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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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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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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 85 Last digit is 5 OR 010 Last digit is 0
Check the Sum!3 Sum of digits is divisible by 36 Number is divisible by 3 AND 29 Sum of digits is divisible by 9
Look at Last Digits4 Last 2 digits form a number divisible by 4
Divisibility Rules
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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
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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
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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?
YesNo
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2 Is 315 divisible by 5?
YesNo
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3 Is 483 divisible by 3?
YesNo
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4 294 is divisible by 6.
TrueFalse
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5 3,926 is divisible by 9.
TrueFalse
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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
64
9Divisibility
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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
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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
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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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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
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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
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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.
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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
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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 one hundred trillion dollars?
Powers of 10
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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
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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 of 10s Notation
(greater than 1)
10 10 101
100 10 x 10 102
1,000 10 x 10 x 10 103
10,000 10 x 10 x 10 x 10 104
100,000 10 x 10 x 10 x 10 x 10 105
1,000,000 10 x 10 x 10 x 10 x 10 x 10 106
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
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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
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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 = 5,000Steps1. Multiply the digits to the left of the zeros in each factor. 50 x 100 5 x 1 = 52. 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
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60 x 400 = _______
steps1. Multiply the digits to the left of the zeros in each factor. 6 x 4 = 242. Count the number of zeros in each factor.
3. Write the same number of zeros in the product.
Multiplying Powers of 10
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60 x 400 = _______
steps1. Multiply the digits to the left of the zeros in each factor. 6 x 4 = 242. 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
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60 x 400 = _______
steps1. Multiply the digits to the left of the zeros in each factor. 6 x 4 = 242. 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 = _______
steps1. Multiply the digits to the left of the zeros in each factor. 5 x 7 = 352. Count the number of zeros in each factor.
3. Write the same number of zeros in the product.
Multiplying Powers of 10
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500 x 70,000 = _______
steps1. Multiply the digits to the left of the zeros in each factor. 5 x 7 = 352. 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
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500 x 70,000 = _______
steps1. Multiply the digits to the left of the zeros in each factor. 5 x 7 = 352. 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
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Your Turn....
Write a rule.
Input Output
50 15,000
7 2,100
300 90,000
20 6,000
Rule
multiply by 300click
Practice Finding Rule
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Input Output
20 18,000
7 6,300
9,000 8,100,000
80 72,000
Write a rule.
Rule
multiply by 900click
Practice Finding Rule
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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
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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
steps1. Cross out the same number of 0's in the dividend as in the divisor.2. Complete the division fact.
Dividing Powers of 10
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700 / 10700 / 10 = 70
8,000 / 10 8,000 / 10 = 800 9,000 / 100
9,000 / 100 = 90
More Examples:
Practice Dividing
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120 / 30120 / 30 = 4
1,400 / 7001,400 / 700 = 2
44,600 / 20044,600 / 200 = 223
This pattern can be used in other problems.
Practice Dividing
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Your Turn....
Complete. Follow the rule.
Rule: Divide by 50
Input Output150250
3,000
3560click
click
click
Practice Dividing Rule
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Find the rule.Input Output120 40240 8
2,700 90
Complete. Find the rule.
click
click
click
Practice Dividing Rule
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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 of 0.1
ExponentialNotation
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
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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 . 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
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Let's look at how to multiply a decimal by a Power of 10 (greater than 1)
Steps1. 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 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
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Steps1. 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 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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Steps1. 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 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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Let's try some together.
10,000 x 0.28 =
$4.50 x 1,000 =
1.04 x 10 =
Practice Multiplying
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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 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
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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
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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
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Let's try some together.
56.7 / 10 =
0.47 / 100 =
$290 / 1,000 =
Practice Dividing
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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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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
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
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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
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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
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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
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? ?
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
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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
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Estimating the quotient helps to break whole numbers into groups.
Estimating
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Estimating: One-Digit Divisor
6898)Divide 8) 68
8)6898
8)68980
Write 0 in remaining place.
80 is the estimate.
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One-Digit Estimation Practice
Estimate:
9)507
Remember to divide 50 by 9Then 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 5Then write 0 in remaining place in quotient.
Is your estimate 90 or 80?
Yes, it is 90Click
One-Digit Estimation Practice
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40 The estimation for 8)241 is 40?
TrueFalse
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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)6,498Round 26 to its greatest place.
30)6,498
Divide 30)64 .
30) 6,4982
30)6,498200 Write 0 in remaining places.
200 is the estimate.
Estimating: Two-Digit Divisor
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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 90Finally, 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
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44 The estimation for 17)489 is 2?
TrueFalse
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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 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 = 1213 - 12 = 1Compare 1 < 3
3 132
3 x 4 = 1212 - 12 = 0Compare 0 < 3
- 12 0
2
Step 2 : Bring down the 2. Can 3 go into 12, yes
4
Click for step 1
Click for step 2
Division
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Step 3: Check your answer.
44 x 3 132
Division
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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
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For example: 47)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
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For example: 47)30 30÷ 7 = 4 R 2 -28 2
This is the way you may have seen it. The R
stands for remainder.
