Dear Family,
Family Letter
Content
Overview
The main goal of Unit 5 of Math Expressions is to enhance skills
in dividing with whole numbers and decimal numbers. Some
additional goals are:
)
to solve real world application problems,
Þ
to use patterns
Þ
to use estimation to check the
Þ
to interpret remainders.
as an aid in calculating,
reasonableness of answers, and
Your child will learn and practice methods such as Place Value
Sections, Expanded Notation, and Digit-by-Digit to gain
speed and accuracy in multidigit and decimal divísion. Money
examples will be used to help students understand division
with decimals.
Throughout Unit 5, your child will solve real world application
problems that require multidigit division. Your child will learn
to estimate using rounding and other methods, and then to
use estimation to determine whether answers are reasonable.
Remainders will be interpreted in real world contexts, and
expressed as fractions or decimals when appropriate. Students
will learn to distinguish between multiplication and division in
real world situations involving decimals.
lf you have any questions, please call or write to me.
àincerely,
Your child'ø þeacher
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Unit 5 addresses the following standards from the Common Core State Standards for Mathematics with
California Additionsi 5.N8T.2, 5.1'lBT.5, 5.N8T.6, 5,N8T.7, 5.NF.5, 5.NF.5a, and all Mathematical Practices.
UNIT 5 LESSON
1
Divide Whole Numbers by One Digit
161
Estimaàa familia
Carta a la familia
Un vistazo
general al
conten¡do
objetivo principal de la Unidad 5 de Math Expressions
es reforzar las destrezas de división con números enteros y
decimales. Algunos objetivos adicionales son:
El
Þ resolver problemas con aplicaciones a la vida diaria,
> usar patrones como ayuda para hacer cálculos,
)
usar la estimación para comprobar si las respuestas son
razonables, y por último,
)
interpretar residuos.
Su niño aprenderá y practicará métodos como el de Secciones
de valor posicional, Notación extendida y Dígito por dígito, para
realizar divisiones de números de varios dígitos y decimales con
mayor rapidez y exactitud. Como ayuda para comprender las
divisiones con decimales, se usarán ejemplos de dinero.
En la Unidad 5 su niño resolverá problemas con aplicaciones a la
vida diaria que requieran el uso de la división de números de varios
dígitos. Aprenderá a estimar usando el redondeo y otros métodos,
y luego usará la estimación para determinar si las respuestas son
razonables, Los residuos se interpretarán dentro de contextos de
la vida diaria y se expresarán como fracciones o decimales cuando
sea apropiado. Los estudiantes aprenderán a distinguir entre la
multiplicación y la división en situaciones de la vida cotidiana que
involucren decímales.
tiene alguna duda o algún comentario, por favor comuníquese
conmigo.
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Atenlamente,
El maestro àe eu niño
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En la Unidad 5 se aplican los siguientes estándares auxiliares, contenidos en los Estándares estata/es comunes
de matemáticas con adiciones para californla: 5,N8T.2,5,1'¡8T,5,5.1'18T,6,5.N8T.7,5.NF,5,5,1'tF.5a y todos los de prácticas
matemáticas.
162 urur
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Divide Whole Numbers by One Digit
Date
Name
5-1
Class
Activity
fÎtiff
Content Standards 5.NBT.6
Mathematical Practices MP.1, MP.2, MP'4, MP.6, MP.8
VOCABUTARY
Digit-by-Digit Method
Expanded Notation
Method
> Compare Division Methods
An airplane travels the same distance every day.
It travels 3,822 miles in a week. How far does the
airplane travel each day?
Place Value Sections
Method
Rectangle Model
?
3,822
7
PIace Value Sections
Build a new
section with
each leftover
amount.
500
7
3,822
-3,500
+
500
7
3,822
322
-3,500
280
322
322
+
500
40
7
40
a$-546
322
3,822
42
-3,500 -280 -42
322
42
42
Expanded Notation
6
t
40
500
40
s00
3,822
3,500
322
7
Show the
zeros in the
multipliers.
7
3,822
3,500
322
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Put in only
one digit at
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a time.
3,822
s46
7 3,822
3,5
35
32
32
-28
-28
42
42
-42
UNIT 5 LESSON
1
Divide Whole Numbers by One Digit
163
*
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Name
Date
Activity
Class
> Division Problems
Write an equation. Then solve.
Show your Work.
1. A farmer has 2,106 cows and 9 barns. lf the farmer
divides the cows into equal groups, how many cows
will he put in each barn?
2. A sidewalk covers 3,372 square feet. lf the sidewalk
is 4 feet wide, what is its length?
?
4ft
3. Olivia has $8. Her mother has $4,784. The amount
Olivia's mother has is how many times the
amount Olivia has?
)
4. A machine produced 4,650 bottles of seltzer and
put them in packs of six bottles. How many 6-packs
did the machine make?
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5. Raj is 3,288 days old. This is 6 times as old as his niece.
How many days old is Raj's niece?
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6. lf a streamer is unrolled, its area is 3,888 square
inches. lf the streamer is 2 inches wide, how
long is it?
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Divide Whole Numbers by One Digit
Date
Name
Class
Activity
> llVork w¡th Remainders
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The problem at the right might seem unfinished.
The leftover numbe¡ at the bottop i.s cg[ed lhe
remainder. We can write'the answer like tþis: 567 R2.
,
53
7. Could there be a remainder of 9 for the problem?
Why or why not?
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8. What is the greatest possible remainder when dividing by 8?
Complete each division and give the remainder,
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10.7w47
11.5 4,914
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UNIT 5 IESSON 1':
20.7w
Divide Whole Numbèrs by Orire otgit
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Name
5-1
Class
>
Date
Activity
Use Mental Math
to Check for Reasonableness
Miguel has 6 boxes to store 1,350 baseball cards.
He divides and finds that each box will have 225 cards.
To check that his answer is reasonable, he uses
estimation and mental math:
i'l know that 1,200 + 6 is 200 and 1,800 + G is 300.
Because 1,350 is between 1,200 and 1,800, my answer
should be between 200 and 300. lt is."
Solve. Then use mental math to check the solution.
