# Lesson Check (MACC.4.NF.3.6)

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```9
Dear Family,
During the next few weeks, our math class will
relate both fractions and money to place value
and will learn how to rename fractions as decimals.
We will also add fractional parts of 10 and 100
and compare decimals through hundredths.
decimal A number with one or more
digits to the right of the decimal
point
decimal point A symbol used to
separate dollars from cents in money
amounts and to separate the ones
and tenths places in a decimal
equivalent decimals Two or more
decimals that name the same amount
hundredth One of one hundred
equal parts
tenth One of ten equal parts
You can expect to see homework that provides
practice with naming decimals in different ways,
including renaming as fractions.
Here is a sample of how your child will be taught
to write a decimal as a fraction.
Write Hundredths as a Fraction
This is how we will use place value to help write a
decimal as a fraction.
Ones
0
.
.
Tenths
Hundredths
6
4
decimal point
© Houghton Mifflin Harcourt Publishing Company
Think: 0.64 is the same as 6 tenths and 4 hundredths, or
64 hundredths.
A place-value chart can
be used to help visually
organize numbers in
relation to the decimal
place. The chart can be
used to pair the numbers
with words, and may
enable a smooth transition
between standard form,
word form, and the decimal
or fraction.
64
So, 0.64 5 ___
100 .
Activity
Use the relationship between dollars and cents and work together to
express the value of a penny, nickel, dime, and quarter as a decimal and as
write the value of each group as a decimal and as a fraction.
Chapter 9
P169
9
Querida familia,
Durante las próximas semanas, en la clase de
matemáticas relacionaremos tanto las fracciones
como el dinero con el valor posicional y aprenderemos a
convertir fracciones en decimales. También sumaremos
partes fraccionales de 10 y de 100 y compararemos
decimales hasta los centésimos.
decimal Un número con uno o más
dígitos a la derecha del punto decimal
para separar dólares de centavos en
cantidades de dinero y para separar el
lugar de las unidades y los décimos en
decimales
decimales equivalentes Dos o más
decimales que nombran la misma
centésimo Una de cien partes iguales
décimo Una de diez partes iguales
Llevaré a la casa tareas para practicar la expresión de
decimales de diferentes maneras, incluso la conversión
en fracciones.
Este es un ejemplo de la manera como aprenderemos a
escribir un decimal como una fracción.
Escribir centésimos como una fracción
Centésimos
.
4
0
6
punto decimal
Piensa: 0.64 es lo mismo que 6 décimos y cuatro centésimos, o
64 centésimos.
Una tabla de valor
posicional se puede usar
para ayudar a organizar
visualmente números
en relación con el lugar
decimal. La tabla puede
usarse para emparejar
números con palabras y
para facilitar la transición
del uso de la forma normal
a la forma en palabras y a
la fracción decimal.
64
.
Por tanto, 0.64 5 ____
100
Usen la relación entre dólares y centavos y trabajen juntos para expresar el valor de una
moneda de uno, de cinco, de diez y de veinticinco centavos en forma decimal y como una
fracción de dólar. Luego hagan pequeños grupos de monedas y ayude a su hijo/a a escribir
el valor de cada grupo en forma decimal y como fracción.
P170
© Houghton Mifflin Harcourt Publishing Company
Así es como usaremos el valor posicional para escribir un
decimal como una fracción
Lesson 9.1
Name
COMMON CORE STANDARD MACC.4.NF.3.6
Relate Tenths and Decimals
Understand decimal notation for fractions, and
compare decimal fractions.
Write the fraction or mixed number and the decimal
shown by the model.
1.
Think: The model is divided
into 10 equal parts. Each
part represents one tenth.
2.
6 ; 0.6
__
10
___
___
3.
4. ___
___
Write the fraction or mixed number as a decimal.
