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1
5th Grade Division
2015­11­25
www.njctl.org
2
Division Unit Topics
Click on the topic to go to that section
• Divisibility Rules
• Division of Whole Numbers
• Division of Decimals
• Glossary & Standards
Teacher Notes
• Patterns in Multiplication and Division
Vocabu
in the p
box the
linked t
of the p
word de
3
Divisibility Rules
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Table of
Contents
4
Divisible Divisible is when one number is divided by another, and the result is an exact whole number.
five
Example: 15 is divisible by 3 three
because 15 ÷ 3 = 5 exactly.
5
Divisible
two
four
BUT, 9 is not divisible by 2 because 9 ÷ 2 is 4 with one left over.
6
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. 7
Divisibility Rules
Look at the last digit in the Ones Place!
2 Last digit is even­0,2,4,6 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
8
Divisibility Rules
Click for Link
Divisibility Rules
You Tube song
9
Divisibility Practice
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
10
Divisibility Practice
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
11
Divisibility Practice 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
12
Is 198 divisible by 2?
Yes
No
Answer
1
13
Is 315 divisible by 5?
Yes
No
Answer
2
14
Is 483 divisible by 3?
Yes
No
Answer
3
15
294 is divisible by 6.
True
False
Answer
4
16
3,926 is divisible by 9.
True
False
Answer
5
17
Divisibility
Some numbers are divisible by more than 1 digit.
Let's practice using the divisibility rules.
18 is divisible by how many digits? Let's see if your choices are correct.
9
Click
Did you guess 2, 3, 6 and 9?
165 is divisible by how many digits? Let's see if your choices are correct.
Click
Did you guess 3 and 5?
46
18
Divisibility
28 is divisible by how many digits? Let's see if your choices are correct.
Click
Did you guess 2 and 4?
530 is divisible by how many digits? Let's see if your choices are correct.
Click
Did you guess 2, 5, and 10?
Now it's your turn......
19
Divisibility Table
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
156
429
446
1,218
1,006
28,550
20
What are all the digits 15 is divisible by?
Answer
6
21
What are all the digits 36 is divisible by?
Answer
7
22
What are all the digits 1,422 is divisible by?
Answer
8
23
What are all the digits 240 is divisible by?
Answer
9
2
24
What are all the digits 64 is divisible by?
Answer
10
25
Patterns in Multiplication and Division
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Table of
Contents
26
Number Systems
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. 27
Number Systems
There are many different number systems that have been used throughout history, and are still used in different parts of the world today.
Sumerian Roman Numerals
wedge = 10, line = 1
28
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 our number system came from. Base ten.
29
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.
30
Base 10
How do you think things would be different if we had six fingers on each hand?
31
Powers of 10
Numbers can be VERY long. $100,000,000,000,000
Wouldn't you love to have one hundred trillion dollars?
Fortunately, our base ten number system has a way to make multiples of ten easier to work with. It is called Powers of 10. 32
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.
33
Powers of 10
10
3
The raised digit is called the exponent. The exponent tells how many tens are multiplied.
34
Powers of 10
A number written with an exponent, like 103, is in exponential notation. A number written in a more familiar way, like 1,000 is in standard notation.
35
Powers of 10 Powers of 10 (greater than 1)
Standard
Notation
10
100
1,000
10,000
100,000
1,000,000
Product
of 10s
10
10 x 10
10 x 10 x 10
10 x 10 x 10 x 10
10 x 10 x 10 x 10 x 10
10 x 10 x 10 x 10 x 10 x 10
Exponential Notation
101
102
103
104
105
106
36
Powers 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.
Because of this, it is easy to MULTIPLY a whole number by a power of 10. 37
Multiplying Powers of 10
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
38
Multiplying Powers of 10
If you have memorized the basic multiplication facts, you can solve problems mentally. Use a pattern when multiplying by powers of 10.
Steps
1. Multiply the digits to the left of the 50 x 100 = 5,000
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 39
Multiplying Powers of 10
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.
40
Multiplying Powers of 10
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.
41
Multiplying Powers of 10
60 x 400 = _______
steps
1. Multiply the digits to the left of the zeros in each 6 x 4 = 24
2. Count the number of zeros in each factor.
60 x 400
factor.
3. Write the same number of zeros in the product.
60 x 400 = 24,000
42
Multiplying Powers of 10
500 x 70,000 = _______
steps
1. Multiply the digits to the left of the zeros in each 5 x 7 = 35
2. Count the number of zeros in each factor.
factor.