21. s)11s0
22.38,ß3
8.6T4,560
24.
8T7
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25. Kim makes necklaces with colored beads. She used ,l,620
beads for 9 necklaces. How many beads did she use
for each necklace if they have the same number of beads?
26. Saul delivers equally 1,155 newspapers in a 7-day week
How many newspapers does he deliver in a day?
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27.Val earns $1,096 a month as a cashier. She makes $8 an hour,
How many hours does she work in a month?
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28. The Martinson school bought 1,890 water bottles to distribute
equally among students over a 5-day period. How many bottles
are distributed each day?
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Divide Whole Numbers by One Digit
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Activity
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content Standards 5.NBT.6
Mathematical Practices MP.l, MP.3, MP.4, MP.6
> Experiment with Two-Digit Divisors
Rectangle Model
Suppose 2,048 sheep are to be sent on a train.
Each railroad car holds 32 sheep.
To
find how many railroad
?
32
for the
cars are needed
sheep, divide 2,048 by 32.
Discuss how these division methods are alike and different.
Step
1
2
Step
Step 4
SteP 3
Digit-by-Digit
66
64
32
(30¡
Round the divisor,
2,048
2,048
-1
92
128
Estimate the first digit:
30 goes into 200
about 6 times.
-128
Multiply and subtract.
Bring down 8 ones.
Estimate the next
digit and multiply.
Expanded Notation
) 64
Round the
divisor.
Estimate the first number:
Multiply and subtract
30 goes into 2,000
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Estimate the next
number and multiply.
60.32:1,920
about 50 times.
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32
(30)
2,048
32
(30)
2,048
=co
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Round the divisor
and estimate the first
number.
UNIT 5 LESSON 2
Multiply and
subtract.
60+4
60+
60
60
f
32
(30)
2,048
1,920
128
128
Make a new
section.
32
(30)
2,048
@.
128
J28
128
0
Estimate the next
numbeÇ and multiply
and subtract.
Explore Dividing by Two-Digit Whole Numbers
f 67
#
Name
5-2
Class
Date
Activity
> Experiment w¡th Two-Digit Divisors (continued)
Look at Exercises 1-3. Would you round the divisor up or
down to estimate the first digit of the quotient?
Complete each exercise, using any method you choose.
1.7s\,ozz
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2. 21FF3t
3. 18Fp61
Does Estimation Always Work?
Complete Exercise 4 as a class. Does rounding give you a
correct estimate of the first digit? Does it give you a correct
estimate of the next digit? Discuss what you can do to finish
the problem.
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Complete and discuss each exercise below. Use any method
you choose.
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Explore Dividing by Two-Digit Whole Numbers
Date
Name
5-3
Class
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Activity
Content Standards 5.NBT.6
Mathematical Practices MP.2, MP.3, MP'8
VOCABUTARY
overestimate
underestimate
> Underest¡mating
Here are two ways to divide 5,185 + 85. Discuss each method
and answer the questions as a class.
(e0)
10 <-
5
(90) 50
85 5,1 85
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425
93 <-
terrus?
4,250
93s
What does
this number
tell
What does
this number
us?
How do we know that the first
estimated number is not right?
What number should we try next?
Solve the problem using that
number.
How do we know that the first
estimated number is not right this
time? Do we need to erase, or
can we just finish solving the
problem? Try it.
1. When we estimate with a number that is too big (overestimate),
we have to erase and change the number. When we estimate
with a number that is too small (underestimate), do we always
have to erase? Explain your answer.
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Solve each division. You may need to adjust one or both of the
estimated numbers.
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UNIT 5 LESSON 3
Too Large, Too Small, or Just Right?
169
#
Name
5-3
Class
Date
Activity
> Too High or Too Low?
Think about what kind of divisor is most likely to lead to an
estimated number that is wrong. Test your idea by doing the
first step of each problem below.
s.
41)2FE
6. 34ws2s
7.2sfs28
8.
1611A61
9. What kind of divisor is most likely to lead to an estimated
number that is wrong? How can you adjust for these cases?
> Mixed Practice w¡th Adjusted
Estimates
Solve.
Show
your work.
10. Hector is packing 1,375 oranges in
crates that hold 24 oranges each
How many crates will Hector fill?
How many oranges will be left over?
for $26 each. This week the
store sold $5,396 worth of skateboards.
11. Skateboards sell
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How many skateboards were sold?
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12. Ashley's dog Tuffy eats 21 ounces of food for each
meal. Ashley has 1,620 ounces of dog food.
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before Ashley needs to buy more food?
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How many ounces of food
will be left after the last meal?
170
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Too Large, Too Small, or Just Right?
Name
Class
>
Activity
Date
E!t??
Content Standards 5.NBT.6
Mathematical Practices MP.1, MP.3, MP.6
Decide What
to Do w¡th the Remainder
Think about each of these ways to use a remainder.
a
Sometimes you ignore the remainder.
1. A roll of ribbon is 1,780 inches long. lttakes 1 yard
of ribbon (36 inches) to wrap a gift.
How many gifts can be wrapped?
Why do you ignore the remainder?
Sometímes.you round up to the next whole number.
2. There are 247 people traveling to the basketball
tournament by bus. Each bus holds 52 people.
How many buses will be needed?
Why do you round up?
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Sometimes you use the remainder to form a fraction.
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3. The 28 students in Mrs. Colby's class will share 98 slices of
pizza equally.
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Look at the division shown here. Explain how to get
the fraction after you find the remainder.
UNIT 5 LEssON 4
lnterpret Remainders
1
71
Name
5-4
Class
Date
Activity
> Decide What to Do w¡th the Remainder (continued)
sometimes you use a decímal number instead
of the remainder.
Suppose 16 friends earned $¡+g at a car wash. They want to divide
the money equally. The division at the right shows that each friend
gets $21, and there are $12 leftover. Dividing the $12, each friend
gets an additional
or
a dollan for a total of $2t.lS.
ft,
21.75
16Þ48
-32
1,of
28
4. A rectangular garden has an area of 882 square meters.
The long side of the garden has a length of 35 meters.