1
4
7
5. ___
6. 3___
7. ___
10
10
10
© Houghton Mifflin Harcourt Publishing Company
_
_
_
10. There are 10 sports balls in the equipment
closet. Three are kickballs. Write the
portion of the balls that are kickballs as a
fraction, as a decimal, and in word form.
5
8. 6___
10
_
9
9. ___
10
_
11. Peyton has 2 pizzas. Each pizza is cut into
10 equal slices. She and her friends eat
14 slices. What part of the pizzas did they
Chapter 9
P171
Lesson Check (MACC.4.NF.3.6)
1. Valerie has 10 CDs in her music case.
Seven of the CDs are pop music CDs.
What is this amount written as a decimal?
2. Which decimal amount is modeled
below?
A 70.0
B
7.0
C
0.7
D
0.07
A 140.0
B
14.0
C 1.4
D 0.14
Spiral Review (MACC.4.OA.2.4, MACC.4.NF.1.1, MACC.4.NF.2.3b)
3. Which number is a factor of 13?
(Lesson 5.1)
A 1
C 4
(Lesson 5.3)
5. How do you write the mixed number
shown as a fraction greater than 1?
(Lesson 7.6)
P172
A 2 rows
C 4 rows
B 3 rows
D 6 rows
6. Which of the following models has an
amount shaded that is equivalent to the
fraction 1_5 ? (Lesson 6.1)
A
C
B
D
6
C __
4
__
D 4
4
© Houghton Mifflin Harcourt Publishing Company
D 7
14
B ___
4
4 photographs displayed in equal rows
on a wall, with the same number of each
type of art in each row. Which of the
following could be the number of rows?
B 3
32
A ___
5
4. An art gallery has 18 paintings and
Lesson 9.2
Name
COMMON CORE STANDARD MACC.4.NF.3.6
Relate Hundredths and Decimals
Understand decimal notation for fractions, and
compare decimal fractions.
Write the fraction or mixed number and the
decimal shown by the model.
1.
Think: The whole is
divided into one hundred
equal parts, so each part
is one hundredth.
2.
77 ; 0.77
___
100
___
___
4.
3.
___
© Houghton Mifflin Harcourt Publishing Company
___
Write the fraction or mixed number as a decimal.
11
37
98
5. ____
6. 8 ____
7. ____
100
100
100
__
__
10. There are 100 pennies in a dollar. What
__
fraction of a dollar is 61 pennies? Write it as
a fraction, as a decimal, and in word form.
______
______
50
100
8. 25 ____
__
6
9. ____
100
__
11. Kylee has collected 100 souvenir thimbles
from different places she has visited with
her family. Twenty of the thimbles are
carved from wood. Write the fraction of
thimbles that are wooden as a decimal.
______
Chapter 9
P173
Lesson Check (MACC.4.NF.3.6)
1. Which decimal represents the shaded
section of the model below?
2. There were 100 questions on the
unit test. Alondra answered 97 of the
questions correctly. What decimal
represents the fraction of questions
A
0.97
B
9.70
C
90.70
D 970.0
A 830.0
C 8.30
83.0
D 0.83
B
Spiral Review (MACC.4.OA.3.5, MACC.4.NF.2.3b, MACC.4.NF.2.3d, MACC.4.NF.2.4c)
3. Which is equivalent to 7_8 ?
__ 1 3
__
A 5
(Lesson 7.2)
9
6
__
4. What is __
10 2 10 ?
(Lesson 7.4)
8 8
__ 1 1
__ 1 1
__
B 4
8 8 8
__ 1 2
__ 1 2
__
C 3
8 8 8
__ 1 2
__ 1 1
__ 1 1
__
D 2
8 8 8 8
5. Misha used _14 of a carton of 12 eggs to
make an omelet. How many eggs did
she use? (Lesson 8.4)
A 2
6. Kurt used the rule add 4, subtract 1 to
generate a pattern. The first term in his
pattern is 5. Which number could be in
Kurt’s pattern? (Lesson 5.6)
B 3
A
4
C 4
B
6
D 6
P174
4
C ___
10
6
D ___
10
C 10
D 14
© Houghton Mifflin Harcourt Publishing Company
1
A ___
10
3
B ___
10
Lesson 9.3
Name
Equivalent Fractions and Decimals
COMMON CORE STANDARD MACC.4.NF.3.5
Understand decimal notation for fractions, and
compare decimal fractions.
