Divisibility Rules Return to Table of Contents Slide 5 / 239 - - PDF document
Slide 1 / 239 Slide 2 / 239 5th Grade Division 2015-11-25 www.njctl.org Slide 3 / 239 Division Unit Topics Click on the topic to go to that section Divisibility Rules Patterns in Multiplication and Division Division of Whole
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Division
2015-11-25 www.njctl.org
Slide 2 / 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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Return to Table of Contents
Slide 4 / 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 Slide 6 / 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 8 / 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 10 / 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 11 / 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 Slide 12 / 239
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
Divisibility Slide 18 / 239
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 19 / 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 20 / 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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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 27 / 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 28 / 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
Slide 29 / 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 31 / 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
Powers of 10 Slide 32 / 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.
Powers of 10 Slide 34 / 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
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 Slide 36 / 239
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 37 / 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 38 / 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
zeros in each factor. 50 x 100 5 x 1 = 5
factor. 50 x 100
the product. 5,000 50 x 100 = 5,000
Multiplying Powers of 10 Slide 39 / 239
60 x 400 = _______ steps
factor. 6 x 4 = 24
Multiplying Powers of 10 Slide 40 / 239
60 x 400 = _______ steps
factor. 6 x 4 = 24
60 x 400
Multiplying Powers of 10 Slide 41 / 239
60 x 400 = _______ steps
factor. 6 x 4 = 24
60 x 400
60 x 400 = 24,000
Multiplying Powers of 10 Slide 42 / 239
500 x 70,000 = _______ steps
factor. 5 x 7 = 35
Multiplying Powers of 10 Slide 43 / 239
500 x 70,000 = _______ steps
factor. 5 x 7 = 35
500 x 70,000
Multiplying Powers of 10 Slide 44 / 239
500 x 70,000 = _______ steps
factor. 5 x 7 = 35
500 x 70,000
500 x 70,000 = 35,000,000
Multiplying Powers of 10 Slide 45 / 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 46 / 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 47 / 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 56 / 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
in the divisor.
Dividing Powers of 10 Slide 57 / 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 58 / 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 59 / 239
Your Turn....
Rule: Divide by 50 Input Output 150 250
3,000
click click click
Practice Dividing Rule Slide 60 / 239
click click click
Practice Dividing Rule Slide 61 / 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
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 69 / 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
10
10
10
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 70 / 239
Let's look at how to multiply a decimal by a Power of 10 (greater than 1) Steps
you get to the number 1.
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 71 / 239
Steps
you get to the number 1.
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 72 / 239
Steps
you get to the number 1.
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 73 / 239
Let's try some together. 10,000 x 0.28 = $4.50 x 1,000 = 1.04 x 10 =
Practice Multiplying Slide 74 / 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 =
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Steps
power of 10.
you get to the number 1.
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 79 / 239
Steps
power of 10.
you get to the number 1.
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
power of 10.
you get to the number 1.
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
Let's try some together. 56.7 / 10 = 0.47 / 100 = $290 / 1,000 =
Practice Dividing Slide 82 / 239
30 73.8 / 10 =
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31 0.35 / 100 =
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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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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
Each equal group contains 5 items, so 15 ÷ 3 = 5
Review from 4th Grade Slide 90 / 239
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 91 / 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 92 / 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 93 / 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 94 / 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 95 / 239
What about remainders? Use the area model to find the quotient. 963 ÷ 20 =
? ?
963 20
R.
Area Model Division Slide 96 / 239
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 101 / 239
Estimating the quotient helps to break whole numbers into groups.
Estimating Slide 102 / 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 103 / 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 105 / 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 .
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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 110 / 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 112 / 239
44 The estimation for 17)489 is 2? True False
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45 Estimate 5,145 ÷ 25.
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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
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
1 3 x 4 = 12 13 - 12 = 1 Compare 1 < 3 3 132 3 x 4 = 12 12 - 12 = 0 Compare 0 < 3
2 Step 2 : Bring down the 2. Can 3 go into 12, yes 4
Click for step 1
Click for step 2
Division Slide 118 / 239
Step 3: Check your answer. 44 x 3 132
Division Slide 119 / 239
49 Divide and Check 8)296 .
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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?
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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 128 / 239
For example: 4 7)30
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 129 / 239
For example: 4 7)30 30÷ 7 = 4 R 2
2 This is the way you may have seen it. The R stands for remainder.
Long Division Slide 130 / 239
Another example: 23 15)358
58
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 131 / 239
57 A group of six friends have 83 pretzels. If they want to share them evenly, how many will be left over?
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58 Four teachers want to evenly share 245
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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
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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
packages left over. A 149 packages, 2 left over B 148 packages, 2 left over
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4 7)30
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 136 / 239
More examples of the remainder written as a fraction: 6)47
5 7
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 137 / 239
37 x 7 + 5 = 259 + 5 = 264 Example: 37 7)264
54
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 138 / 239
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 144 / 239
Find 4575 25 Step 1 : Can 25 go into 4, no so can 25 go into 45, yes 1
20 25 x 1 = 25 45 - 25 = 20 Compare 20 < 25 25 4575 25 x 8 = 200 207 - 200 = 7 Compare 7 < 25 7
7 5
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 145 / 239
Step 3: Check your answer. 183 x 25
Long Division Practice Slide 146 / 239
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 147 / 239
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.
