Transcript Division-2013-04-24x - Swedesboro

New Jersey Center for Teaching and Learning
Progressive Mathematics Initiative
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5th Grade
Division
2013-04-24
www.njctl.org
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Division Unit Topics
• Divisibility Rules
• Patterns in Multiplication and Division
• Division of Whole Numbers
• Division of Decimals
Click on the topic to
go to that section
Divisibility Rules
Click to return to the
table of contents
Divisible
When one number can be divided by another and the result is an
exact whole number.
five
Example: 15 is divisible by 3
because 15 ÷ 3 = 5 exactly
three
BUT 9 is not divisible by 2
because 9 ÷ 2 is 4 with one left
over.
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.
Divisibility Rules
Look at the last digit in the Ones Place!
2
Last digit is even-0,2,4,6,8
5
Last digit is 5 OR 0
10
Last digit is 0
Check the Sum!
3
6
9
Sum of digits is divisible by 3
Number is divisible by 3 AND 2
Sum of digits is divisible by 9
Look at Last Digits
4
Last 2 digits form a number divisible by 4
Let's Practice!
Is 34 divisible by 2?
Yes, because the digit in the ones place is an even
number. Therefore, 34 / 2 = 17
Is 1,075 divisible by 5?
Yes because the digit in the ones place is a 5.
Therefore, 1,075 / 5 = 215
Is 740 divisible by 10?
Yes, because the digit in the ones place is a 0.
Therefore, 740 / 10 = 74
x
Is 258 divisible by 3?
Yes, because the sum of its digits is divisible by 3.
2 + 5 + 8 = 15 Look 15 / 3 = 5
Therefore, 258 / 3 = 86
Is 193 divisible by 6?
Yes, because the sum of its digits is divisible by 3 AND 2.
1 + 9 + 2 = 12 Look 12 /3 = 4
Therefore, 192 / 6 = 32
x
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
Therefore, 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
Therefore, 520 / 4 = 130
x
1
Is 198 divisible by 2?
Yes
No
2
Is 315 divisible by 5?
Yes
No
3
Is 483 divisible by 3?
Yes
No
4
294 divisible by 6?
True
False
5
3,926 is divisible by 9
True
False
Some numbers are divisible by more than one digit.
Using the Divisibility Rules, let's practice.
18 is divisible by how many digits?
Let's see if your choices are correct.
Click
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?
Click
28 is divisible by how many digits?
Let's see if your choices are correct.
Did you guess 2 and 4?
Click
530 is divisible by how many digits?
Let's see if your choices are correct.
Did you guess 2, 5, and 10?
Click
Now it's your turn......
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
6
What are all the digits 15 is divisible by?
7
What are all the digits 36 is divisible by?
8
What are all the digits 1,422 are divisible by?
9
What are all the digits 240 are divisible by?
10
What are all the digits 64 is divisible by?
Patterns in Multiplication and
Division
Click to return to the
table of contents
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.
2
100 can be written as 10 x 10 or 10 .
3
1,000 can be written as 10 x 10 x 10 or 10 .
3
10
The raised digit is called the exponent. The exponent tells
how many tens are multiplied.
3
A number written with an exponent, like 10 , is in exponential
notation.
A number written in a more familiar way, like 1,000 is in
standard notation.
Powers of 10 from ten to one million.
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
1
102
103
10 4
10
5
106
10
It is easy to MULTIPLY a whole number by a power of 10.
Add on as many 0s as appear in the power of 10.
Examples:
28 x 10 = 280
Add on one 0
28 x 100 = 2,800
Add on two 0s
28 x 1,000 = 28,000
Add on three 0s
If you have memorized the basic multiplication facts,
you can solve problems mentally.
Use a pattern when multiplying by powers of 10.
50 x 100
5,000
steps
1. Multiply the digits to the left
of the zeros in each factor.
50 x 100 5 x 1 = 5
2. Count the number of zeros in
each factor.
50 x 100
3. Write the same number of
zeros in the product.
5,000
50 x 100 = 5,000
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.
60 x 400 = _______
steps
1. Multiply the digits to the left of the zeros in each factor.
6 x 4 = 24
2. Count the number of zeros in each factor.
60 x 400
3. Write the same number of zeros in the product.
60 x 400 = _______
steps
1. Multiply the digits to the left of the zeros in each
factor.