Write the number as hundredths in fraction form and
decimal form.
5
5 5 _______
5 3 10 5 ____
50
___
1. ___
10
10 10 3 10 100
Think: 5 tenths is the same as 5 tenths
and 0 hundredths. Write 0.50.
50 ; 0.50
___
100
9
2. ___
3. 0.2
10
4. 0.8
© Houghton Mifflin Harcourt Publishing Company
Write the number as tenths in fraction form and
decimal form.
40
10
5. ____
6. ____
100
100
6
8. Billy walks __
10 mile to school each day.
6
Write __
as hundredths in fraction form
10
and in decimal form.
7. 0.60
9. Four states have names that begin with
the letter A. This represents 0.08 of all the
states. Write 0.08 as a fraction.
Chapter 9
P175
Lesson Check (MACC.4.NF.3.5)
1. The fourth-grade students at Harvest
School make up 0.3 of all students at
the school. Which fraction is equivalent
to 0.3?
A
B
C
D
3
__
2. Kyle and his brother have a marble
set. Of the marbles, 12 are blue. This
50
represents ___
100 of all the marbles. Which
50
decimal is equivalent to ___
100 ?
A
10
30
__
10
3
___
100
33
___
100
50
B
5.0
C
0.50
D 5,000
Spiral Review (MACC.4.OA.3.5, MACC.4.NF.1.1, MACC.4.NF.2.4c, MACC.4.NF.3.6)
45
3. Jesse won his race by 3 ___
seconds.
100
What is this number written as a decimal?
(Lesson 9.2)
A
0.345
B
3.45
34.5
D 345
P176
A 2 inches
B 4 inches
C 5 inches
D 6 inches
9
5. Of Katie’s pattern blocks, __
12 are triangles.
9
What is __
in simplest form? (Lesson 6.3)
1
A __
4
__
B 2
3
__
C 3
4
9
D ___
12
pictures on poster board. Each piece of
tape was 3_8 inch long. How much tape did
Marge use? (Lesson 8.4)
12
6. A number pattern has 75 as its first term.
The rule for the pattern is subtract 6.
What is the sixth term? (Lesson 5.6)
A 39
B 45
C 51
D 69
© Houghton Mifflin Harcourt Publishing Company
C
4. Marge cut 16 pieces of tape for mounting
Lesson 9.4
Name
COMMON CORE STANDARD MACC.4.NF.3.6
Relate Fractions, Decimals,
and Money
Understand decimal notation for fractions, and
compare decimal fractions.
Write the total money amount. Then write the amount as a
fraction or a mixed number and as a decimal in terms of dollars.
1.
2.
18 ; 0.18
\$0.18; ___
100
______
______
Write as a money amount and as a decimal in terms of dollars.
25
3. ____
100
79
4. ____
31
5. ____
100
__
8
6. ____
100
__
42
7. ____
100
__
100
__
__
Write the money amount as a fraction in terms of dollars.
8. \$0.87
9. \$0.03
__
10. \$0.66
__
11. \$0.95
__
12. \$1.00
__
__
Write the total money amount. Then write the amount as a
fraction and as a decimal in terms of dollars.
© Houghton Mifflin Harcourt Publishing Company
13. 2 quarters 2 dimes
____
14. 3 dimes 4 pennies
____
16. Kate has 1 dime, 4 nickels, and 8 pennies.
Write Kate’s total amount as a fraction in
terms of a dollar.
_______
15. 8 nickels 12 pennies
____
75
17. Nolan says he has ___
of a dollar. If he
100
only has 3 coins, what are the coins?
