Divisibility Rules Division of Decimals Glossary & Standards - - PDF document

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5th Grade

Division

2015-11-25 www.njctl.org

Slide 3 / 239 Division Unit Topics

· Patterns in Multiplication and Division · Division of Whole Numbers · Division of Decimals

Click on the topic to go to that section

· Divisibility Rules · Glossary & Standards

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Divisibility Rules

Return to Table of Contents

Slide 5 / 239 Divisible

Divisible is when one number is divided by another, and the result is an exact whole number. Example: 15 is divisible by 3 because 15 ÷ 3 = 5 exactly. three five

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BUT, 9 is not divisible by 2 because 9 ÷ 2 is 4 with one left over. two four

Divisible

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Slide 7 / 239 Divisibility

A number is divisible by another number when the remainder is 0. There are rules to tell if a number is divisible by certain other numbers.

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Look at the last digit in the Ones Place! 2 Last digit is even-0,2,4,6 or 8 5 Last digit is 5 OR 0 10 Last digit is 0 Check the Sum! 3 Sum of digits is divisible by 3 6 Number is divisible by 3 AND 2 9 Sum of digits is divisible by 9 Look at Last Digits 4 Last 2 digits form a number divisible by 4

Divisibility Rules Slide 9 / 239 Divisibility Rules

Click for Link Divisibility Rules You Tube song

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Let's Practice! Is 34 divisible by 2? Yes, because the digit in the ones place is an even number. 34 / 2 = 17 Is 1,075 divisible by 5? Yes, because the digit in the ones place is a 5. 1,075 / 5 = 215 Is 740 divisible by 10? Yes, because the digit in the ones place is a 0. 740 / 10 = 74

Divisibility Practice Slide 11 / 239

Is 258 divisible by 3? Yes, because the sum of its digits is divisible by 3. 2 + 5 + 8 = 15 Look 15 / 3 = 5 258 / 3 = 86 Is 192 divisible by 6? Yes, because the sum of its digits is divisible by 3 AND 2. 1 + 9 + 2 = 12 Look 12 /3 = 4 192 / 6 = 32

Divisibility Practice Slide 12 / 239

Is 6,237 divisible by 9? Yes, because the sum of its digits is divisible by 9. 6 + 2 + 3 + 7 = 18 Look 18 / 9 = 2 6,237 /9 = 693 Is 520 divisible by 4? Yes, because the number made by the last two digits is divisible by 4. 20 / 4 = 5 520 / 4 = 130

Divisibility Practice

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1 Is 198 divisible by 2? Yes No

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2 Is 315 divisible by 5? Yes No

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3 Is 483 divisible by 3? Yes No

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4 294 is divisible by 6. True False

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5 3,926 is divisible by 9. True False

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18 is divisible by how many digits? Let's see if your choices are correct. Did you guess 2, 3, 6 and 9? 165 is divisible by how many digits? Let's see if your choices are correct. Did you guess 3 and 5? Some numbers are divisible by more than 1 digit. Let's practice using the divisibility rules.

Click Click

6 4 9

Divisibility

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28 is divisible by how many digits? Let's see if your choices are correct. Did you guess 2 and 4? 530 is divisible by how many digits? Let's see if your choices are correct. Did you guess 2, 5, and 10? Now it's your turn...... Click Click

Divisibility Slide 20 / 239

Complete the table using the Divisibility Rules.

(Click on the cell to reveal the answer)

Divisible

by2 by 3 by 4 by 5 by 6 by 9 by 10 39 no yes no no no no no 156 yes yes yes no yes no no 429 no yes no no no no no 446 yes no no no no no no 1,218 yes yes no no yes no no 1,006 yes no no no no no no 28,550 yes no no yes no no yes

Divisibility Table Slide 21 / 239

6 What are all the digits 15 is divisible by?

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7 What are all the digits 36 is divisible by?

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8 What are all the digits 1,422 is divisible by?

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9 What are all the digits 240 is divisible by?

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10 What are all the digits 64 is divisible by?

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Patterns in Multiplication and Division

Return to Table of Contents

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A number system is a systematic way of counting numbers. For example, the Myan number system used a symbol for zero, a dot for one or twenty, and a bar for five.

Number Systems Slide 28 / 239

There are many different number systems that have been used throughout history, and are still used in different parts of the world today. Sumerian wedge = 10, line = 1 Roman Numerals

Number Systems Slide 29 / 239 Our Number System

Generally, we have 10 fingers and 10 toes. This makes it very easy to count to ten. Many historians believe that this is where

• ur number system came from. Base ten.

Slide 30 / 239 Base Ten

We have a base ten number system. This means that in a multi- digit number, a digit in one place is ten times as much as the place to its right. Also, a digit in one place is 1/10 the value of the place to its left.

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How do you think things would be different if we had six fingers on each hand?