How long is the short side?
Sometímes the remainder is the answer
to
16
12
the problem.
5. A bagel shop has 138 bagelsto be packed into boxes
of 12 to be sol!. The extra bagels are for the workers.
How many bagels will the workers get?
Why
is
the remainder the answer?
> Solve Problems lnvolving
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Solve.
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6. At the Cactus Flower Cafe, all the tips are divided equally
among the waiters. Last night, the 16 waiters took in
$1,t08 in tips. How much did each waiter get?
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7. A gardener needs to move 2,150 pounds of dirt. He can
carry 98 pounds in his wheelbarrow. How many trips will
he need to make with the wheelbarrow?
172
urulr s LEssoN 4
lnterpret Remainders
Date
Name
Class
Activity
> Solve Problems lnvolving
Remainders (continued)
Solve.
Show your work.
8. Mia must work 133 hours during the month of May.
Therè are 2"1working days in May this year. How many
hours per day will Mia work if she works the same
number of hours each day?
9. Colored markers cost 78 cents each. Pablo has $21.63 in
his pocket. How many markers can Pablo buy?
10. A meat packer has 180 kilograms of ground meat' He
will divide it equally into 50 packages. How much will
each package weigh?
11. ln volleyball, there are 12 players on the court. lf
75 people all want to play volleyball at a gym that has
more than enough courts, how many of them must sit
out at one time?
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12. At the Fourth of July celebration, 1,408 ounces of
lemonade will be shared equally by 88 people. How
many ounces of lemonade will each person get?
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to ride the bus each day. He
took Y+.ù to the bank and asked to have it changed
13. Armando needs quarters
into quarters. How many quarters did he get?
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UNIT 5 LESSON 4
lnterpret Remainders
173
5-4
Class
Name
Date
Activity
> What's the Error?
Deor Moth Students,
I om moving, ond I need to pock my sordines.
I hove 1J00 cons of sordines, ond i know I
con
fit
tl8 cons in eoch box.
I divided to figure out how mony boxes I
needed. I bought 35 boxes, but i hod some
cons leftover. Whot did I do wrong?
35
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144
260
240
20
Your friend,
Puzzled Penguin
14. Write a response
to Puzzled
Penguin.
> Write Your Own Problem
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15. Write a word problem that involves a division that has
a remainder. Solve your problem and explain what
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lnterpret Remainders
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G[fÐ Conten
Mathematlcal
P
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1, MP.6
¿rnsldorg broW noizivi0 svlo2 q
> Practice Dividing
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Name
5-5
Class
Date
Activity
> Solve Division Word Problems
Solve.
ShoW
your t¡tork.
16. The Thomas's rectangular backyard has an area of
2,352 square feet. lf the yard is 56 feet long, how wide is it?
17. Milo wants to make guacamole for a party. Avocados
are on sale for 84C each. How many avocados can Milo
buy if he has $l.lSZ
18. One quart is equal to 32 ounces. How many quarts are
equal To 6,672 ounces?
19. Students in the marching band sold calendars to raise
money for new uniforms. Violet sold 24 calendars for a
total of $186. How much did each calendar cost?
20. only 37 fans came to watch the volleyball team's first match
At the last match,2,035 fans came to watch. The number
of fans at the last match was how many times the
number at the first?
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21. Ayala has 655 computer files she wants to put on CDs.
lf she can fit 18 fíles on each CD, how many CDs will she need?
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22. Ms. Adams wrote a 36-page short story that she wants to
send to publishers. She buys a 500-sheet package of paper
and prints as many copies of the story as she can. How many
sheets does she have left over?
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Division Practice
Date
Name
Class
Activity
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Content Standards 5.NBT.7
Mathematical Practices MP.l, MP.4, MP.6, MP.7, MP'8
> Divide a Decimal by a One'Digit
Number
Three friends set up a lemonade stand and made $ZO'ZS.
They will share the money equally. Study the steps below to see
how much money each person should get.
When the $20 ¡s
split 3 ways, each
person gets $6.
There ¡s $Z left.
We change the $2
to 20 dimes and
add the other
2 dimes. There are
22 dimes.
6
6.
3fñ.zs
-18
3T2o.zs
-18
When we split
22 dimes 3 ways,
each person gets
7 dimes. There is
1 dime left.
6.7
3Tæ.::
-18
6.75
3fñ.2s
-18
2.2
2.2
-2.1
-2.1
2.2
2
We change the
dime to 10 cents
and add the other
5 cents. Now we
split 15 cents
3 ways.
.15
1
-.15
Solve
2. s)58.68
1. 8T47.68
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Write an equation. Then solve.
of rope. She wants to cut it into
3 equal pieces to make jump ropes for her 3 friends' How
long will each jump rope be?
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.9.
3. 6Þ162
has 8.169 meters
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6. Tonio has7.47 pounds of rabbit food. He will divide it
equally among his 9 rabbits. How much food will each
rabbit get?
UNIT 5 LESSON 6
Divide Decimal Numbers by Whole Numbers
177
Name
5-6
Class
Date
Activity
> Divide a Decimal by a Two-Digit
Number
A company bought 38 sandwiches for a business meeting.
Each sandwich costs the same amount. The sandwiches
cost $ 161.12 in all. What was the price of each sandwich?
To answer this questíon, we have to divide the total price
among the 38 sandwiches. We round the diviso4 38, up to 40
to estimate the multipliers.
When $tet ¡s
divided into
38 parts, each part
is $4. There is
$9 left.
We change the
$g to 90 dimes and
add the other dime
There are 91 dimes.
When we split
91 dimes into
38 parts, each part
is 2 dimes. There
are 15 dimes left.
We change the
15 dimes to 150
pennies and add
the other 2 pennies.
Now we split 152
pennies 38 ways.
4.24
38)161.12
øq
(40)
38
-152
-1s2
9
9.1
9.1
9.1
-7.6
-7.6
1.5
1.52
-1.52
5olve.
7. 51 374.8s
s. 22F8O8
e. 7sF0668
10.
36fs472
o
r
o
c
@
f
Write an equation. Then solve.