3. Write the same number of zeros in the product.
43
Multiplying Powers of 10
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.
44
Multiplying Powers of 10
500 x 70,000 = _______
steps
1. Multiply the digits to the left of the zeros in each 5 x 7 = 35
2. Count the number of zeros in each factor.
500 x 70,000
factor.
3. Write the same number of zeros in the product.
500 x 70,000 = 35,000,000 45
Practice Finding Rule
Your Turn....
Write a rule.
Input
Output
50
15,000
7
2,100
Rule
click
300
90,000
20
6,000
multiply by 300
46
Practice Finding Rule
Write a rule.
Input
20
7
9,000
80
Output
18,000
Rule
6,300
8,100,000
click
multiply by 900
72,000
47
30 x 10 =
Answer
11
48
800 x 1,000 =
Answer
12
49
900 x 10,000 =
Answer
13
50
700 x 5,100 =
Answer
14
51
70 x 8,000 =
Answer
15
52
40 x 500 =
Answer
16
53
1,200 x 3,000 =
Answer
17
54
35 x 1,000 =
Answer
18
55
Dividing Powers of 10
Remember, a digit in one place is 1/10 the value of the place to its left.
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
value.
42,000 / 1,000 = 42
value.
Take off two 0's to show that it is 1/100 of the Take off three 0's to show that it is 1/1,000 of the 56
Dividing Powers of 10
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.
57
Practice Dividing
More Examples:
700 / 10
700 / 10 = 70
8,000 / 10 8,000 / 10 = 800
9,000 / 100
9,000 / 100 = 90
58
Practice Dividing
This pattern can be used in other problems.
120 / 30
120 / 30 = 4
1,400 / 700
1,400 / 700 = 2
44,600 / 200
44,600 / 200 = 223
59
Practice Dividing Rule
Your Turn....
Complete. Follow the rule.
Rule: Divide by 50
Input
150
250
3,000
Output
click
click
click
3
5
60
60
Practice Dividing Rule
Complete. Find the rule.
Find the rule.
Output
Input
40
120
click
240
click
8
2,700
click
90
61
800 / 10 = Answer
19
62
16,000 / 100 =
Answer
20
63
1,640 / 10 =
Answer
21
64
210 / 30 =
Answer
22
65
80 / 40 =
Answer
23
66
640 / 80 =
Answer
24
67
4,500 / 50 =
Answer
25
68
Powers of 10
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
0.1
0.01
0.001
0.0001
0.00001
0.000001
Product of 0.1
0.1
0.1 x 0.1
0.1 x 0.1 x 0.1
0.1 x 0.1 x 0.1 x 0.1
0.1 x 0.1 x 0.1 x 0.1 x 0.1
0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1
Exponential
Notation
10­1
10­2
10­3
10­4
10­5
10­6
69
Powers of 10
What if the exponent is zero? (100)
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
104 103 102 101 100 10­1 10­2 10­3
10­4
.
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. 70
Multiplying Powers of 10
Let's look at how to multiply a decimal by a Power of 10 (greater than 1)
Example: 1,000 x 45.6 = ?
Steps
1. Locate the decimal point in the power of 10.
1,000 = 1,000. 2. Move the decimal point LEFT until you get to the number 1.
3. Move the decimal point in the other the same number of places, but to the RIGHT. Insert 0's as needed. That's your answer.
1 0 0 0 . (3 places)
factor 4 5 . 6 0 0 So, 1,000 x 45.6 = 45,000
71
Multiplying Powers of 10
Let's look at how to multiply a decimal by a Power of 10 (greater than 1)
Example: 1,000 x 45.6 = ?
Steps
1. Locate the decimal point in the power of 10.
1,000 = 1,000. 2. Move the decimal point LEFT until you get to the number 1.
3. Move the decimal point in the other the same number of places, but to the RIGHT. Insert 0's as needed. That's your answer.
1 0 0 0 . (3 places)
factor 4 5 . 6 0 0 So, 1,000 x 45.6 = 45,000
72
Multiplying Powers of 10
Let's look at how to multiply a decimal by a Power of 10 (greater than 1)
Example: 1,000 x 45.6 = ?
Steps
1. Locate the decimal point in the power of 10.
1,000 = 1,000. 2. Move the decimal point LEFT until you get to the number 1.