Base 10 Slide 32 / 239

Numbers can be VERY long. Fortunately, our base ten number system has a way to make multiples of ten easier to work with. It is called Powers of 10. $100,000,000,000,000 Wouldn't you love to have

• ne hundred trillion dollars?

Powers of 10 Slide 33 / 239 Powers of 10

Numbers like 10, 100 and 1,000 are called powers of 10. They are numbers that can be written as products of tens. 100 can be written as 10 x 10 or 102. 1,000 can be written as 10 x 10 x 10 or 103.

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The raised digit is called the exponent. The exponent tells how many tens are multiplied.

103

Powers of 10 Slide 35 / 239

A number written with an exponent, like 103, is in exponential notation.

Powers of 10

A number written in a more familiar way, like 1,000 is in standard notation.

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Powers of 10 Standard Product Exponential Notation

• f 10s

Notation (greater than 1) 10 10 10

1

100 10 x 10 10

2

1,000 10 x 10 x 10 10

3

10,000 10 x 10 x 10 x 10 10

4

100,000 10 x 10 x 10 x 10 x 10 10

5

1,000,000 10 x 10 x 10 x 10 x 10 x 10 10

6

Powers of 10

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Because of this, it is easy to MULTIPLY a whole number by a power of 10. Remember, in powers of ten like 10, 100 and 1,000 the zeros are placeholders. Each place holder represents a value ten times greater than the place to its right.

Powers of 10 Slide 38 / 239

To multiply by powers of ten, keep the placeholders by adding on as many 0s as appear in the power of 10. Examples: 28 x 10 = 280 Add on one 0 to show 28 tens 28 x 100 = 2,800 Add on two 0s to show 28 hundreds 28 x 1,000 = 28,000 Add on three 0s to show 28 thousands

Multiplying Powers of 10 Slide 39 / 239

If you have memorized the basic multiplication facts, you can solve problems mentally. Use a pattern when multiplying by powers of 10. 50 x 100 = 5,000 Steps

• 1. Multiply the digits to the left of the 



 
 
 zeros in each factor. 50 x 100 5 x 1 = 5

• 2. Count the number of zeros in each

factor. 50 x 100

• 3. Write the same number of zeros in

the product. 5,000 50 x 100 = 5,000

Multiplying Powers of 10 Slide 40 / 239

60 x 400 = _______ steps

• 1. Multiply the digits to the left of the zeros in each 



 
 
 
 
 
 factor. 6 x 4 = 24

• 2. Count the number of zeros in each factor.
• 3. Write the same number of zeros in the product.

Multiplying Powers of 10 Slide 41 / 239

60 x 400 = _______ steps

• 1. Multiply the digits to the left of the zeros in each 



 
 
 
 
 
 factor. 6 x 4 = 24

• 2. Count the number of zeros in each factor.

60 x 400

• 3. Write the same number of zeros in the product.

Multiplying Powers of 10 Slide 42 / 239

60 x 400 = _______ steps

• 1. Multiply the digits to the left of the zeros in each

factor. 6 x 4 = 24

• 2. Count the number of zeros in each factor.

60 x 400

• 3. Write the same number of zeros in the product.

60 x 400 = 24,000

Multiplying Powers of 10

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500 x 70,000 = _______ steps

• 1. Multiply the digits to the left of the zeros in each

factor. 5 x 7 = 35

• 2. Count the number of zeros in each factor.
• 3. Write the same number of zeros in the product.

Multiplying Powers of 10 Slide 44 / 239

500 x 70,000 = _______ steps

• 1. Multiply the digits to the left of the zeros in each 



 
 
 
 
 
 factor. 5 x 7 = 35

• 2. Count the number of zeros in each factor.

500 x 70,000

• 3. Write the same number of zeros in the product.

Multiplying Powers of 10 Slide 45 / 239

500 x 70,000 = _______ steps

• 1. Multiply the digits to the left of the zeros in each

factor. 5 x 7 = 35

• 2. Count the number of zeros in each factor.

500 x 70,000

• 3. Write the same number of zeros in the product.

500 x 70,000 = 35,000,000

Multiplying Powers of 10 Slide 46 / 239

Your Turn.... Write a rule. Input Output 50 15,000 7 2,100 300 90,000 20 6,000 Rule multiply by 300

click

Practice Finding Rule Slide 47 / 239

Input Output 20 18,000 7 6,300 9,000 8,100,000 80 72,000 Write a rule. Rule multiply by 900

click

Practice Finding Rule Slide 48 / 239

11 30 x 10 =

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12 800 x 1,000 =

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13 900 x 10,000 =

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14 700 x 5,100 =

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15 70 x 8,000 =

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16 40 x 500 =

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17 1,200 x 3,000 =

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18 35 x 1,000 =

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Because of this, it is easy to DIVIDE a whole number by a power of 10. Take off as many 0s as appear in the power of 10. Example: 42,000 / 10 = 4,200 Take off one 0 to show that it is 1/10 of the value. 42,000 / 100 = 420 Take off two 0's to show that it is 1/100 of the value. 42,000 / 1,000 = 42 Take off three 0's to show that it is 1/1,000 of the value. Remember, a digit in one place is 1/10 the value of the place to its left.