Each student will work 11 shifts at the school store.
23)253
Long Division Example Slide 148 / 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 149 / 239
Find 374 ÷ 22 Step 1 22) 374
Think 20) 374
1
Step 2 22) 374
1
1 x 22
Step 3 22) 374
15 15 less than 22
1
Step 4 22) 374
154
1
bring down Step 5 22) 374
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 150 / 239
66 A candy factory produces 984 pounds of chocolate in 24 hours. How many pounds
1 hour? A 38 B 40 C 41 D 45
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67 Teresa got a loan of $7,680 for a used
How much will each payment be? A $230 B $320 C $325
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68 Solve 16)176
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69 Solve 329 ÷ 47
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70 If 280 chairs are arranged into 35 rows, how many chairs are in each row?
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71 There are 52 snakes. There are 13 cages. If each cage contains the same number
cage?
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72 Solve 46)3,588
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73 Solve 3,672 ÷ 72
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74 Enter your answer. 1,534 ÷ 26 =
From PARCC EOY sample test #27
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Let's Practice
Divide, Multiply, Subtract, Compare, Bring Down, Write the Remainder as a Fraction, Check your work
36) 633 36
252
21 36
21
17 36
x 102 510 + 612 +
21
633
Remember your Steps: Solve 633 36 CHECK
Divisor x Quotient + Remainder = Dividend
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75 What is the remainder when 402 is divided by 56? A 8 B 7 C 19 D 10
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76 What is the remainder when 993 is divided by 38? A 5 B 8 C 13 D 26
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77 Divide 80) 104 (Put answer in as a mixed number.)
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78 Divide 556 ÷ 35 (Put answer in as a mixed number.)
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79 Divide 45) 1442 (Put answer in as a mixed number.)
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80 Divide 4453 ÷ 55 (Put answer in as a mixed number.)
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81 Divide 83) 8537 (Put answer in as a mixed number.)
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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
08
3 5 people will each get 11 pencils, and there will be 3 left over.
Interpreting the Remainder Slide 169 / 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
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 170 / 239 Slide 171 / 239
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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
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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
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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 178 / 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 179 / 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
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89 Which answer has the decimal point in the correct location? A 561 B 56.1 C 5.61
224.4
D 0.561
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90 Which answer has the decimal point in the correct location? A 51 B 5.1 C 0.51
0.459
D 0.051
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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
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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
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93 20.52 6
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94 321.6 4
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95 2.198 7
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96 70.62 11
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97 251.2 4
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Be careful, sometimes a zero needs to be used as a place holder.
35.56
0 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 190 / 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
0 2 3 9.
C Put a 1 in the quotient.
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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
2 5 0.6
C Bring down the 0.
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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
0 4 8 8.
C Put a 2 in the quotient.
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101 0.636 6
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102 2.406 3
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Be careful! Sometimes there is not enough to make a group, so put a zero in the quotient.
0.608
48
8 .076
Zero Place Holder Slide 196 / 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.
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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.
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105 .435 5
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Instead of writing a remainder, continue to divide the remainder by the divisor (by adding zeros) to get additional decimal points.
75.6
3 6
4
8 9.4
Instead of leaving the 4 as a remainder, add a zero to the dividend.
Another Way to Handle Remainders Slide 200 / 239
75.60
3 6
40
8 9.45
Add a zero to the dividend. No remainder now.
Another Way to Handle Remainders Slide 201 / 239
106 3.26 5
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107 87.3 2
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108 0.795 6
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109 0.843 30
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110 0.363 15
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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 207 / 239
$284
34
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 208 / 239
$284.0
34
4 0
5 56.8
Since the answer is in money, write the answer as $56.80.
Decimal Division Example Slide 209 / 239
$82.000
12
50
10
30
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 210 / 239
111 5 $63
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112 $782 ÷ 9 =
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113 7 $593
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114 4 $352
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115 $48 ÷ 22 =
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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 216 / 239
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 217 / 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 218 / 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 219 / 239
116 0.3 42.48
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117 Divide 2.592 ÷ 0.08 =
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118 Enter your answer. 6.3 ÷ 0.1 =
From PARCC EOY sample test #19
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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
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121 20 divided by 0.25
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122 Yogurt costs $.50 each, and you have $7.25. How many can you buy?
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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.
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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 229 / 239
24 ÷ 8 = 3
24 8 3 24 8 = 3
Dividend Dividend Dividend
The number being divided in a division equation.
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2 5
11 ÷ 2 = 5 R.1
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
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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.
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A small, raised number that shows how many times the base is used as a factor.
2
Base
Exponent
2= x
3
2 x
3 x
"3 to the second power"
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A number written using a base and an exponent.
Standard Word
One Thousand
Exponential
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A systematic way of counting numbers, where symbols/digits and their order represent amounts.
Base Ten Roman Numerals Others
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=
Any integer powers of the number ten. (Ten is the base, the exponent is the power).
2 100
=
3 1,000
=
10x10 = 10 = 10x10x10 = Slide 236 / 239
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The number that is the result of dividing one number by another.
Quotient
Quotient
Quotient
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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
Remainder
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A general term meaning "the way most commonly written". A number written using
Standard Word
Three and five tenths
Expanded
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