OBJECTIVE: Divide decimal dividends by two-digit divisors,
estimating, quotients, reasoning about the placement of the
decimal point, and making connections to a written method.
Fluency Practice – Rename
Tenths and Hundredths









10 tenths = 1.0
90 tenths = 9.0
93 tenths = 9.3
100 tenths = 10.0
800 tenths = 80.0
483 tenths = 48.3
365 tenths = 36.5
9 hundredths = .09
10 hundredths= 0.10
90 hundredths = .90
97 hundredths = .97
100 hundredths = 1.00
900 hundredths = 9.00
970 hundredths = 9.70
1,000 hundredths = 10.00
5,946 hundredths= 59.46
8,000 hundredths = 80.00
8,417 hundredths = 84.17
Fluency Practice – Divide
Decimals by Multiples of 10
1.2 ÷ 3 = 0.4
 1.2 ÷ 30 = 0.04
 9.6 ÷ 3 = 3.2
 9.6 ÷ 30 = 0.32
8÷4= 2
 8 ÷ 40 = 0.2
 0.45 ÷ 5 = 0.09
 0.45 ÷ 50 = 0.009

Fluency Practice –
Estimate the Quotient

15.4 ÷ 32 = (Think unit form.)
 154 tenths ÷ 32

Round the divisor first and then find a multiple
of 30 close to 154 tenths.
 Divisor = 30 and dividend 150 tenths or 15.0

Write a new division equation to find the
estimated quotient.
 150 tenths ÷ 30 or 15.0 ÷ 30 = 5 tenths = .5

Try the following problems. (Estimate the
quotient.)
 2.53 ÷ 43 2.40 ÷ 40 = 0.06
 29.8 ÷ 31 30 ÷ 30 = 1
 15.98 ÷ 78 16.0 ÷ 80 = .2
Concept Development – Problem 1 & 2
904 ÷ 32 and 456 ÷ 16
 Estimate the quotient
 904 divided by 32 is about 30 and 456 divided
by 16 is about 30.
 Solve the above problem using the standard
algorithm.

28 r 8
32 904
-64
264
- 256
8
28 r 8
16 456
-32
136
- 128
8
Concept Development – Problem 1 & 2

What can you say about 904 ÷ 32 and 456 ÷ 16?
 The quotients are equal.

Does this mean they are equivalent?
 Not necessarily because the dividend and divisor are
different.

How can we determine if they are equivalent?
 We need to divide it farther down to determine if they
are truly equivalent. We can do this by adding the
decimal point in and zeros to the right of the decimal.
 Where is the decimal point located?
○ After the last digit (ones place value) in each dividend.
Concept Development – Problem 1 & 2
Let’s continue with our division problem.
 Think of 9040 tenths and 4560 tenths.

Are the two problems
equivalent?
2 8 .25
2 8 .5
32 904 .00
16 456 .0
No, because the problem
-64
-32
on the left is 28.25 and the
264
number on the right is
6
13
- 256
28.5.
- 128
80
80
-64
-80
160
-160
0
0
Note: Decimal point moves straight up.
Concept Development – Problem 3



834.6 ÷ 26
Estimate the quotient and then solve using the
standard algorithm.
What is your estimate?
 810 ÷ 30 = 27

What is the actual quotient?
 32.1

Does you answer make sense?
3 2 .1
26 834.6
-78
54
- 52
 Yes, because it is fairly close to the estimate.

26
How can we check to make sure the quotient is
-26
correct?
 Complete the opposite function of the original problem
which is multiplication.
0
Concept Development – Problem 3
Check your work.
 Does the product match the dividend?

 Yes the dividend and product are equal.
32.1
x 26
1926
+6420
834.6
Concept Development – Problem 4



48.36 ÷ 39
Estimate the quotient and then solve using the
standard algorithm.
What is your estimate?
 40 ÷ 40 = 1

What is the actual quotient?
 1.24

Does you answer make sense?
1 .2.4
39 48.36
-39
93
- 78
 Yes, because it is fairly close to the estimate.