Dividing Powers of 10 Slide 57 / 239

If you have memorized the basic division facts, you can solve problems mentally. Use a pattern when dividing by powers of 10. 60 / 10 = 60 / 10 = 6 steps

• 1. Cross out the same number of 0's in the dividend as

in the divisor.

• 2. Complete the division fact.

Dividing Powers of 10 Slide 58 / 239

700 / 10 700 / 10 = 70 8,000 / 10 8,000 / 10 = 800 9,000 / 100 9,000 / 100 = 90 More Examples:

Practice Dividing Slide 59 / 239

120 / 30 120 / 30 = 4 1,400 / 700 1,400 / 700 = 2 44,600 / 200 44,600 / 200 = 223 This pattern can be used in other problems.

Practice Dividing Slide 60 / 239

Your Turn....

• Complete. Follow the rule.

Rule: Divide by 50 Input Output 150 250

3,000

3 5 60

click click click

Practice Dividing Rule

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Find the rule. Input Output 120 40 240

8

2,700 90

• Complete. Find the rule.

click click click

Practice Dividing Rule Slide 62 / 239

19 800 / 10 =

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20 16,000 / 100 =

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21 1,640 / 10 =

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22 210 / 30 =

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23 80 / 40 =

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24 640 / 80 =

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25 4,500 / 50 =

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Remember Powers of 10 (greater than 1) Let's look at Powers of 10 (less than 1) Powers of 10 (less than 1) Standard Notation Product

• f 0.1

Exponential Notation 0.1 0.1 10-1 0.01 0.1 x 0.1 10-2 0.001 0.1 x 0.1 x 0.1 10-3 0.0001 0.1 x 0.1 x 0.1 x 0.1 10-4 0.00001 0.1 x 0.1 x 0.1 x 0.1 x 0.1 10-5 0.000001 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 10-6

Powers of 10 Slide 70 / 239

The number 1 is also called a Power of 10, because 1 = 100 10,000s 1,000s 100s 10s 1s 0.1s 0.01s 0.001s 0.0001s 10

4 10 3 10 2 10 1 10 0 . 10

• 1

10

• 2

10

• 3

10

• 4

Each exponent is 1 less than the exponent in the place to its left. This is why mathematicians defined 100 to be equal to 1. What if the exponent is zero? (100)

Powers of 10 Slide 71 / 239

Let's look at how to multiply a decimal by a Power of 10 (greater than 1) Steps

• 1. Locate the decimal point in the power
• f 10.
• 2. Move the decimal point LEFT until 



 
 
 
 
 
 
 you get to the number 1.

• 3. Move the decimal point in the other

factor the same number of places, but to the RIGHT. Insert 0's as needed. That's your answer. So, 1,000 x 45.6 = 45,000

1,000 = 1,000 .

1 0 0 0 . (3 places) 4 5 . 6 0 0 Example: 1,000 x 45.6 = ?

Multiplying Powers of 10 Slide 72 / 239

Steps

• 1. Locate the decimal point in the power
• f 10.
• 2. Move the decimal point LEFT until 



 
 
 
 
 
 
 you get to the number 1.

• 3. Move the decimal point in the other

factor the same number of places, but to the RIGHT. Insert 0's as needed. That's your answer. So, 1,000 x 45.6 = 45,000

1,000 = 1,000 .

1 0 0 0 . (3 places) 4 5 . 6 0 0 Let's look at how to multiply a decimal by a Power of 10 (greater than 1) Example: 1,000 x 45.6 = ?

Multiplying Powers of 10

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Steps

• 1. Locate the decimal point in the power
• f 10.
• 2. Move the decimal point LEFT until 



 
 
 
 
 
 you get to the number 1.

• 3. Move the decimal point in the other

factor the same number of places, but to the RIGHT. Insert 0's as needed. That's your answer. So, 1,000 x 45.6 = 45,000

1,000 = 1,000 .

1 0 0 0 . (3 places) 4 5 . 6 0 0 Let's look at how to multiply a decimal by a Power of 10 (greater than 1) Example: 1,000 x 45.6 = ?

Multiplying Powers of 10 Slide 74 / 239

Let's try some together. 10,000 x 0.28 = $4.50 x 1,000 = 1.04 x 10 =

Practice Multiplying Slide 75 / 239

26 100 x 3.67 =

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27 0.28 x 10,000 =

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28 1,000 x $8.98 =

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29 7.08 x 10 =

SLIDE 14

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Steps

• 1. Locate the decimal point in the 



 
 
 
 
 
 power of 10.

• 2. Move the decimal point LEFT until

you get to the number 1.