6 x 4 = 24
2. Count the number of zeros in each factor.
60 x 400
3. Write the same number of zeros in the product.
60 x 400 = 24,000
500 x 70,000 = _______
steps
1. Multiply the digits to the left of the zeros in each
factor.
5 x 7 = 35
2. Count the number of zeros in each factor.
3. Write the same number of zeros in the product.
500 x 70,000 = _______
steps
1. Multiply the digits to the left of the zeros in each factor.
5 x 7 = 35
2. Count the number of zeros in each factor.
500 x 70,000
3. Write the same number of zeros in the product.
500 x 70,000 = _______
Steps
1. Multiply the digits to the left of the zeros in each factor.
5 x 7 = 35
2. Count the number of zeros in each factor.
500 x 70,000
3. Write the same number of zeros in the product.
500 x 70,000 = 35,000,000
Your Turn....
Write a rule.
Input
Output
50
15,000
7
2,100
300
90,000
20
6,000
rule
Write a rule.
Input
Output
20
18,000
7
6,300
9,000
8,100,000
80
72,000
rule
11
30 x 10 =
12
800 x 1,000 =
13
900 x 10,000 =
14
700 x 5,100 =
15
70 x 8,000 =
16
40 x 500 =
17
1,200 x 3,000 =
18
35 x 1,000 =
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
42,000 / 100 = 420
42,000 / 1,000 = 42
Take off one 0
Take off two 0s
Take off three 0s
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 0s in the dividend
as in the divisor.
2. Complete the division fact.
More Examples:
700 / 10
700 / 10 = 70
8,000 / 10
8,000 / 10 = 800
9,000 / 100
9,000 / 100 = 90
This pattern can be used in other problems
.
1,400 / 700
120 / 30
120 / 30 = 4
1,400 / 700 = 2
44,600 / 200
44,600 / 200 = 223
Your Turn....
Complete. Follow the rule.
Rule: Divide by 50
Input
150
250
3,000
Output
Complete. Find the rule.
Find the rule.
Input
Output
120
40
240
8
2,700
90
19
800 / 10 =
20
16,000 / 100 =
21
1,640 / 10 =
22
210 / 30 =
23
80 / 40 =
24
640 / 80 =
25
4,500 / 50 =
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
-1
10-2
10-3
10 -4
10-5
10-6
10
The number 1 is also called a Power of 10
because 1 = 10
0
10,000s 1,000s 100s 10s 1s
4
10
3
10
2
10
1
10
0
10
.
0.1s 0.01s 0.001s 0.0001s
-1
10
-2
10
-3
10
-4
10
Each exponent is 1 less than the exponent in
the place to its
0
left. This is why mathematicians defined 10 to be equal to 1.
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 1 0 0 0 . (3 places)
to the number 1.
3. Move the decimal point in the other factor
the same number of places, but to the
RIGHT. Insert 0s as needed.
4 5.6 0 0
That's your answer.
So, 1,000 x 45.6 = 45,000
Let's try some together.
10,000 x 0.28 =
$4.50 x 1,000 =
1.04 x 10 =
26
100 x 3.67 =
27
0.28 x 10,000 =
28
1,000 x $8.98 =
29
7.08 x 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.
1,000 = 1,000.
2. Move the decimal point LEFT until you get to 1 0 0 0
the number 1.
3. Move the decimal point in the other number
the same number of places to the LEFT. Insert
0s as needed.
So, 45.6 / 1,000 = 0.00456
. (3 places)
0 0 4 5 .. 6
Let's try some together.
56.7 / 10 =
0.47 / 100 =
$290 / 1,000 =
30
73.8 / 10 =
31
0.35 / 100 =
32
$456 / 1,000 =
33
60 / 10,000 =
34
$89 / 10 =
35
321.9 / 100 =
Division of Whole Numbers
Click to return to the
table of contents
Some division terms to remember....
•
The number to be divided into is known as the dividend
•
The number which divides the other number is known as
the divisor
•
The answer to a division problem is called the quotient
4 quotient
divisor 5
20 ÷ 5 = 4
20 dividend
20 = 4
__
5
Estimating the Quotient helps to break
whole numbers into groups.
Estimating: One-Digit Divisor
8) 689
Divide 8) 68
8
8)689
80
8)689
Write 0 in remaining
place.
80 is the estimate.
x
Let's Practice: One-Digit Estimation
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
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
36
The estimation for 8)241 is 40?
True
False
37
Estimate 663 ÷ 7
38
Estimate 4)345
39
Solve using Estimation Marta baby-sat for
four hours and earned $19. ABOUT how much
money did Marta earn each hour that she babysat?