15 6
How can we check to make sure the quotient is - 156
correct?
 Complete the opposite function of the original problem
which is multiplication.
0
Concept Development – Problem 4
Check your work.
 Does the product match the dividend?

 Yes the dividend and product are equal.
1.24
x 39
1116
+3720
48.36
Concept Development – Problem 5



8.61 ÷ 41
Estimate the quotient and then solve using the
standard algorithm.
What is your estimate?
 8.0 ÷ 40 = .2

What is the actual quotient?
 .21

Does you answer make sense?
.2 1
41 8.61
-82
41
- 41
 Yes, because it is fairly close to the estimate.

How can we check to make sure the quotient is
correct?
 Complete the opposite function of the original problem
which is multiplication.
0
Concept Development – Problem 5
Check your work.
 Does the product match the dividend?

 Yes the dividend and product are equal.
.21
x 41
021
+ 840
8.61
Application Problem

Find the whole number quotient and
remainder of the following two expressions:
 201 ÷ 12 __
> 729 ÷ 45 (Use >, <, or = to complete
the sentence.
1 6 .75
12 201.00
-12
81
- 72
90
-84
60
- 60
0
1 6 .2
45 729.0
-45
279
- 270
90
-90
0
End of Lesson Activities
Debrief
 Problem Set
 Exit Ticket
 Homework

Exit Ticket

1. Estimate. Then, divide using the standard
algorithm and check.
 a) 45.15 ÷ 21
 b) 14.95 ÷ 65

2. We learned today that division expressions
that have the same quotient and remainders are
not necessarily equal to each other. Explain how
this is possible.
Problem Set

156 ÷ 24 and 102 ÷ 15 both have a
quotient of 6 and a remainder of 12.
 (a) Are the division expressions equivalent
to each other? Use your knowledge of
decimal division to justify your answer.
 (b) Construct your own division problem with
a two-digit divisor that has a quotient of a 6
and a remainder of 12 but is not equivalent
to the problems in 1(a).
Problem Set
 Divide, then check your work with multiplication.
 36.14 ÷ 13
62.79 ÷ 23
12.21 ÷ 11
6.89 ÷ 13
 249.6 ÷ 52
24.96 ÷ 52
300.9 ÷ 59
30.09 ÷ 59
 The weight of 72 identical marbles is 183.6 grams.
What is the weight of each marble? Explain how you
know the decimal point of your quotient is placed
reasonably.
 Cameron wants to measure the length of his classroom
using his foot as a length unit. His teacher tells that it
takes him 92 steps. How long is Cameron’s foot in
meters?
 A blue rope is three times as long as a red rope. A
green rope is 5 times as long as the blue rope. If the
total length of the three ropes is 508.25 meters, what is
the length of the blue rope?
Homework
1. Create two whole number division problems
that have a quotient of 9 and a remainder of 5.
Justify which is greater using decimal division.
 2. Divide, then check your work with
multiplication.

 a) 75.9 ÷ 22
b) 97.28 ÷ 19
 3. Divide
 a) 5,224 ÷ 43
c) 77.14 ÷ 38
d) 12.18 ÷ 29
b)1,908 ÷ 36
 4.
Use the quotients in Problem 3 to write the
quotients for the following. Explain how you decided
where to place the decimal in the quotient.
 a) 522.4 ÷ 43 and 52.24 ÷ 43
b) 190.8 ÷ 36 and 19.08 ÷ 36
Homework

5. The height of Burj Dubai, the tallest in the
world (2013), has a total of 162 stories. If the
building is 828 meters tall, about how many
meters tall is each story?

6. Elaine has a desktop that is 4.5 feet by 5.5 feet, and
she is going to cover it with patches of wallpaper that
each measure 18 inches wide and 24 inches long.
 How many patches will Elaine need to cover the entire desktop?
Justify your answer.