• 3. Move the decimal point in the other

number the same number of places to the LEFT. Insert 0's as needed. So, 45.6 / 1,000 = 0.0456 Let's look at how to divide a decimal by a Power of 10 (less than 1) Example: 45.6 / 1,000 1,000 = 1,000 . 1 0 0 0 . (3 places)

0 0 4 5 . 6

Dividing Powers of 10 Slide 80 / 239

Steps

• 1. Locate the decimal point in the 



 
 
 
 
 
 
 power of 10.

• 2. Move the decimal point LEFT until

you get to the number 1.

• 3. Move the decimal point in the other

number the same number of places to the LEFT. Insert 0's as needed. So, 45.6 / 1,000 = 0.0456 Let's look at how to divide a decimal by a Power of 10 (less than 1) Example: 45.6 / 1,000 1,000 = 1,000 . 1 0 0 0 . (3 places)

0 0 4 5 . 6

Dividing Powers of 10 Slide 81 / 239

Steps

• 1. Locate the decimal point in the 



 
 
 
 
 
 
 
 power of 10.

• 2. Move the decimal point LEFT until

you get to the number 1.

• 3. Move the decimal point in the other

number the same number of places to the LEFT. Insert 0's as needed. So, 45.6 / 1,000 = 0.0456 Let's look at how to divide a decimal by a Power of 10 (less than 1) Example: 45.6 / 1,000 1,000 = 1,000 . 1 0 0 0 . (3 places)

0 0 4 5 . 6

Dividing Powers of 10 Slide 82 / 239

Let's try some together. 56.7 / 10 = 0.47 / 100 = $290 / 1,000 =

Practice Dividing Slide 83 / 239

30 73.8 / 10 =

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31 0.35 / 100 =

SLIDE 15

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32 $456 / 1,000 =

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33 60 / 10,000 =

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34 $89 / 10 =

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35 321.9 / 100 =

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Division of Whole Numbers

Return to Table of Contents

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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

Review from 4th Grade

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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

Review from 4th Grade Slide 92 / 239

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

Review from 4th Grade Slide 93 / 239

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.

Review from 4th Grade Slide 94 / 239

Let's try another example. Use the area model to find the quotient of 135 ÷ 5. How can you break up 135? Remember... you want the numbers to be divisible by 5. 5 100 35

Area Model Division Slide 95 / 239

? ?

You can break 135 into 90 + 45 and then divide each part by 15. Ask yourself... What is 90 ÷ 15? What is 45 ÷ 15? (or 15 x n = 90?) (or 15 x n = 45?) The quotient of 135 ÷ 15 is equal to the sum of the two partial quotients. Let's try another example. Use the area model to find the quotient of 135 ÷ 15. 135 15

Area Model Division Slide 96 / 239

What about remainders? Use the area model to find the quotient. 963 ÷ 20 =

? ?

963 20

R.

Area Model Division

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36 Use the area model to find the quotient. 645 ÷ 15 =

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37 Use the area model to find the quotient. Write any reminder as a fraction. 695 ÷ 30=

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38 Use the area model to find the quotient. Write any reminder as a fraction. 385 ÷ 75 =

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39 A teacher drew an area model to find the value of 6,986 ÷ 8. · Determine the number that each letter in the model represents and explain each of your answers. · Write the quotient and remainder for · Explain how to use multiplication to check that the quotient is correct. You may show your work in your explanation.

From PARCC PBA sample test #15

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Some division terms to remember.... · The number to be divided into is known as the dividend. · The number which divides the dividend 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

Division Key Terms Slide 102 / 239

Estimating the quotient helps to break whole numbers into groups.

Estimating

SLIDE 18

Slide 103 / 239 Estimating: One-Digit Divisor

689 8) Divide 8) 68 8)689 8 8)689 80 Write 0 in remaining place. 80 is the estimate.

Slide 104 / 239 One-Digit Estimation Practice

Estimate: 9)507 Remember to divide 50 by 9 Then write 0 in remaining place in quotient. Is your estimate 50 or 40? Yes, it is 40.

Click

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Estimate : 5)451 Remember to divide 45 by 5 Then write 0 in remaining place in quotient. Is your estimate 90 or 80? Yes, it is 90

Click

One-Digit Estimation Practice Slide 106 / 239

40 The estimation for 8)241 is 40? True False

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41 Estimate 663 ÷ 7.

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42 Estimate 4)345 .

SLIDE 19

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43 Solve using Estimation. Marta baby-sat fo r four hours and earned $19. ABOUT how much money # # # # # # # # # # # # # # # # # did Marta earn each hour that she baby-sat?

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26)6,498 Round 26 to its greatest place. 30)6,498 Divide 30)64 . 30) 6,498 2 30)6,498 200 Write 0 in remaining places. 200 is the estimate.