ô
=
11. A rectangle has an area of 35.75 square meters
and a length of 11 meters. What is its width?
?
l
I
0,
o-
o
c
f
t
co
ø
12. Katsu bought 18 pounds of apples for 923.04.
What was the price for each pound?
178
urulr s LEssoN
6
'11 m
Area =
33.75 sq. m
l=
(o
o
o
3
E
Â)
a
Divide Decimal Numbers by Whole Nurnbers
Date
Name
5-6
Class
Activity
> Add Zeros to the Dividend
Adding zeros at the end of a numbel after the decimal point,
does not change the value of the number. This idea can help us
solve some division problems.
Eight friends bought movie t¡ckets. The total cost for the tickets
was $78. How much d¡d each friend pay?
When the $78 is divided
among 8 people, each
person pays $9, and there
is $6 still left to divide.
Add a decimal point and
a 0. Bring down the 0
(trade $6 for 60 dimes) and
continue to divide. Each
person pays 7 dimes more,
and there are 4 dimes left
to divide.
9
8FB'
-72
6
c(ú
è
E
ooq)
c
I
.9,
o
Add another 0 after the
decimal point. Bring down
the 0 (trade 4 dimes for
40 pennies) and finish
dividing. Each person pays
5 pennies more, for a total
of $9.2s.
9.7
9.75
8FE¡-72
8FB¡õ-
6.0
5.6
.4
6.0
5.6
.40
.40
-72
-
13. Jun rode her bike to the bookstore and back. According
to her bike's odometel the round trip distance was
6.65 miles. She started the division at the right to figur:e
out the one-way distance to the bookstore. Add a 0
to the end of the dividend and finish the division.
The distance to the bookstore
is
miles.
0.6
-.6
.0s
-.04
01
È
=
o
o
(l
T
.=
E
=co
E
o
f
o
I
Solve.
14.6fs4.7s
1s.
sflHLz
16.8)310
17. 26T422,s
@
UNIT 5 LESSON 6
Divide Decimal Numbers by Whole lrlumbers
179
-
5-6
Name
Date
Class Activity
> Patterns ¡n Division by Powers of l0
10, such as 101, ,l02, and 103 represent
repeated multiplication with 10. The exponent tells you how
Recall
that powers of
many times to use 10 as a factor.
101
: 10
102: 10 x
10: 100 103: 10 x lO x 10:
1,000
Study the patterns in Exercises 18 and 19. Then complete
Exercises 20-23.
10:916.2+1oo:-
2',.916.2+
916.2
22.
+ l,ooo:
:4,07G+lo2:4,076+ l0r
4,07G
23.7.9+ l0r
:_
7.g+lo2:
+ 103:
7.9
+
103
-
24. Complete these statements to summ arize your work in Exercises l8-23.
-
-
right
b. Dividing a number by 102, or 100, shiftsthe digitstothe right
c. Dividing a number by 103, or 1,OOO, shiftsthe digitstothe right
a. Dividing a number by
101,
or 10, shifts the digits to the
place(s).
place(s).
place(s)
> Patterns Relating Multiplication and Division
use the multiplication problem to help you solve the division problem
r,1 r1+r'
=
o
l
õ
o
C
f
c1'
8x-:3.2
g
Ø
=
23.0.032+8:
0.32
-:
29.6.3+9:
Urutf 5 LESSON
@
IA'
26.3.2+8:
gx
_:
=
@
C)
ó
3
0.032
Solve by using mental math.
180
I
E
='
25.32+8:
8x-=32
27.0.32+8:
8x
@
o
30.0.15+3:_
6
31.4.g+6:
oivide Decimal Numbers by Whole Numbers
!,
!¡
a
Class
>
Date
Name
5-7
t?ft""
Activity
content Standards 5.N8T.2, 5.NBT.7
Mathematical Practices MP.1, MP.z, MP.3, MP.6, MP.8
Use Money
to See Sh¡ft Patterns
Jordan earns SZ{Z a week. The money is shown here.
Jordan's Earnings in Dollars
24
$
5Z+2. 1:
3
$Z+E
Answer each question about how much Jordan earns in coins.
1. How many dimes ($O.tO) does he
earn?
Jordan,s Earnings in Dimes
2
430
100
2. What happens to each dollar? Why?
ru
rooo@llroo@
roo@
10
(D
roo@
3. What happens to the number showing Jordan's
earnings? Why?
c(d
o
E
o
o
4. When you divide by 0.1, does each digit shift
.o
right or left? Why?
¡l
o)
c
I
fL
J
o
I(d
I
=
=o
o)
a
o
5. How many places does each digit shift? Why?
I
o
UNIT 5 LESSON 7
Divide Whole Numbers by Decimal Numbers
181
ê
Name
Class
Date
Activity
> Use Money to See Sh¡ft Patterns (continued)
6. How many pennies ($O.Ot) does he earn?
Jordan's Earnings in Pennies
24,300
7. What happens
to each dollar?
0,000
0,000
8. What happens to the number showing Jordan's
earnings?
+
000
1
000
roo(!
000
100
0.01
000
0.01:24,300
9. When you divide by 0.01, does each digit shift
right or left? Why?
10. How many places does each digit shift? Why?
11. How many tenths of a cent ($O.OOt) does he
earn?
12. What happens
to each dollar?
Joldan's Earnings in Tenths of a Cent
243
000
r00,000{ r0,000{
ru
t00,000{ 10,000{ 1000\
t0,000\ 000{
t0,000{
243
+ 0.001=
@
13. What happens to the number showing Jordan's
earnings? Why?
Io
c
G
=
o
f
='
I
!)
õ
o
c
14. When you divide by 0.001, does each digit shift
right or left? Why?
f
1'
_g
Ø
J
@
c)
ó
3
g
!
15. How many places does each digit shift? Why?
182
ururr s LEssoN 7
Divide Whole Numbers by Decimal Numbers
Date
Name
Class
Activity
> Relate Decimal Division to Multiplication
Solve.
Show Y ovr work.
16. Mrs. Moreno made 1 liter of grape jelly. She will pour it
into jars that each hold 0.1 liter. How many jars will
she need?