Estimating: Two-Digit Divisor
26)6,498
Round 26 to its
greatest place.
x
30)6,498
2
30) 6,498
200
30)6,498
Divide 30)64
Write 0 in remaining
places.
200 is the estimate.
Let's Practice Two-Digit Estimation
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
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
40
The estimation for 17)489 is 2?
True
False
41
Estimate 5,145 ÷ 25.
42
Estimate 41)2,130
43
Estimate 31)7,264
44
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 cookies
last?
When we are dividing, we are breaking apart into equal groups
Find 132
Step 1: Can 3 go into
1, no so can 3 go into
Click for step 1
13, yes
Step 2: Bring down the
2. Can 3 go into 12, yes
Click for step 2
3
3
44
132
- 12
12
- 12
0
3 x 4 = 12
13 - 12 = 1
Compare 1 < 3
3 x 4 = 12
12 - 12 = 0
Compare 0 < 3
Step 3: Check your answer.
44
x 3
132
45
Divide and Check 8)296
46
Divide and Check 9)315
47
Divide and check 252 ÷ 6 =
48
Divide and check 9470 ÷ 2 =
49
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?
50
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?
51
There are 6 outs in an inning. How many innings
would have to be played to get 348 outs?
52
How many numbers between 23 and 41 have
NO remainder when divided by 3?
A
4
B
5
C
6
D
11
Sometimes when we break apart a whole number into groups
there is an amount left over.
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.
For example:
4
7)30
-28
2
30 ÷ 7 = 4 R 2
This is the way you may
have previously written it,
with the R meaning the
remainder.
Another example:
23
15)358
-30
58
-45
13
358 ÷ 15 = 23 R 13
We say there are 13 left over (R)
because you can not make a
group of 15 out of 13.
53
A group of six friends have 83 pretzels. If they
want to evenly share them, how many will be left
over?
54
Four teachers want to evenly share 245 pencils.
How many will be left over?
55
Twenty students want to evenly share 48 slices of
pizza. How many slices will be left over?
56
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
4 2
7)30 7
-28
2
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.
More examples of the remainder written as a fraction:
5
7 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
Example:
5
37 7
7 )264
-21
54
-49
5
Check the answer using multiplication and
addition.
Way 1:
37 x 7 + 5 = 259 + 5 = 264
Way 2:
37
x 7
259
+ 5
264
quotient
x divisor
+ remainder
dividend
57
Divide and Check 4)43
(Put answer in as a mixed number.)
58
Divide and check 61 ÷ 3 =
(Put answer in as a mixed number.)
59
Divide and check 145 ÷ 7
(Put answer in as a mixed number.)
60
Divide and Check 2)811
(Put answer in as a mixed number.)
61
Divide and check 309 ÷ 2 =
(Put answer in as a mixed number.)
Divide by a 2 Digit Divisor
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
Find 4575
Step 1: Can 25 go into
4, noClick
so can
go into
for25step
1
45, yes
Step 2: Bring down the
7. Can 25 go into 207,
yes Click for step 2
183
25
4575
- 25
20 7
- 200
75
- 75
0
Step 3: Bring down the
5. Can 25 go into 75, yes
Click for step 3
25
25 x 1 = 25
45 - 25 = 20
Compare 20 < 25
25 x 8 = 200
207 - 200 = 7
Compare 7 < 25
25 x 3 = 75
75 - 75 = 0
Compare 0 < 25
Step 3: Check your answer.
183
x 25
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?
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?
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.
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?
Let's try some problems together, using
our "Silly" Sentence Steps.
62
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
63
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
64
Solve 16)176
65
Solve 329 ÷ 47
66
If 280 chairs are arranged into 35 rows, how
many chairs are in each row?
67
There are 52 snakes. There are 13 cages. If each
cage contains the same number of snakes, how
many snakes are in each cage?
68
Solve 46)3,588
69
Solve 3,672 ÷ 72
When dividing by a Two-Digit Divisor there may be a Remainder. Follow the
Division Steps
.
Divide
Multiply
Subtract
Compare
Bring Down
Repeat
If the Difference in the Last Step of Division is not a Zero, 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 does not make a full group of 77.
Problem:
5 62
77
77) 447
-385
62
Use Multiplication and Addition to check you
Answer.