Estimating: Two-Digit Divisor Slide 111 / 239 Two-Digit Estimation Practice

Estimate: 31)637 Remember to round 31 to its greatest place 30, then divided 63 by 30. Finally, write 0's in remaining places in quotient. Is your estimate 20 or 30? Yes, it is 20.

click to reveal

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Estimate: 87)9,321 Remember to round 87 to its greatest place 90, then divide 93 by 90 Finally, write 0's in remaining places in quotient. Is your estimate 100 or 1,000? Yes, it is 100.

click to reveal

Two-Digit Estimation Practice Slide 113 / 239

44 The estimation for 17)489 is 2? True False

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45 Estimate 5,145 ÷ 25.

SLIDE 20

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46 Estimate 41) 2,130 .

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47 Estimate 31)7,264 .

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48 Solve using Estimation. Brandon bought cookies to pack in his

• lunch. He bought a box with 28 cookies. If

he packs five cookies in his lunch each day , ABOUT how many days will the days will the cookies last?

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When we are dividing, we are breaking apart into equal groups. Find 132 3 Step 1 : Can 3 go into 1, no so can 3 go into 13, yes 4

• 12

1 3 x 4 = 12 13 - 12 = 1 Compare 1 < 3 3 132 3 x 4 = 12 12 - 12 = 0 Compare 0 < 3

• 12

2 Step 2 : Bring down the 2. Can 3 go into 12, yes 4

Click for step 1

Click for step 2

Division Slide 119 / 239

Step 3: Check your answer. 44 x 3 132

Division Slide 120 / 239

49 Divide and Check 8)296 .

SLIDE 21

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50 Divide and Check 9)315

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51 Divide and Check 252 ÷ 6.

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52 Divide and Check 9470 ÷ 2.

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53 Adam has a wire that is 434 inches long. He cuts the wire into 7-inch lengths. How many pieces of wire will he have?

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54 Bill and 8 friends each sold the same number of tickets. They sold 117 tickets in all. How many tickets were sold by each person?

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55 There are 6 outs in an inning. How many innings would have to be played to get 348 outs?

SLIDE 22

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56 How many numbers between 23 and 41 have NO remainder when divided by 3? A 4 B 5 C 6 D 11

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Sometimes, when we split a whole number into equal groups, there will be an amount left over. The left over number is called the remainder. John and Lad are splitting the $9 that John has in his wallet. Move the money to give John half and Lad half.

Click when finished.

Division Problem Slide 129 / 239

For example: 4 7)30

• 28

2 We say there are 2 left over, because you can not make a group of 7 out of 2. Lets look at remainders with long division.

Long Division Slide 130 / 239

For example: 4 7)30 30÷ 7 = 4 R 2

• 28

2 This is the way you may have seen it. The R stands for remainder.

Long Division Slide 131 / 239

Another example: 23 15)358

• 30

58

• 45

13 We say there are 13 left over (R) because you can not make a group of 15 out of 13. 358 ÷ 15 = 23 R 13

Long Division Slide 132 / 239

57 A group of six friends have 83 pretzels. If they want to share them evenly, how many will be left over?

SLIDE 23

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58 Four teachers want to evenly share 245

• pencils. How many will be left over?

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59 Twenty students want to share 48 slices of pizza. How many slices will be left over, if each person gets the same number

• f slices?

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60 Suppose there are 890 packages being delivered by 6 planes. Each plane is to take the same number of packages and as many as possible. How many packages will each plane take? How many will be left over? Fill in the

• blanks. Each plane will take _______
• packages. There will be _______

packages left over. A 149 packages, 2 left over B 148 packages, 2 left over

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4 7)30

• 28

2 2 7 Instead of writing an R for remainder, we will write it as a fraction of the 30 that will not fit into a group of 7. So 2/7 is the remainder.

Long Division Slide 137 / 239

More examples of the remainder written as a fraction: 6)47

• 42

5 7

• The Remainder means that there

is 5 left over that can't be put in a group containing 6 To Check the answer, use multiplication and addition. 7 x 6 + 5 = 42 + 5 = 47 5 6 Multiply the quotient and the divisor. Then, add the remainder. The result should be the dividend.

Long Division Examples Slide 138 / 239

37 x 7 + 5 = 259 + 5 = 264 Example: 37 7)264

• 21

54

• 49

5 Check the answer using multiplication and addition.Way 1: Way 2: 37 quotient x 7 x divisor 259 + 5 + remainder 264 dividend 5 7

Long Division Example

SLIDE 24

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61 Divide and Check 4)43 (Put answer in as a mixed number.)

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62 Divide and Check 61 ÷ 3 = (Put answer in as a mixed number.)

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63 Divide and Check 145 ÷ 7 (Put answer in as a mixed number.)

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64 Divide and Check 2)811 (Put answer in as a mixed number.)

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65 Divide and Check 309 ÷ 2 = (Put answer in as a mixed number.)

