The Standard Algorithm Slide 136 / 176

Let's try another example. Find the quotient of 108 ÷ 3.

• 1. Set up the problem.
• 2. Check to see if 3 goes into

the first digit of the dividend. "Does 3 go into 1?" No!

• 3. Since 3 does not go into 1, place

a zero in the quotient above the 1. 3 108 3 108

The Standard Algorithm Slide 137 / 176

• 4. Now see how many times 3 goes

into the first two digits of the dividend.

"How many times does 3 go into 10?"

• 5. Since 3 goes into 10 three times, place

a 3 in the quotient above the zero and then multiply 3 x 3.

• 6. Subtract and bring down the next digit.
• 7. Now divide 18 by 3. Since 3 goes into

18 six times, place a 6 in the quotient above the 8.

• 8. Multiply 6 x 3 and subtract. 108 ÷ 3 = 36

3 108 3 108 03 9 3 108 03

• 9

18 3 108 036

• 9

18

• 18

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Both of these examples worked out perfectly! We ended up with zero both times. Sometimes, that will not happen and you will have a remainder! Here's an example. Divide 57 by 4.

57 ÷ 4 = 14 R1

4 57 4 57 14

• 4

17

• 16

1 This is the remainder!

click

Remainders

SLIDE 24

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There are SO many steps to remember when dividing. How will I remember all of them?? Here's a quick list of steps to use when dividing:

• 1. Divide
• 2. Multiply
• 3. Subtract
• 4. Bring Down

Steps for Dividing Slide 140 / 176

Use the steps you've learned to find the quotient of 640 ÷ 5 .

• 1. Divide
• 2. Multiply
• 3. Subtract
• 4. Bring Down

128

• 5

14

• 10

40

• 40

5 640

click

Practice Slide 141 / 176

How about this one?? 216 ÷ 3 ... the steps!

• 1. Divide
• 2. Multiply
• 3. Subtract
• 4. Bring Down

Practice Slide 142 / 176

67 Find the quotient. 588 ÷ 7 =

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68 Find the quotient. 384 ÷ 4 =

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69 Find the quotient. 711 ÷ 9 =

SLIDE 25

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70 Enter your answer in the box. 522 ÷ 9 =

From PARCC sample test

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71 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. If there are 6 shelves, how many planes will go on each shelf?

Students type their answers here

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72 For field day, students will be organized into teams of 8. If there are 224 students participating in field day, how many teams can be made?

Students type their answers here

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73 A basketball team scored a total of 747 points for the

• season. This was 9 times the number of points scored in

the first game. How many points were scored suring the first game? A 73 B 75 C 82 D 83

From PARCC sample test

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

Students type their answers here

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Be sure to read this problem carefully! There's a lot of information and more than one step! Jon has $120 in the bank. He puts in another $58. He spends $45 on new sneakers and wants to spend the rest

• n t-shirts. If each t-shirt cost $9, how many can he buy?

Practice

SLIDE 26

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75 Hayley has 272 beads. She buys 38 more beads. She will use 89 beads to make bracelets and the rest to make

• necklaces. She will use 9 beads for each necklace.

What is the greatest number of necklaces Hayley can make?

Students type their answers here

From PARCC sample test

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76 Uniforms are sold in packages of 8. The store’s 119 employees will each be given 3 uniforms. How many packages will the store need to order?

Students type their answers here

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Oh no... This problem looks scary!! Don't worry about solving division problems with larger dividends. It may take a little longer, but just follow the steps! 7 3703

Practice Slide 154 / 176

Let's try another one! Find the quotient of 7430 ÷ 5.

Practice Slide 155 / 176

5 3749 Let's try one more problem. Find the quotient of 3749 ÷ 5 .

Practice Slide 156 / 176

77 Solve. 1746 ÷ 3 =

SLIDE 27

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78 Solve. 1944 ÷ 9 =

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79 Solve. 6259 ÷ 5 =

Students type their answers here

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80 The circus made $5607 from ticket sales during the first week in August. Each ticket cost $9. How many tickets were sold?

Students type their answers here

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81 The circus also made $1004 from selling balloons for $4

• each. How many balloons were sold?

Students type their answers here

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82 The circus also made $1443 from selling popcorn. If each bag of popcorn costs $3, how many bags were sold?

Students type their answers here

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83 Ms. Hershey has 1,478 M&Ms to divide among 9 students. Will each student receives the same amount? Explain.

SLIDE 28

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84 Four teachers offer an after-school chess club. The table shows the number of students who joined. Part A The teachers will divide the total group of students who joined into teams of no more than 6 students. What is the least number of teams that will include all of the students?

Grade 
 of Students Third 12 Fourth 36 Fifth 9 From PARCC sample test

Answer

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85 Part B The chess club started with 18 chess sets. The teachers

• rdered 3 cases of 15 chess sets. They will divide the

total number of chess sets so that each teacher receives an equal number. Then they will give any extra sets to the school library. What is the greatest number of chess sets each of the 4 teachers should get?

From PARCC sample test

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86 The number of science fair projects entered for each grade in a city-wide science fair is shown. Part A The science fair projects are set up on tables. There are 99 long tables used. Each long table holds 7 projects. The rest of the projects are set up on short tables. Each short table can hold 4 projects. What is the fewest number of short tables that will be needed for the rest of the projects? A 202 B 203 C 354 D 355

From PARCC sample test

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87 Part B (Continued from previous slide.) The science fair judges will be science teachers and

• volunteers. Each judge will only have time to view 5

science fair projects. There are 133 science teachers. What is the fewest number of volunteers needed to have enough judges for all of the projects? A 290 B 396 C 422 D 423

From PARCC sample test

Slide 167 / 176

88 Jian's family sells honey from beehives. They collected 3,311 ounces from the beehives this season. They will use the honey to completely fill 4-ounce jars or 6-ounce jars. Jian's family will sell 4-ounce jars for $5 each or 6-ounce jars for $8. Jian says if they use only 4-ounce jars, they could make $4,140 because 3,311 ÷ 4 = 827 R 3. That rounds up to 828, and 828 multiplied by $5 is $4,140. Part A Explain the error that Jian made when finding the amount

• f money his family could make if they use only 4-ounce
• jars. Show your explanation.

From PARCC sample test

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89 Part B (Continued from previous slide.) Explain how to determine the money Jian's family could make if they use only 6-ounce jars. Include the total amount of money and the total number of 6-ounce jars in your explanation.

From PARCC sample test

SLIDE 29

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Quotients with Zeros

Click to return to the table of contents

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Look closely at this problem. Find the quotient of 3549 ÷ 7.

7 3549 0507

• 35

04

49

• 49

You'll have to start out by placing a zero in the quotient because 7 does not go into 3. When you bring down the 4, you will need to place another zero in the quotient because 7 does not go into 4. This zero serves as a place-holder. When you bring the 9 down, you'll be able to divide and finish the problem! 3549 ÷ 7 = 507

Quotient Slide 171 / 176

90 Solve. 2721 ÷ 3 =

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91 Solve. 2832 ÷ 4 =

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

Students type their answers here

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

Students type their answers here

SLIDE 30

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94 The Tatum family has budgeted $1540 for food for five

• days. How much money can they spend on food each

day?

Students type their answers here

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95 A team runs a race. There are 4 people on the team, and each person runs the same distance. The team runs a total distance of 5,280 feet. What is the distance, in feet, that each person runs?

From PARCC sample test