Think: How many tenths are there in 1 whole?
Complete the equation: 1 + 0.1
=
.
This answer is the same as 1 x
17. Mr. Moreno made 2 liters of spaghetti sauce. He will
pour it into jars that each hold 0.1 liter. How many
jars will he need?
Think: How many tenths are there in 1 whole?
How many tenths are there in 2 wholes?
Complete the equation: 2
+ 0.1 =
.
This answer is the same as 2 x
18. The Morenos made a kiloliter of fruit punch for a large
party. They will pour it into punch bowls that each hold
0.01 kiloliter. How many bowls will they need?
Think: How many hundredths are there in 1 whole?
c
ñ
ct
E
o
Complete the equation: 1 + 0.01
o
E)
,g
=
.9
This answer is the same as 1 x
-
ã
=
À
Ë
f
o
e
(ú
x
19. When we divide a number by a decimal number less than one,
why is the quotient greater than the original number?
c
È
=o
E
ct)
a
o
T
@
UNIT 5 LESSON 7
Divide Whole Numbers by Decimal Numbers
183
Name
5-7
Class
Date
Activity
> What's the Error?
Deor Moth Students,
I wos obsent todoy. My friend told me we leorned to
divide by 0.1 ond 0.01. She soid thot when you divide
by 0.1, the digits shift one ploce, ond when you divide
by 0.01, they shift two ploces. Here ore two problems
from my homework.
rl5
+ 0.1 =
rl.5
rl5
+ 0.01 =
Are my onswers correct?
If
0.$5
not, con you exploin whot
I did wrong?
Your friend,
Puzzled Penguin
20. Write a response to the Puzzled Penguin.
>
Change Decimal Divisors to Whole Numbers
You can use the strategy below to change a division problem
with a decimal divisor to an equivalent problem with a whole
number divisor.
Discuss each step used
Step 1: Write 6
@
Io
E
J
to find 6 + 0,2.
@
o
Step 2: Make an equivalent fraction with a whole
number divisor by muttiptying
úu I
U9
the form of
Now you can diü-ide 60 by 2.
13.
¡;
21. Why is the answer to 60
f
6 + 0.2 :
#
+ 0.2 as a fraction.
#
xt:
O9
f
Ip,
, Í3
60
2
o
ç
f
!c
q
ø
+ 2 the same as the answer to 6 + 0.2?
l
=
@
o
o
3
E
D
a
184
ururr 5 LEssoN 7
Divide Whole Numbers by Decimal Numbers
Date
Name
5-7
Class
Activity
> Change Decimal Divisors to Whole Numbers
(continued)
You can use the strategy of multiplying both numbers by 10 even
when a division problem is given in long division format.
Step 1: Put a decimal point after the whole number.
0.2I6.
Step 2: Multiply both numbers by 10, which shifts the
digits one place left. Show this by moving the
decimal point one place right. Add zeros if
0.2.
i6¡:
U ,U
necessary.
30.
Step 3: lnstead of drawing arrows, you can make little
marks called carets (") to show where you put
the "new" decimal points. Now divide 60 by 2.
0.2^ ) 6.0^
22. Why does moving both decimal points the same number
of places give us the same answer?
Answer each question to describe how to find 6 + 0.02 and
6
+ 0.002.
23. Suppose you want to find 6
(!
By
+
0.02.
what number can you multiply 0.02 to get a whole number?
ct
E
oo
o)
.g
E
.9
Describe and show how to move the decimal points
6 + 0.02 by long division.
to solve
o.o2 )6.
!
f
fr
È
f
o
g
6
I
=
=o
24. Suppose you want to find 6
By
+
0.002.
what number can you multiply 0.002 to get a whole number?
o)
f
ro
@
Describe and show how
6 + 0.002.
UNIT 5 LESSON 7
to move the decimal points to solve
o.oo2 )6.
Divide Whole Numbers by Decimal Numbers
185
Name
5-7
Class
Date
Activity
> Practice Dividing by Decimals
Solve.
2s. o.s)25
26.0.07fs6
27. O.8f4s6
28.0.6s)910
2e.0.12w
30. 0.004116-
31. O.s)468
32.0.75f270
33.0.3)s6-
34.0.06f42
3s.
0.072w6
Solve
36.2.4f1s2
Show v our work.
37. A dime weighs about 0.08 ounce. Jake has a pound
(16 ounces) of dimes. About how many dimes does
he have?
38. A quarter weighs about 0.2 ounce. Naoki has
2 pounds (32 ounces) of quarters. About how
many quarters does he have?
o
I
o
G
J
o
f
39. A dime is about 0.14 centimeter thick. Zeynep
made a stack of dimes 35 centimeters high.
About how many dimes did she use?
5'
r
0)
ð
o
c
f
c1'
g
Ø
f=.
@
o
o
40. A newborn mouse weighs about 0.25 ounce. A
newborn cat weighs about 4 ounces. A newborn cat
weighs how many times as much as a newborn mouse?
186 urur s LEssoN
7
Divide Whole Numbers by Decimal Numbers
3
E
Ð
l
Date
Name
Class
>
Activity
Use Money
t?it?"
Content Standards 5.N8T.2, 5.NBT.7
Mathematical Practices MP.l , MP.2, MP.3, MP.6, MP'7
to See Sh¡ft Patterns
It costs $O.Et2 (31 cents and fr cent) to make one Cat's
Marble. The money is shown here.
Eye
Cost of a Cat's Eye Marble
031
$
@o
Ë
$0.312
+ 1= $0.312
@
@
2
\
{
Answer each question about the different coins.
312
1. How many dimes ($o.tO) does it cost to make
one Cat's Eye Marble?
0.1@ o.oz@
+
2. What happens to the number that shows
the cost?
0.1
0.312 +
0.1:3.12
3. When you divide by 0.1, does each digit shift to
the right or left? Why?
c(ú
a
E
oo
CD
.E
g
.!2
õJ
fL
4. How many places does each digit shift? Why?
Ê
J
o
e
(ü
I
¡=
=co
c
ED
=
o
T
o
UNIT 5 LESSON 8
Divide with Two Decimal Numbers
187
5-8
Name
Date
Class Activity
> Use Money to See Sh¡ft Patterns (continued)
5. How many pennies ($O.Ot) does it cost
one Cat's Eye Marble?