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You can divide by two-digit divisors to find out how many groups there are or how many are in each group. When dividing by a two-digit divisor, follow the steps you used to divide by a one-digit divisor. Repeat until you have divided all the digits of the dividend by the divisor. STEPS Divide Multiply Subtract Compare Bring down next number

Long Division with 2-digit Divisor

SLIDE 25

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Find 4575 25 Step 1 : Can 25 go into 4, no so can 25 go into 45, yes 1

• 25

20 25 x 1 = 25 45 - 25 = 20 Compare 20 < 25 25 4575 25 x 8 = 200 207 - 200 = 7 Compare 7 < 25 7

• 200

7 5

• 75

Step 2 : Bring down the 7. Can 25 go into 207, yes 8

Click for step 1

Step 3 : Bring down the 5. Can 25 go into 75, yes 25 x 3 = 75 75 - 75 = 0 Compare 0 < 25 3

Click for step 2 Click for step 3

Long Division Practice Slide 146 / 239

Step 3: Check your answer. 183 x 25

Long Division Practice Slide 147 / 239

• Mr. Taylor's students take turns working

shifts at the school store. If there are 23 students in his class and they work 253 shifts during the year, how many shifts will each student in the class work?

Long Division Example Slide 148 / 239

1

Step 1 Compare the divisor to the dividend to decide where to place the first digit in the quotient. Divide the tens. Think: What number multiplies by 23 is less than or equal to 25. Step 2 Multiply the number of tens in the quotient times the divisor. Subtract the product from the dividend. Bring down the next number in the dividend. Step 3 Divide the result by 23. Write the number in the ones place of the quotient. Think: What number multiplied by 23 is less than or equal to 23? Step 4 Multiply the number in the ones place of the quotient by the divisor. Subtract the product from 23. If the difference is zero, there is no remainder.

23) 253 1

• 23

23

• 23

Each student will work 11 shifts at the school store.

23)253

Long Division Example Slide 149 / 239

Division Steps can be remembered using a "Silly" Sentence. David Makes Snake Cookies By Dinner. Divide Multiply Subtract Compare Bring Down What is your "Silly" Sentence to remember the Division Steps?

Long Division Slide 150 / 239

Find 374 ÷ 22 Step 1 22) 374

Think 20) 374

1

Step 2 22) 374

1

• 22

1 x 22

Step 3 22) 374

• 22

15 15 less than 22

1

Step 4 22) 374

• 22

154

1

bring down Step 5 22) 374

• 22

154

• 154

17

repeat Final Step 17 x 22 34 340 374

+

divide multiply

subtract

compare

bring down

repeat

Check Click boxes to show work

Silly Steps Example

SLIDE 26

Slide 151 / 239

66 A candy factory produces 984 pounds of chocolate in 24 hours. How many pounds

• f chocolate does the factory produce in

1 hour? A 38 B 40 C 41 D 45

Slide 152 / 239

67 Teresa got a loan of $7,680 for a used

• car. She has to make 24 equal payments.

How much will each payment be? A $230 B $320 C $325

Slide 153 / 239

68 Solve 16)176

Slide 154 / 239

69 Solve 329 ÷ 47

Slide 155 / 239

70 If 280 chairs are arranged into 35 rows, how many chairs are in each row?

Slide 156 / 239

71 There are 52 snakes. There are 13 cages. If each cage contains the same number

• f snakes, how many snakes are in each

cage?

SLIDE 27

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72 Solve 46)3,588

Slide 158 / 239

73 Solve 3,672 ÷ 72

Slide 159 / 239

74 Enter your answer. 1,534 ÷ 26 =

From PARCC EOY sample test #27

Slide 160 / 239 Slide 161 / 239

Let's Practice

Divide, Multiply, Subtract, Compare, Bring Down, Write the Remainder as a Fraction, Check your work

36) 633 36

• 273

252

• 17

21 36

21

17 36

x 102 510 + 612 +

21

633

Remember your Steps: Solve 633 36 CHECK

Divisor x Quotient + Remainder = Dividend

Slide 162 / 239

75 What is the remainder when 402 is divided by 56? A 8 B 7 C 19 D 10

SLIDE 28

Slide 163 / 239

76 What is the remainder when 993 is divided by 38? A 5 B 8 C 13 D 26

Slide 164 / 239

77 Divide 80) 104 (Put answer in as a mixed number.)

Slide 165 / 239

78 Divide 556 ÷ 35 (Put answer in as a mixed number.)

Slide 166 / 239

79 Divide 45) 1442 (Put answer in as a mixed number.)

Slide 167 / 239

80 Divide 4453 ÷ 55 (Put answer in as a mixed number.)

Slide 168 / 239

81 Divide 83) 8537 (Put answer in as a mixed number.)

SLIDE 29

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In word problems, we need to interpret the what the remainder means. For example: Celina has 58 pencils and wants to share them with 5 people. 11 5) 58

• 5

08

• 5

3 5 people will each get 11 pencils, and there will be 3 left over.

Interpreting the Remainder Slide 170 / 239

What does the remainder below mean? Violet is packing books. She has 246 books and, 24 fit in a box. How many boxes does she need? 10 24) 246

• 24

06 The remainder means she would have 6 books that would not fit in the 10 boxes. She would need 11 boxes to fit all the books.