3. Move the decimal point in the other the same number of places, but to the RIGHT. Insert 0's as needed. That's your answer.
1 0 0 0 . (3 places)
factor 4 5 . 6 0 0 So, 1,000 x 45.6 = 45,000
73
Practice Multiplying
Let's try some together.
10,000 x 0.28 =
$4.50 x 1,000 =
1.04 x 10 = 74
100 x 3.67 =
Answer
26
75
0.28 x 10,000 =
Answer
27
76
1,000 x $8.98 =
Answer
28
77
7.08 x 10 =
Answer
29
78
Dividing Powers of 10
Let's look at how to divide a decimal by a Power of 10 (less than 1)
Example: 45.6 / 1,000
Steps 1. Locate the decimal point in the power of 10.
2. Move the decimal point LEFT until to the number 1.
1,000 = 1,000.
you get 1 0 0 0 . (3 places)
3. Move the decimal point in the other number the same number of places to the LEFT. Insert 0 0 4 5 . 6
0's as needed.
So, 45.6 / 1,000 = 0.0456 79
Dividing Powers of 10
Let's look at how to divide a decimal by a Power of 10 (less than 1)
Example: 45.6 / 1,000
Steps 1. Locate the decimal point in the power of 10.
2. Move the decimal point LEFT until to the number 1.
1,000 = 1,000.
you get 1 0 0 0 . (3 places)
3. Move the decimal point in the other number the same number of places to the LEFT. Insert 0 0 4 5 . 6
0's as needed.
So, 45.6 / 1,000 = 0.0456 80
Dividing Powers of 10
Let's look at how to divide a decimal by a Power of 10 (less than 1)
Example: 45.6 / 1,000
Steps 1. Locate the decimal point in the power of 10.
2. Move the decimal point LEFT until to the number 1.
1,000 = 1,000.
you get 1 0 0 0 . (3 places)
3. Move the decimal point in the other number the same number of places to the LEFT. Insert 0 0 4 5 . 6
0's as needed.
So, 45.6 / 1,000 = 0.0456 81
Practice Dividing
Let's try some together.
56.7 / 10 = 0.47 / 100 = $290 / 1,000 = 82
73.8 / 10 =
Answer
30
83
0.35 / 100 =
Answer
31
84
$456 / 1,000 = Answer
32
85
60 / 10,000 = Answer
33
86
$89 / 10 =
Answer
34
87
321.9 / 100 =
Answer
35
88
Division of Whole Numbers
Return to
Table of
Contents
89
Review from 4th Grade
When you divide, you are breaking a number apart into equal groups. The problem 15 ÷ 3 means that you are making 3 equal groups out of 15 total items.
Each equal group contains 5 items, so 15 ÷ 3 = 5
90
Review from 4th Grade
How will knowing your multiplication facts really well help you to divide numbers?
click to reveal
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
click
4
24 ÷ 8
click
3
30 ÷ 6
click
5
63 ÷ 9
click
7
91
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.
Answer
Review from 4th Grade
How can you divide 56 into two numbers that are each divisible by 4? ( ? + ? = 56)
4
?
?
56
92
Review from 4th Grade
?
?
40
4
16
Answer
You can break 56 into 40 + 16 and then divide each part by 4.
4
56
Ask yourself... What is 40 ÷ 4?
(or 4 x n = 40?) What is 16 ÷ 4? (or 4 x n = 16?)
The quotient of 56 ÷ 4 is equal to the sum of the two partial quotients.
93
Area Model Division
How can you break up 135? Remember... you want the numbers to be divisible by 5.
5
100
Answer
Let's try another example. Use the area model to find the quotient of 135 ÷ 5.
5
35
94
Area Model Division
Let's try another example. Use the area model to find the quotient of 135 ÷ 15.
You can break 135 into 90 + 45 and then divide each part by 15.
?
15
135
Answer
?
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.
95
Area Model Division
What about remainders?
?
?
R.
Answer
Use the area model to find the quotient. 963 ÷ 20 =
20
20
963
96
Answer
36 Use the area model to find the quotient.
645 ÷ 15 =
15
40 + 3 =
97
Answer
37 Use the area model to find the quotient. Write any reminder as a fraction.
695 ÷ 30=
10 + 3 =
98
Answer
38 Use the area model to find the quotient. Write any reminder as a fraction.
385 ÷ 75 =
99
• 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.