312
to make
300
+
6. What happens to the number that shows
the cost?
rf
0.20
0.01
0.312
+0.01:31.2
7. When you divide by 0.01, does each digit shift
to the right or left? Why?
8. How many places does each digit shift? Why?
9. How many tenths of a cent ($O.OOt) does it
cost to make one Cat's Eye Marble?
312
roo{ 10{
+
10. What happens
z{
0.001
to the number that shows
the cost?
0.312 + 0.001= 312
o
11. When you divide by 0.001, does each digit shift
to the right or left? How many places? Why?
xo
E
GI
=
o
=
=
ã
=
I
A'
12. Are the shift patterns for dividing by 0.1, O.Ol,
and 0.001 the same when the product (dividend)
is a decimal number as when the product (dividend)
is a whole number? Wh¡¡ or why not?
õ
o
c
f
!c
g
6'
J
f
(o
c,
0
3
!
!¡
f
188
urulr s LEssoN 8
Divide with Two Decimal Numbers
Date
Name
5-8
> Change Decimal Divisors to Whole Numbers
To divide a decimal by a decimal, use the same strategy
you used when you divided a whole number by a decimal.
D¡scrsr each step used to find 0.06
Step 1: Write 0.06
+
+ 0.2.
0.06+0.2:tf
0.2 as a fraction.
Step 2: Make an equivalent fraction
with a whole number divisor bY
multiplyins :bf by 1 in the form
ruow diùÏde 0.6 by 2.
of
$fxt:%5"
10
_
102
0.6
iå.
13. Why does 0.06
+
0.2 have the same answer as 0'6
+
2?
Here are the steps for using the strategy when the problem
is in long division form.
É
(ú
o.
E
o
O
o
.9
õf
Step 1: Set up the problem.
o.2Io 06
Step 2: Multiply both numbers by 10. This shifts
the digits one place left. Show this by
moving the decimal point one place right.
0.2. 0.0.6
Step 3: You don't have to draw arrows. Carets (^)
show where each "new" decimal Point
belongs. Now divide 0.6 by 2.
0.2^Jo'0^6
U
U
3
fL
È
f
o
e
(ú
I
É
E
=o
14. Why does moving both decimal points the
same number of places give a problem with
the same answer
as
the original problem?
CD
o
I
o
UNIT 5 LESSON 8
Divide with Two Decimal Numbers
189
,f
Name
Class
Date
Activity
> Change Decimal Divisors to
Whole Numbers (continued)
15. How would you solve 0.06 + 0.02 with long division?
What number do you need to multiply both numbers
by to make 0.02 a whole number?
o.o2
16. How would you solve 0.06 + 0.002 with long division?
What number do you need to multiply both numbers
by to make 0.002 a whole number?
o.oo2
)õ06
)¡¡6--
Solve each division problem. Show your work.
n. o.enz
18. 0.04re36rt
1e.0.6fù372
20. 0.14n.28
Write an equation. Then solve.
21. A sand and gravel company has .l2.6 tons of
gravel to haul today. Each truck can carry 0.9 ton
of gravel. How many trucks will be needed?
@
xo
q
(c)
f
o
=
='
I
Ât
22. A developer is building an amusement park on a
rectangular lot with an area of 1.35 square miles.
The length of one side of the lot is 0.45 mile.
?
r:.tl.r
ururr s LEssoN 8
'o
çg
6',
f
0.45 mi
@
c)
0
3
What is the length of the other side?
190
õ
o
E
f
!
0)
f
Divide with Two Decimal Numbers
*
'
5-9
Class
Activity
Date
Name
l?:t?"
Content Standards 5.N8T.6, 5.NBT.7
Mathematical Practices MP.1, MP.2, MP.7
> Divide Mentally
Use the fact
that 1,715 + 35 : 49 to solve each problem
1.3sI17rs
2.35f'17L5
3. 0.3s 0.1715
4.35T17,150
s.3.5F,7rt
6.0.35F,715
7.3.5T'17:.5
8. O.3sF.71s
> Solve Division
Problems
Solve. lf both numbers are whole numbers, give your
answer as a whole number with a remainder.
e.
0.6)s4
10.
O.O8nz
12. O.OTTOAS
11. O.s)O¿s
13. o.os)Erts
14.7w
1s. o.o4s)zl
17. o.o2)sB^8
18.6)eSo
19. O.O4f"l17
-8s
16. 42Epse
(!
o.
E
oo
o
.=
.9
!
=
fL
Ë
=
o
20. 0.081 64.881
e
(ú
I
c
¡Ë
=co
=o)
)
o
I
@
UNIT 5 LESSON 9
Division Practice
191
Name
5-9
Class
Date
Activity
> Check for Reasonable
Answers
Solve. Check that your answer is reasonable.
Show your work
21. The Clark family is having a big lawn party. They have
196 chairs, and they want to put 8 chairs at each table.
How many chairs will be left over?
22. Liam needs to buy 640 eggs for a soccer breakfast. lf eggs
come in cartons of 18, how many cartons should he buy?
23. Jacob made $SOZ th¡s year delivering newspapers. lf he makes the
same amount monthly, how much money did he make each month?
24. Johna and Pedro made a rectangular banner to display
at the school volleyball game. The area of the banner is
7 square meters, and its length is 4 meters. What is the
width of the banner?
25. Lakisha and Raj went to an electronics store. Lakisha bought
a television for $¡SA.¿0. This is 28 times as much as Raj spent
on a new video game. How much did Raj's video game cost?
o
T
o
E
@
=
ô
26. The Ramsey family collects and sells maple syrup. Last
month they collected 57.8 liters of syrup. They will
pour it into bottles that hold 0.85 liter. How many
bottles will the Ramseys fill?
5'
I
À)
õ
ço
f
llc
g
ø
f=
(o
o
o
3
E
Â)
27. Kyle spent $Zl .Zg on postage stamps today. Each stamp
cost 44 cents ($0.++). How many stamps did Kyle buy?