Interpreting the Remainder Slide 171 / 239 Slide 172 / 239 Slide 173 / 239

84 Apples cost $4 for a 5 pound bag. If you have $19, how many bags can you buy? A 2 B 3 C 4 19 4 = 4 R 3 D 5

Slide 174 / 239

SLIDE 30

Slide 175 / 239 Slide 176 / 239

87 Greg is volunteering at a track meet. He is in charge of providing the bottled water. Greg knows these facts. · The track meet will last 3 days. · There will be 117 athletes, 7 coaches, and 4 judges attending the track meet. · Once case of bottled water contains 24 bottles. The table shows the number of bottles of water each athlete coach, and judge will get for each day of the track meet. What is the fewest number of cases of bottled water Greg will need to provide for all the athletes, coaches, and judges at the track meet. Show your work or explain how you found your answer using equations.

From PARCC PBA sample test #16

Slide 177 / 239

Division of Decimals

Return to Table of Contents

Slide 178 / 239 Dividing Decimals

To divide a decimal by a whole number: Use long division. Bring the decimal point up in the answer.

63.93

21 31 3 Slide 179 / 239

8.12 4 2.03 0.812 4 81.2 4 0.0812 4 20.3 0.203 0.0203

Match the quotient to the correct problem.

Decimal Division Examples Slide 180 / 239

88 Which answer has the decimal point in the correct location? A 1285 B 1.285 C 12.85

64.25 5

D 128.5

SLIDE 31

Slide 181 / 239

89 Which answer has the decimal point in the correct location? A 561 B 56.1 C 5.61

224.4

4

D 0.561

Slide 182 / 239

90 Which answer has the decimal point in the correct location? A 51 B 5.1 C 0.51

0.459

9

D 0.051

Slide 183 / 239

91 Select the answer with the decimal point in the correct location. A 0.1234 B 1.234 C 12.34 D 123.4

37.02 3

E 1234

Slide 184 / 239

92 Select the answer with the decimal point in the correct location. A 501 B 50.1 C 5.01 D 0.501

.2505 5

E 0.0501

Slide 185 / 239

93 20.52 6

Slide 186 / 239

94 321.6 4

SLIDE 32

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95 2.198 7

Slide 188 / 239

96 70.62 11

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97 251.2 4

Slide 190 / 239

Be careful, sometimes a zero needs to be used as a place holder.

35.56

• 35

0 56

• 56

7 5.08

7 can not go into 5. So, put a 0 in the quotient, and bring the 6 down.

Zero Place Holder Slide 191 / 239

98 What is the next step in this division problem? A Put a 2 in the quotient. B Put a 0 in the quotient.

27.21

• 27

0 2 3 9.

C Put a 1 in the quotient.

Slide 192 / 239

99 What is the next step in this division problem? A Put a 0 in the quotient. B Put a 2 in the quotient.

3.205

• 30

2 5 0.6

C Bring down the 0.

SLIDE 33

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100 What is the next step in this division problem? A Put a 0 in the quotient. B Put a 4 in the quotient.

64.48

• 64

0 4 8 8.

C Put a 2 in the quotient.

Slide 194 / 239

101 0.636 6

Slide 195 / 239

102 2.406 3

Slide 196 / 239

Be careful! Sometimes there is not enough to make a group, so put a zero in the quotient.

0.608

• 56

48

• 48

8 .076

Zero Place Holder Slide 197 / 239

103 What is the first step in this division problem? A Put a 0 in the ones place of the quotient. B Put a 0 in the tenths place of the quotient.

.468 6

C Put a 7 in the quotient.

Slide 198 / 239

104 What is the first step in this division problem? A Put a 0 in the quotient in the tenths and hundredths place. B Put a 0 in the quotient in the ones place.

.1104 24

C Put a 4 in the quotient.

SLIDE 34

Slide 199 / 239

105 .435 5

Slide 200 / 239

Instead of writing a remainder, continue to divide the remainder by the divisor (by adding zeros) to get additional decimal points.

75.6

• 72

3 6

• 32

4

8 9.4

Instead of leaving the 4 as a remainder, add a zero to the dividend.

Another Way to Handle Remainders Slide 201 / 239

75.60

• 72

3 6

• 3 2

40

• 40

8 9.45

Add a zero to the dividend. No remainder now.

Another Way to Handle Remainders Slide 202 / 239

106 3.26 5

Slide 203 / 239

107 87.3 2

Slide 204 / 239

108 0.795 6

SLIDE 35

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109 0.843 30

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110 0.363 15

Slide 207 / 239

When you have a remainder, you can add a decimal point and zeros to the end of a whole number dividend. Example: You want to save $284 over the next 5 months. How much money do you need to save each month? $284 ÷ 5 = _____

Decimal Division Example Slide 208 / 239

$284

• 25

34

• 30

4 5 56

Don't leave the remainder 4, or write it as a fraction, add a decimal point and zeros to get the cents.