Answer
39 A teacher drew an area model to find the value of 6,986 ÷ 8.
From PARCC PBA sample test #15
100
Division Key Terms
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. 4 quotient
divisor 5 20 dividend
20 ÷ 5 = 4
__
20
5
= 4
101
Estimating
Estimating the quotient helps to break whole numbers into groups.
102
Estimating: One­Digit Divisor
8) 689
Divide 8) 68
8
8)689
80
8)689
Write 0 in remaining place.
80 is the estimate.
103
One­Digit 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?
Click
Yes, it is 40.
104
One­Digit Estimation Practice
Estimate :
5)451
Remember to divide 45 by 5
Then write 0 in remaining place in quotient.
Is your estimate 90 or 80?
Click
Yes, it is 90
105
40 The estimation for 8)241 is 40?
Answer
True
False
106
÷ 7.
Answer
41 Estimate 663 107
Answer
42 Estimate 4)345 .
108
Answer
43 Solve using Estimation. Marta baby­sat fo
r four hours and earned $19. ABOUT how much money
did Marta earn each hour
that she baby­sat?
109
Estimating: Two­Digit Divisor
26)6,498
Round 26 to its greatest place.
30)6,498
2
30) 6,498
200
30)6,498
Divide 30)64 .
Write 0 in remaining places.
200 is the estimate.
110
Two­Digit 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?
click to reveal
Yes, it is 20.
111
Two­Digit Estimation Practice
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? click to reveal
Yes, it is 100.
112
44 The estimation for 17)489 is 2?
Answer
True
False
113
÷ 25.
Answer
45 Estimate 5,145 114
Answer
46 Estimate 41) 2,130 .
115
Answer
47 Estimate 31)7,264 .
116
Answer
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? 117
Division
When we are dividing, we are breaking apart into equal groups.
Find 132 3
44
Step 1: Can 3 go 3 132
into 1, no so can ­ 12 Click for step 1
3 go into 13, yes
1 2
­ 12 0
Step 2: Bring down the 2. Can 3 Click for step 2
go into 12, yes
3 x 4 = 12
13 ­ 12 = 1
Compare 1 < 3
3 x 4 = 12
12 ­ 12 = 0
Compare 0 < 3
118
Division
Step 3: Check your answer.
44
x 3 132
119
Answer
49 Divide and Check 8)296 .
120
Answer
50 Divide and Check 9)315
121
÷ 6.
Answer
51 Divide and Check 252 122
÷ 2.
Answer
52 Divide and Check 9470 123
Answer
53 Adam has a wire that is 434 inches long. He cuts the wire into 7­inch lengths. How many pieces of wire will he have?
124
Answer
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?
125
Answer
55 There are 6 outs in an inning. How many innings would have to be played to get 348 outs?
126
56 How many numbers between 23 and 41 have NO remainder when divided by 3?
A 4
C 6
D 11
Answer
B 5
127
Division Problem
John and Lad are splitting the $9 that John has in his wallet. Move the money to give John half and Lad half.
Sometimes, when we split a whole number into equal groups, there will be an amount left over. Click when finished.
The left over number is called the remainder.
128
Long Division
Lets look at remainders with long division.
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.
129
Long Division
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.
130
Long Division
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
131
Answer
57 A group of six friends have 83 pretzels. If they want to share them evenly, how many will be left over?
132
Answer
58 Four teachers want to evenly share 245 pencils. How many will be left over?
133
Answer
59 Twenty students want to share 48 slices of pizza. How many slices will be left over, if each person gets the same number of slices?
134
A
149 packages, 2 left over
B
148 packages, 2 left over
Answer
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. 135
Long Division
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. 4
2
7
7)30
­28
2
136
Long Division Examples
More examples of the remainder written as a fraction: 7 5
6
6)47
­42­
5
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 Multiply the quotient and the divisor. Then, add the remainder. The result should be the dividend.
137
Long Division Example
Example:
37
7)264
­21
54
­49
5
5
7
Check the answer using multiplication and addition.Way 1:
37 x 7 + 5 = 259 + 5 = 264
Way 2:
37
quotient
x divisor
x 7 259
+ 5 + remainder
264
dividend
138
Answer
61 Divide and Check 4)43
(Put answer in as a mixed number.)
139
Answer
62 Divide and Check 61 ÷ 3 =
(Put answer in as a mixed number.)