5 x 77 + 62 = 447
OR
77
x 5
375
+ 62
447
Let's Practice
Remember your Steps: Divide, Multiply, Subtract, Compare,
Bring Down
Write the Remainder as a Fraction
Solve 633 ÷ 36
17 21
36
36) 633
- 36
273
- 252
21
Check your work
CHECK
17
x 36
102
+ 510
612
+ 21
633
Divisor x Quotient +
Remainder = Dividend
70
What is the remainder when 402 is divided by
56?
A
8
B
7
C
19
D
10
71
What is the remainder when 993 is divided by
38?
A
5
B
8
C
13
D
26
72
Divide 80) 104
(Put answer in as a mixed number.)
73
Divide 556 ÷ 35
(Put answer in as a mixed number.)
74
Divide 45)1442
(Put answer in as a mixed number.)
75
Divide 4453 ÷ 55
(Put answer in as a mixed number.)
76
Divide 83)8537
(Put answer in as a mixed number.)
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 people will each get 11 pencils
-5
and there will be 3 left over.
3
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.
77
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?
A
47
B
48
C
49
D
50
78
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?
A
6
B
7
C
8
D
9
79
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
80
For the class trip, 51 people fit on a bus and 267
people are going. How many buses will be
needed?
A
10
B
11
C
12
D
13
Division of Decimals
Click to return to the
table of contents
Divide 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
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
81
Which answer has the decimal point in the
correct location?
A
1285
B
1.285
C
12.85
D
128.5
5
64.25
82
Which answer has the decimal point in the
correct location?
A
561
B
56.1
C
5.61
D
0.561
4
224.4
83
Which answer has the decimal point in the
correct location?
A
51
B
5.1
C
0.51
D
0.051
9
0.459
84
Select the answer with the decimal point in the
correct location.
A
0.1234
B
1.234
C
12.34
D
123.4
E
1234
3 37.02
85
Select the answer with the decimal point in the
correct location.
A
501
B
50.1
C
5.01
D
0.501
E
0.0501
5 .2505
86
6
20.52
87
4
321.6
88
7
2.198
89
11 70.62
90
4
251.2
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't go into 5,
so put a 0 and
bring the 6
down.
91
What is the next step in this division problem?
9.
3
27.21
-27
02
A
Put a 2 in the quotient
B
Put a 0 in the quotient
C
Put a 1 in the quotient
92
What is the next step in this division problem?
0.6
5
3.205
- 30
2
A
Put a 0 in the quotient
B
Put a 2 in the quotient
C
Bring down the 0
93
What is the next step in this division problem?
8.
8
64.48
-64
04
A
Put a 0 in the quotient
B
Put a 4 in the quotient
C
Put a 2 in the quotient
94
6
0.636
95
3
2.406
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
96
What is the first step in this division problem?
6
.468
A
Put a 0 in the quotient in the ones place
B
Put a 0 in the quotient in the tenths place
C
Put a 7 in the quotient
97
What is the first step in this division problem?
24 .1104
A
Put a 0 in the quotient in the tenths and
hundredths place 0
B
Put a 0 in the quotient in the ones place
C
Put a 4 in the quotient
98
5
.435
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
36
-32
4
Instead of
leaving the 4 as
a remainder,
add a zero to
the dividend.
9.45
8
75.60
-72
36
- 32
40
- 40
0
Add a zero to the
dividend.
No remainder now.
99
5
3.26
100 2
87.3
101 6
0.795
102 30 0.843
103 15 0.363
With a whole number dividend, you can add a decimal point and
zeros when you have a remainder.
Example:
You want to save $284 over the next 5 months. How much
money do you need to save each month?
$284 ÷ 5 = _____
56
5
$284
- 25
34
- 30
4
Don't leave it as remainder
4, or as 4/5 add a decimal
point and zeros.
56.8
5
$284.0
- 25
34
- 30
40
-40
0
Since the answer is
in money, write the
answer as $56.80
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
104 5
$63
105 $782 ÷ 9 =
106 7
$593
107 4
$352
108 $48 ÷ 22 =
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
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
By what power of 10 should the divisor and dividend
be multiplied?
.007
4.9
0.3
42.69
By what power of 10 should the divisor and dividend
be multiplied?
7.59
2.0826
÷
÷
2.2
0.06
means
means
109 0.3
42.48
110 Divide
2.592
÷ 0.08 =
111 0.3
0.6876
112
20 divided by 0.25
113 Yogurts each cost $.50 each and you have
$7.25. How many can you buy?