Long Division
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Another example: 2315)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
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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 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 of 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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47)30 -28 2
27
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
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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
56
Multiply the quotient and the divisor. Then, add the remainder. The result should be the dividend.
Long Division Examples
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37 x 7 + 5 = 259 + 5 = 264
Example:
377)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
57
Long Division Example
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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.
STEPSDivideMultiplySubtractCompareBring down next number
Long Division with 2-digit Divisor
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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 = 2545 - 25 = 20Compare 20 < 25
25 4575
25 x 8 = 200207 - 200 = 7Compare 7 < 25
7 - 200 7 5 - 75 0
Step 2 : Bring down the 7. Can 25 go into 207, yes
8
Click for step 1Step 3 : Bring down the 5. Can 25 go into 75, yes
25 x 3 = 7575 - 75 = 0Compare 0 < 25
3
Click for step 2
Click for step 3
Long Division Practice
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Step 3: Check your answer.
183 x 25
Long Division Practice
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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
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1Step 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) 2531
-2323
-230
Each student will work 11 shifts at the school store.
23)253
Long Division Example
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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
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Find 374 ÷ 22Step 1
22) 374 Think 20) 374
1
Step 2
22) 3741
-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 0
17 repeat
Final Step 17 x 22 34340374+
divide
multiply
subtract
compare
bring down
repeat
Check
Click boxes to show work
Silly Steps Example
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66 A candy factory produces 984 pounds of chocolate in 24 hours. How many pounds of chocolate does the factory produce in 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 car. She has to make 24 equal payments. 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 of snakes, how many snakes are in each 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) 63336-273252-
17 2136
21
1736x
102510+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. 115) 58 -5 08 - 5 3
5 people will each get 11 pencils,and there will be 3 left over.
Interpreting the Remainder
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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? 1024) 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
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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
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8.124
2.03
0.8124
81.24
0.08124
20.30.2030.0203
Match the quotient to the correct problem.
Decimal Division Examples
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88 Which answer has the decimal point in the correct location?
A 1285
B 1.285
C 12.85
64.255
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
224.44
D 0.561
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90 Which answer has the decimal point in the correct location?
A 51
B 5.1
C 0.510.4599
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
37.023
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
.25055
E 0.0501
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93 20.526
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94 321.64
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95 2.1987
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96 70.6211
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97 251.24
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Be careful, sometimes a zero needs to be used as a place holder.
35.56 -35 0 56 - 56 0
7
5.08
7 can not go into 5. So, put a 0 in the quotient, and bring the 6 down.
Zero Place Holder
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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.
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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 - 30 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 -64 0 4
8
8.
C Put a 2 in the quotient.
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101 0.6366
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102 2.4063
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Be careful! Sometimes there is not enough to make a group, so put a zero in the quotient.
0.608 -56 48 -48 0
8
.076
Zero Place Holder
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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.
.4686
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.
.110424
C Put a 4 in the quotient.
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105 .4355
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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 -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
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75.60 -72 3 6 - 3 2 40 - 40 0
8
9.45
Add a zero to the dividend.
No remainder now.
Another Way to Handle Remainders
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106 3.265
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107 87.32
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108 0.7956
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109 0.84330
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110 0.36315
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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
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$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
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$284.0- 25 34 - 30 4 0 - 4 0 0
5
56.8
Since the answer is in money, write the answer as $56.80.
Decimal Division Example
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$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
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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
DividendDivisor
Divisor as a Decimal
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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:
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By what power of 10 should the divisor and dividend be multiplied?
.007
0.3
4.9
42.69
Divisor as Decimal Practice
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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
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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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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.
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Dividend
24 ÷ 8 = 32483
248 = 3
Dividend Dividend
Dividend
The number being divided in a division equation.
Back to
Instruction
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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
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Divisor
24 ÷ 8 = 32483 25
8 = 3R1
Divisor Divisor
The number the dividend is divided by. A number that divides another number
without a remainder.
Must divide evenly.
Back to
Instruction
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ExponentA small, raised number that shows how many times the
base is used as a factor.
32Base
Exponent
32= x 33
3 = x x 33 3332
x 2333
x 33"3 to the second power"
Back to
Instruction
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Back to
Instruction
Exponential Notation
A number written using a base and an exponent.
1,000
Standard Word
One Thousand
Exponential
103
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Back to
Instruction
Number SystemA systematic way of counting
numbers, where symbols/digits and their order represent amounts.
Base Ten Roman Numerals Others
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Back to
Instruction
101 10=
Power of 10
Any integer powers of the number ten. (Ten is the base, the exponent is the
power).
102 100= 103 1,000=
10x10 =10 = 10x10x10 =
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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
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Back to
Instruction
RemainderWhen 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 remainder115 R.1
2
Remainder
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Back to
Instruction
Standard Notation
A general term meaning "the way most commonly written". A number written using only digits, commas and a decimal point.
3.5Standard Word
Three and five tenths
Expanded
3 + 0.5