140
63 Divide and Check 145 ÷ 7
Answer
(Put answer in as a mixed number.)
141
64 Divide and Check 2)811
Answer
(Put answer in as a mixed number.)
142
65 Divide and Check 309 ÷ 2 =
Answer
(Put answer in as a mixed number.)
143
Long Division with 2­digit Divisor
You can divide by two­digit divisors to find out how many groups there are or how many are in each group.
When dividing by a two­digit divisor, follow the steps you used to divide by a one­digit divisor. Repeat until you have divided all the digits of the dividend by the divisor.
STEPS
Divide
Multiply
Subtract
Compare
Bring down next number
144
Long Division Practice
Find 4575 25
183
Step 1: Can 25 25 4575
go into 4, no so ­ 25 can 25 go into 45, 20
7
yes
­ 200
Step 2: Bring down the 7. Can Click for step 2
25 go into 207, yes
Step 3: Bring down the 5. Can 25 go into 75, yes
Click for step 3
25 x 1 = 25
45 ­ 25 = 20
Compare 20 < 25
75
­ 75
0
25 x 8 = 200
207 ­ 200 = 7
Compare 7 < 25
25 x 3 = 75
Click for step 1
75 ­ 75 = 0
Compare 0 < 25
145
Long Division Practice
Step 3: Check your answer.
183
x 25 146
Long Division Example
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?
147
Long Division Example
23)253
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? 11
23) 253
­23
23
­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.
0
Each student will work 11 shifts at the school store.
148
Long Division 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?
149
Silly Steps Example
Click boxes to show work
Find 374 ÷ 22
Step 1
1
22) 374 divide
Think 20) 374
Step 4
1
bring 22) 374
­22
down
154
bring down
Step 5
17 repeat
Step 2
1
22) 374
multiply
­22
1 x 22
Step 3
1
subtract
22) 374
­22
15 15 less than 22
compare
22) 374
­22
repeat
154
­154
0
Final Step
17
x 22
34
Check
+340
374
150
A
38
B
40
C
41
D
45
Answer
66 A candy factory produces 984 pounds of chocolate in 24 hours. How many pounds of chocolate does the factory produce in 1 hour?
151
A
$230
B
$320
C
$325
Answer
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?
152
Answer
68 Solve 16)176
153
÷ 47
Answer
69 Solve 329 154
Answer
70 If 280 chairs are arranged into 35 rows, how many chairs are in each row?
155
Answer
71 There are 52 snakes. There are 13 cages. If each cage contains the same number of snakes, how many snakes are in each cage?
156
Answer
72 Solve 46)3,588
157
÷ 72
Answer
73 Solve 3,672 158
74 Enter your answer.
Answer
1,534 ÷ 26 =
From PARCC EOY sample test #27
159
Division Steps
Divide
Multiply
.
Subtract
Compare
Bring Down
Repeat
When dividing by a Two­Digit Divisor, there may be a Remainder. Follow the Division Steps. If the Difference in the Last Step of Division is not a Zero, and there are no other numbers to Bring Down, this is the Remainder.
The definition of a Remainder is an amount "left over" that does not make a full group (Divisor).
Write the Remainder as a Fraction.
top number Difference 62
bottom number Divisor 77
This means there are 62 "left over" that do not make a full group of 77.
Use Multiplication and Addition to check you Answer. Problem:
5
62
77
5 x 77 + 62 = 447
77) 447
­385 62
OR
77
x 5
375
+ 62
447
160
Let's Practice
Remember your Steps: Divide, Multiply, Subtract, Compare, Bring Down,
Write the Remainder as a Fraction,
Check your work 21
36
17
36) 633
­ 36
Solve 633 36
273
­ 252
21
17
CHECK
36
x
Divisor 102
x Quotient + 510
+ Remainder = Dividend
612
+ 21
633
161
A
8
B
7
C
19
D
10
Answer
75 What is the remainder when 402 is divided by 56?
162
A
5
B
8
C
13
D
26
Answer
76 What is the remainder when 993 is divided by 38?
163
77 Divide 80) 104
Answer
(Put answer in as a mixed number.)
164
78 Divide 556 ÷ 35
Answer
(Put answer in as a mixed number.)
165
Answer
79 Divide 45) 1442
(Put answer in as a mixed number.)
166
80 Divide 4453 ÷ 55
Answer
(Put answer in as a mixed number.)