192
urrrrr s LESsoN 9
f
Division Practice
ü
ì
5-10
Class
Activity
Date
Name
l?:lt"
€ontent Standards 5.N8T.5, 5.NBT.6, 5.N8T.7,
5,NF.5, 5.NF.5a Mathematical Practices MP,1, MR2,
MP.3, MP.6, MP.8
> Multiply or Divide?
Read the problem. Then answer the questions.
1. A turtle walks 0.2 mile in
t
hour. How far can it walk in 0.5 hour?
a. Do you need to multiply or divide to solve?
b. W¡ll the answer be more or less than 0.2 miles?
c.
What is the answer?
2. Gus ran 3,6 miles. He took a sip of water every 0.9 mile.
How many sips did he take?
a. Do you need to multiply or divide to solve?
t2
b. W¡ll the answer be greater or less than 3.6?
c.
What is the answer?
3. Last year 135 cows on Dixie's Dairy Farm had calves.
This year 0.6 times that many cows had calves. How many
cows had calves this year?
a. Do you need to multiply or divide to solve?
b. Will the answer be greater or less than 135?
c.
c(ú
è
What is the answer?
4. A box contains 1.2 pounds of cereal. A serving weighs
0.08 pounds. How many servings are in the box?
E
oo
o)
Ë
,9
ô
fL
o
g
(ú
I
¡=
=co
o)
f
a. Do you need to multiply or divide to solve?
b. W¡ll the answer be greater or less than 1.2?
c.
What is the answer?
5. A rectangular patio has an area of 131.52 square meters
The width of the patio is 9.6 meters. What is its length?
o
Í.
o
a. Do you negd to multiply or divide to solve?
b. W¡ll the answer be greater or less than 131.52 meters?
c.
What is the answer?
UNIT 5 LESSON
1O
Distinguish Between Multiplication and Division
193
Name
5-10
Class
Date
Activity
> Results of Whole Number and
Decimal Operations
Answer each question.
x
6. ff a and b are whole numbers greater than 1, will b
be greater than or less than a? Why?
a
7.lf a is a whole number and d is a decimal less than 1, will
d x a be greater than or less than a? Why?
8. lf a and b are whole numbers greater than 1, will a
be greater than or less than a? Why?
9. lf a is a whole number and d is a decimal less than
will a + d be greater than or less than a? Why?
+b
1,
@
-oc
@
Ð
o
5
5'
I
Use reasoning to compare the expressions. Write
Do not compute the actual values.
o
o
o
), (, or :.
c
f
1'
g
Ø
=,
10.42 x 356
356
+
42
11. 0.65
12.832
+ 67
832
+
0.67
13.738 x 66
14. 126
+ 0.9
561
561
+ 0.65
o
o
3
!t
A'
16.64 x 0.64
194 u¡¡r
x
@
5 LEssoN 1o
126
64
x
+
738 x
a
0.66
0.9
15. 3,500
x
0.7
3,500
0.64
17. 5,602
+
42
5,602
x
+
7
0.42
Distinguish Between Multiplication and Division
I
5-10
Class
Date
Name
Activity
> Make Predictions
Show v our work.
Solve.
18. Farmer Ortigoza has 124.6 acres of land. Farmer Ruben
has 0.8 times as much land as Farmer Ortigoza.
a. Does Farmer Ruben have more or less than 124.6 acres?
b. How many acres does Farmer Ruben have?
19. Mee Young has 48 meters of crepe paper. She will cut it
into strips that are each 0.6 meter long.
a.
Will Mee Young get more or fewer than 48 strips?
b. How many strips will Mee Young get?
20. Jenn's garden is a rectangle with length 3.5 meters and
width 0.75 meters.
a. ls the area of the garden greater or less than
3.5 square meters?
b. What is the area of the garden?
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21. Roberto can l¡ft 103.5 pounds. That is 0.9 times the
amount his friend Vance can lift.
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lift more or less than
103.5 pounds?
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b. How many pounds can Vance lift?
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22. The Daisy Cafe served 18 liters of hot chocolate today
Each serving was in a cup that held 0.2 liter.
a. Did the cafe serve more or fewer than 18 cups of
hot chocolate?
b. How many cups did the cafe serve?
UNIT 5 LESSON
1O
Distinguish Between Multiplication and Division
195
Name
5-10
Date
Class Activity
> Mixed Practice
Solve. Check your work.
æ.
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27.
x
0.4
0.8
24.4Wß
2s.27f&91
26.34fLs64
28.
29.
30.
x
28
0.63
31.0.8Fs2
32.0.13)G8e
35.
36
x
0.37
0.09
x
0.75
0.14
0.35
x94
33. o.e6)z6o-8
34.
37.
38
51 .3
x
6.2
78.6
x49
I.en
x
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4.29
0.27
> Mixed Real World Applications
Solve. Check that your answer is reasonable.
ShoW
yo.rr Work.
39. Polly bough! 12 beach balls for her beach party. She
spent $23.64. How much did each beach ball cost?
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40. The 245 f¡fth graders at Miller School are going on a
tríp to the aquarium. Each van can carry 16 students.
How many vans will be needed for the trip?
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41. Today Aaliyah ran 4.5 miles per hour for three'fourths
(0.2S) of an hour. How far did Aaliyah run today?
196
ururr s LEssoN
1o
Distinguish Between Mult¡plication and Division
5-f
Class
Date
Name
1
Activity
fttlfftf
Content Standârds 5.NBT.7
Mathematical Practices MP.l, MP.7
> Math and Currency
When you travel from one country to another, you sometimes
need to exchange your currency for the currency used in the
country ypu are visiting, An exchange rate is the rate at which
one currency can be exchanged for another.
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Currencies are usually compared to 1 U.S. dollar (1 USD) when
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they are exchanged. For exarnple, 1 USD may be exchanged for
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¡65 6.5 Chinese yuans or 0.95 Canadian dollars. The exact amount
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of the exchange often varies from day to day.
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Show v our work.