Decimal Division Example Slide 209 / 239

$284.0

• 25

34

• 30

4 0

• 4 0

5 56.8

Since the answer is in money, write the answer as $56.80.

Decimal Division Example Slide 210 / 239

$82.000

• 7

12

• 7

50

• 49

10

• 7

30

• 28

2 7 11.714

Since the answer is in money, add a decimal point and 3 zeros. Round the answer to the nearest cent (hundredths place). $82 ÷ 7 = $11.71

Decimal Division Example

SLIDE 36

Slide 211 / 239

111 5 $63

Slide 212 / 239

112 $782 ÷ 9 =

Slide 213 / 239

113 7 $593

Slide 214 / 239

114 4 $352

Slide 215 / 239

115 $48 ÷ 22 =

Slide 216 / 239

To divide a number by a decimal: · Change the divisor to a whole number by multiplying by a power of 10 · Multiply the dividend by the same power of 10 · Divide · Bring the decimal point up in the answer Dividend Divisor

Divisor as a Decimal

SLIDE 37

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2.4 15.696 Multiply by 10, so that 2.4 becomes 24. 15.696 must also be multiplied by 10. 24 156.96 .64 6.4 Multiply by 100, so that .64 becomes 64. 6.4 must also be multiplied by 100. 64 640

Divisor as Decimal Examples: Slide 218 / 239

By what power of 10 should the divisor and dividend be multiplied? .007 0.3 4.9 42.69

Divisor as Decimal Practice Slide 219 / 239

By what power of 10 should the divisor and dividend be multiplied? 7.59 ÷ 2.2 means 2.0826 ÷ 0.06 means

Divisor as Decimal Examples Slide 220 / 239

116 0.3 42.48

Slide 221 / 239

117 Divide 2.592 ÷ 0.08 =

Slide 222 / 239

118 Enter your answer. 6.3 ÷ 0.1 =

From PARCC EOY sample test #19

SLIDE 38

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119 Enter your answer 6.3 x 0.1 =

From PARCC EOY sample test #19

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120 0.3 0.6876

Slide 225 / 239

121 20 divided by 0.25

Slide 226 / 239

122 Yogurt costs $.50 each, and you have $7.25. How many can you buy?

Slide 227 / 239

Glossary & Standards

Return to Table of Contents

Slide 228 / 239

Standards for Mathematical Practices MP8 Look for and express regularity in repeated reasoning. MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure.

Click on each standard to bring you to an example of how to meet this standard within the unit.

SLIDE 39

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Back to Instruction

Base Ten

In a multi digit number, a digit in one place is ten times as much as the place to its right and 1/10 the value of the place to its left. Slide 230 / 239

Dividend

24 ÷ 8 = 3

24 8 3 24 8 = 3

Dividend Dividend Dividend

The number being divided in a division equation.

Back to Instruction

Slide 231 / 239

Back to Instruction

2 5

11 ÷ 2 = 5 R.1

Divisible

When one number is divided by another, and the result is an exact whole number.

15 is divisible by 3 because 15 ÷ 3 = 5 exactly.

3 5

Slide 232 / 239

Divisor

24 ÷ 8 = 3

24 8 3

25 8 = 3 R1

Divisor Divisor

The number the dividend is divided by. A number that divides another number without a remainder.

Must divide evenly.

Back to Instruction

Slide 233 / 239

Exponent

A small, raised number that shows how many times the base is used as a factor.

3

2

Base

Exponent

3

2= x

3 3

3 = x x 3 3 3

3

3

2 x

2 3 3

3 x

3 3

"3 to the second power"

Back to Instruction

Slide 234 / 239

Back to Instruction

Exponential Notation

A number written using a base and an exponent.

1,000

Standard Word

One Thousand

Exponential

103

SLIDE 40

Slide 235 / 239

Back to Instruction

Number System

A systematic way of counting numbers, where symbols/digits and their order represent amounts.

Base Ten Roman Numerals Others

Slide 236 / 239

Back to Instruction

101 10

=

Power of 10

Any integer powers of the number ten. (Ten is the base, the exponent is the power).

10

2 100

=

10

3 1,000

=

10x10 = 10 = 10x10x10 = Slide 237 / 239

Back to Instruction

Quotient

The number that is the result of dividing one number by another.

12 ÷ 3 4 =

Quotient

12 4 3

Quotient

12

4

3 =

Quotient

Slide 238 / 239

Back to Instruction

Remainder

When a number is divided, the remainder is anything that is left over. (Anything in addition to the whole number.)

2 5

11 ÷ 2 = 5 R.1

3 5

No remainder

11 5 R.1

2

Remainder

Slide 239 / 239

Back to Instruction

Standard Notation

A general term meaning "the way most commonly written". A number written using

• nly digits, commas and a decimal point.

3.5

Standard Word

Three and five tenths

Expanded

3 + 0.5