167
81 Divide 83) 8537
Answer
(Put answer in as a mixed number.)
168
Interpreting the Remainder
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.
169
Interpreting the Remainder
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.
170
A
47
B
48
C
49
D
50
Answer
82 If you have 341 oranges to transport from Florida to New Jersey, and 7 oranges are in each bag, how many bags will you need to ship all of the oranges?
171
A
6
B
7
C
8
D
9
Answer
83 At the bakery, donuts are only sold in boxes of 12. If 80 donuts are needed for the teacher's meeting, how many boxes should be bought?
172
84 Apples cost $4 for a 5 pound bag. If you have $19, how many bags can you buy?
B 3
19 4 = 4 R 3
Answer
A 2
C 4
D 5
173
85 The school is ordering carry cases for the calculators. If there are 203 calculators and 16 fit in a case, how many cases need to be ordered?
A
10
B
11
C
12
D
13
174
A
5
B
6
C
7
D
8
Answer
86 For the class trip, 51 people fit on a bus and 267 people are going. How many buses will be needed?
175
Answer
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 From PARCC PBA sample test #16
equations.
176
Division of Decimals
Return to
Table of
Contents
177
Dividing Decimals
To divide a decimal by a whole number:
Use long division.
Bring the decimal point up in the answer.
21 31
3
63.93
178
Decimal Division Examples
Match the quotient to the correct problem.
4
8.12
4
81.2
4
0.812
4
0.0812
0.0203 0.203
2.03
20.3
179
A
1285
B
1.285
C
12.85
D
128.5
5
64.25
Answer
88 Which answer has the decimal point in the correct location?
180
89 Which answer has the decimal point in the correct location?
561
B
56.1
C
5.61
D
0.561
4
224.4
Answer
A
181
90 Which answer has the decimal point in the correct location?
51
B
5.1
C
0.51
D
0.051
9
0.459
Answer
A
182
91 Select the answer with the decimal point in the correct location.
0.1234
B
1.234
C
12.34
D
123.4
E
1234
3 37.02
Answer
A
183
92 Select the answer with the decimal point in the correct location.
501
B
50.1
C
5.01
D
0.501
E
0.0501
5 .2505
Answer
A
184
20.52
Answer
93 6
185
321.6
Answer
94 4
186
2.198
Answer
95 7
187
70.62
Answer
96 11
188
251.2
Answer
97 4
189
Zero Place Holder
Be careful, sometimes a zero needs to be used as a place holder.
5.08
7 35.56
­35
0 56
­ 56
0
7 can not go into 5. So, put a 0 in the quotient, and bring the 6 down.
190
98 What is the next step in this division problem?
3 27.21
­27
0 2
A
Put a 2 in the quotient. B
Put a 0 in the quotient. C
Put a 1 in the quotient. Answer
9.
191
99 What is the next step in this division problem?
5 3.205
­ 30
2
A
Put a 0 in the quotient. B
Put a 2 in the quotient.
C
Bring down the 0.
Answer
0.6
192
100 What is the next step in this division problem?
8 64.48
­64
0 4
A
Put a 0 in the quotient. B
Put a 4 in the quotient. C
Put a 2 in the quotient. Answer
8.
193
0.636
Answer
101 6
194
2.406
Answer
102 3
195
Zero Place Holder
Be careful! Sometimes there is not enough to make a group, so put a zero in the quotient.
.076
8
0.608
­56
48
­48
0
196
first step in this division 6 .468
A
Put a 0 in the ones place of the quotient. B
Put a 0 in the tenths place of the quotient. C
Put a 7 in the quotient. Answer
103 What is the problem?
197
first step in this division 24 .1104
A
Put a 0 in the quotient in the tenths and hundredths place.
B
Put a 0 in the quotient in the ones place. C
Put a 4 in the quotient. Answer
104 What is the problem?
198
.435
Answer
105 5
199
Another Way to Handle Remainders
Instead of writing a remainder, continue to divide the remainder by the divisor (by adding zeros) to get additional decimal points.
9.4
8 75.6
­72
3 6
­ 32
4
Instead of leaving the 4 as a remainder, add a zero to the dividend.
200
Another Way to Handle Remainders
9.45
8 75.60
­72 3 6
­ 3 2
40
­ 40
0 Add a zero to the dividend.
No remainder now.