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1. Suppose 5 U.S. dollars (5 USD) can be exchanged for
64 Mexican pesos. What operation would be used to find
the value of 1 USD in pesos?
Find the value
UNIT 5 LESSON
11
of
1 USD in pesos.l USD
:
pesos
Focus on Mathematical Practices
197
Name
5-1f
Class
Date
Activity
> Math and Currency (continued)
Complete the exchange rate column of the table.
Country
Equivalent
Amounts
Currency Unit
yen
2. Japan
3. England
pound
4. Germany
Euro
Exchange Rate
20 USD = 1,530 yen
10 USD :6.1
50 USD
:
pounds
35 Euros
1 USD
1
:
USD:
1
-yen
USD:
pounds
Euros
Visiting another country often means exchanging more than
1 USD for the currency of that country.
5. The exchange rate for francs, the currency of Switzerland,
is 10 USD : 8.8 francs. At that rate, how many francs
would be exchanged for 25 USD?
6. A traveler in Latvia exchanged 5 USD lor 2.G lats. At that
rate, what is the cost of a souvenir in lats if the cost is 3 USD?
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7. A tourist would like to exchange .l00 USD for kuna, the
currency of Croatia. At the rate 12 USD 66 kuna, how
many kuna should the tourist receive?
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8. The cost to visit a famous tourist attraction in Russia is
381.25 rubles. What is the cost in USD if the exchange
rate is 3 USD : 91.5 rubles?
198
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11
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Focus on Mathematical Practices
Date
Name
UNIT 5
Review/Test
1. Select the expression that involves a shift of the digits to the right
2 places. Mark all that apply.
+ 1,000
30 + 102
9
2+103
7+10
400 + 101
8+1oO
2.
Classify each quotient as being equal to 52, equal to 5.2, or equal
0.52. Write the letter of the quotient in the correct box.
A52+102
D 520 + 102
B 52+101
E 520 + 103
3.
Explain why
C 520+101
F 5,200 + 103
0.s2
5.2
52
0.04þ5
has
to
the same answer
as
4)360
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4. Why does dividing
than
5 by a decimal less than 1 give a quotient greater
5?
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5. A farmer ships 4 times
as many oranges as tangerines. The farmer ships
8,260 oranges. How many tangerines does he ship? Write an equation.
Then solve.
UNIT 5 TEST
199
Name
UNIT 5
Date
Review/Test
6. Jamal buys postcards of Washington,
D.C., for $,l0.20, not including tax
Each postcard costs $O.AS. How many postcards does Jamal buy?
postcards
7.
Paige's backyard has an area of 95.9 square meters. The length of the
yard is 14 meters, what is its width?
14m
Area
:95.9
m2 7
meters
8.
Mr. Adams divides 223 markers equally among the 26 students in his
class. He puts the extra markers in a box. what is the least number of
markers he puts in the box?
markers
9. A park creates new habitats for
182 monkeys. Each habitat
will house
8 or fewer monkeys.
Part A
What
is
the least number of habitats the zoo will need?
habitats
Part
B
What did you do with the remainder? Explain why.
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10. Solve. Express the remainder as a whole number. Show your work.
Draw a model to show how you solved the problem.
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Date
Name
UNIT 5
Review/Test
11. Circle the word or phrase that makes the sentence true.
When you divide by 100, each digit shifts
one place
right
to the
by
left
two
places
three places
12. Select each quotient that is correct. Mark allthat apply.
300
+ 100:3
+ 10:0.03
27 + 100:0.27
60 + 10:600
3
13. F¡ll in the table to complete the pattern of dividing by
powers of ten.
x 10
4.72
+ 0.1
4.72
4.72
+
4.72 x
4.72
+
0.01
14. Solve. 2,412
4.72
x
472
1,000
+ 3. Explain how you know your answer
is reasonable.
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15. Nina is putting equal amounts of oatmeal into 4 containers.
She has 37.6 ounces of oatmeal. How many ounces of
oatmeal should she put into each container?
ounces
UNIT 5 TEST
201
Name
UNIT 5
Date
Review/Test
16. Select each quotient equal to 0.28. Mark all that apply
+ 102
28 + 103
280 + 103
2.8 + 101
28 + 101
2.8
17. Lunch for the band costs $137.20. The band has
56 members. How much does each member's
lunch cost?
$
18. Marco got a quotient of 70 when he divided 49 by 0.07.
Part A
What
Part
is
the correct answer for this problem?
B
What mistake did Marco make?
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Date
Name
UNIT 5
Review/Test
19. Write the letter of the expression next to the number that
shows its quotient.
A 845 +27
31 R4
B 190+6
24 R10
c
31 R8
612+15
D 363+9
24 R9
E
298
+
12
40 R12
F
441
+
18
40
R3
20. James lives 3.42 kilometers from school. Megan lives 0.76
kilometer from school. The distance James lives from school
is how many times as long as the distance Megan lives from
school? Show your work.
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21. F¡ll in the table to complete the pattern of dividing by
powers of ten.
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36
+
101
+ 102
36 + 1036
UNIT 5 TEST
36+10
36+
36
+
0.36
1000
203
Name
UNIT 5
Date
Review/Test
For numbers 22a-22c, read the word problem and circle the phrase from
the box that make the sentence correct.
22a. ln a movie, 289 aliens plan to visit Earth. Each ship
can hold as many as 3 aliens. What is the least number
of ships needed?
ignore it
For
the remainder in this problem, you should round it up
form a fraction with it
22b. Basma cuts ribbon to tie onto balloons for the carnival.
She has 925.6 inches of ribbon in all. lf each ribbon must
be 24 inches long, how many ribbons can she cut?
ignore it
For the remainder in this problem, you should
round it up
form a fraction with it
22c. Six miners divide 15 ounces of gold dust equally. How
many ounces of gold dust does each miner receive?
ignore it
For the remainder in this problem, you should
round it up
form a fraction with it
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23. Write the correct number in each box in the place value
sections to find the quotient.
300
+
+
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a
llc
70+
2
372
g
Ø
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2,976
576
16
-2,400
560
-16
8
576
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16
0
3
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