201
3.26
Answer
106 5
202
87.3
Answer
107 2
203
Answer
108 6 0.795
204
0.843
Answer
109 30
205
0.363
Answer
110 15
206
Decimal Division Example
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 = _____
207
Decimal Division Example
56
5
$284
­ 25
34
­ 30
4
Don't leave the remainder 4, or write it as a fraction, add a decimal point and zeros to get the cents.
208
Decimal Division Example
56.8
5
$284.0
­ 25
34
­ 30
4 0
­ 4 0
0
Since the answer is in money, write the answer as $56.80.
209
Decimal Division Example
11.714
7
$82.000
­ 7
12
­ 7
50
­ 49
10
­ 7
30
­28
2
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
210
Answer
111 5 $63
211
Answer
112 $782 ÷ 9 =
212
Answer
113 7 $593
213
Answer
114 4 $352
214
Answer
115 $48 ÷ 22 =
215
Divisor as a Decimal
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
Divisor
Dividend
216
Divisor as Decimal Examples:
2.4
15.696
24 156.96
Multiply by 10, so that 2.4 becomes 24.
15.696 must also be multiplied by 10.
.64
6.4
64
640
Multiply by 100, so that .64 becomes 64.
6.4 must also be multiplied by 100.
217
Divisor as Decimal Practice
By what power of 10 should the divisor and dividend be multiplied?
.007
4.9
0.3
42.69
218
Divisor as Decimal Examples
By what power of 10 should the divisor and dividend be multiplied?
7.59 ÷ 2.2 2.0826 ÷ 0.06
means
means
219
116
Answer
0.3 42.48
220
117 Divide
Answer
2.592 ÷ 0.08 =
221
118 Enter your answer.
Answer
6.3 ÷ 0.1 =
From PARCC EOY sample test #19
222
119 Enter your answer
Answer
6.3 x 0.1 =
From PARCC EOY sample test #19
223
120
Answer
0.3 0.6876
224
121
Answer
20 divided by 0.25
225
Answer
122 Yogurt costs $.50 each, and you have $7.25. How many can you buy?
226
Teacher Notes
Glossary & Standards
Vocabu
in the p
box the
linked of the p
word d
Return to
Table of
Contents
227
Standards for Mathematical Practices
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.
MP8 Look for and express regularity in repeated reasoning.
Click on each standard to bring you to an example of how to meet this standard within the unit. 228
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. Back to Instruction
229
Dividend
The number being divided in a division equation.
3
8 24
Dividend
Dividend
24 ÷ 8 = 3
Dividend
24
= 3
8
Back to Instruction
230
Divisible
When one number is divided by another, and the result is an exact whole number.
5
5
15 is divisible by 3 because 3
15 ÷ 3 = 5 exactly.
2
11 ÷ 2 = 5 R.1
Back to Instruction
231
Divisor
The number the dividend is divided by. A number that divides another number without a remainder.
3
8 24
Divisor
24 ÷ 8 = 3
Divisor
25
= 3
R1
8
Must divide evenly.
Back to Instruction
232
Exponent
A small, raised number that shows how many times the base is used as a factor.
Exponent
3
2
= x 2
3 = x x 3
3 3 3 3 x 32
2
Base
"3 to the second power"
3 3 3 3 3 x 33
Back to Instruction
233
Exponential Notation
A number written using a base and an exponent.
Standard
1,000
Word
One Thousand
Exponential
103
Back to Instruction
234
Number System
A systematic way of counting numbers, where symbols/digits and their order represent amounts.
Base Ten
Roman Numerals
Others
Back to Instruction
235
Power of 10
Any integer powers of the number ten. (Ten is the base, the exponent is the power).
10 =
1=
10x10 =
2
10x10x10 =
3
= 1,000
10
10 10 10 100
=
Back to Instruction
236
Quotient
The number that is the result of dividing one number by another.
Quotient
12 ÷ 3 = 4 Quotient
4 3 12
12
= 4 3
Quotient
Back to Instruction
237
Remainder
When a number is divided, the remainder is anything that is left over. (Anything in addition to the whole number.)
5
5
Remainder
2
11 ÷ 2 = 5 R.1
5 R.1 2 11
3
No remainder
Back to Instruction
238
Standard Notation
A general term meaning "the way most commonly written". A number written using only digits, commas and a decimal point.
Standard
3.5
Word
Three and five tenths
Expanded
3 + 0.5
Back to Instruction
239