_______
Chapter 9
P177
Lesson Check (MACC.4.NF.3.6)
1. Which of the following names the total
money amount shown as a fraction in
terms of a dollar?
81
2. Crystal has ___
100 of a dollar. Which of the
following could be the coins Crystal has?
A 3 quarters, 1 dime, 1 penny
B 2 quarters, 6 nickels, 1 penny
C 2 quarters, 21 pennies
D 1 quarter, 4 dimes, 1 nickel, 1 penny
43
A ___
1
___
B 43
10
43
C ___
57
43
D ____
100
Spiral Review (MACC.4.NF.1.1, MACC.4.NF.3.6)
3
(Lesson 6.2)
3
A __
5
__
B 2
6
8
__
9
4
D ___
10
C
5. Which decimal is shown by the model?
B
P178
1.0
the pretzels. Which fraction is equivalent
to _38 ? (Lesson 6.2)
9
A ___
24
3
C ___
16
___
B 15
20
__
D 1
5
6. Mr. Guzman has 100 cows on his dairy
farm. Of the cows, 57 are Holstein. What
decimal represents the portion of cows
that are Holstein? (Lesson 9.2)
(Lesson 9.2)
A 10.0
4. Penelope bakes pretzels. She salts _38 of
C 0.1
D 0.01
A
0.43
B
0.57
C
5.7
D 57.0
© Houghton Mifflin Harcourt Publishing Company
3. Joel gives _13 of his baseball cards to his
sister. Which fraction is equivalent to _1 ?
Name
HE8B;CÃEBL?D=ÃÄÃED;O
PROBLEM SOLVING
Lesson 9.5
COMMON CORE STANDARD MACC.4.MD.1.2
Solve problems involving measurement and
conversion of measurements from a larger unit
to a smaller unit.
Use the act it out strategy to solve.
1. Carl wants to buy a bicycle bell that costs
\$4.50. Carl has saved \$2.75 so far. How much
more money does he need to buy the bell?
Use 4 \$1 bills and 2 quarters to model \$4.50.
Remove bills and coins that have a value of
\$2.75. First, remove 2 \$1 bills and 2 quarters.
Next, exchange one \$1 bill for 4 quarters and
remove 1 quarter.
Count the amount that is left.
So, Carl needs to save \$1.75 more.
\$1.75
____
2. Together, Xavier, Yolanda, and Zachary have
\$4.44. If each person has the same amount,
how much money does each person have?
____
3. Marcus, Nan, and Olive each have \$1.65
in their pockets. They decide to combine
the money. How much money do they have
altogether?
© Houghton Mifflin Harcourt Publishing Company
____
4. Jessie saves \$6 each week. In how many
weeks will she have saved at least \$50?
____
5. Becca has \$12 more than Cece. Dave has
\$3 less than Cece. Cece has \$10. How much
money do they have altogether?
____
Chapter 9
P179
Lesson Check (MACC.4.MD.1.2)
1. Four friends earned \$5.20 for washing a
car. They shared the money equally. How
much did each friend get?
A
\$1.05
B
\$1.30
C
\$1.60
D \$20.80
2. Which represents the value of one \$1 bill
and 5 quarters?
A \$1.05
B \$1.25
C \$1.50
D \$2.25
Spiral Review (MACC.4.OA.2.4, MACC.4.NF.1.1, MACC.4.NF.1.2, MACC.4.NF.3.6)
dollar is this? (Lesson 9.4)
A
B
C
D
9
____
100
9
___
10
90
____
100
99
____
100
5. I am a prime number between 30 and
40. Which number could I be? (Lesson 5.5)
A 31
B 33
C 36
D 39
P180
9
12 of his free throws at
9
practice. What is __
in simplest form?
12
(Lesson 6.3)
1
A __
4
3
B __
9
__
C 1
2
3
D __
4
1
6. Georgette is using the benchmark __ to
2
compare fractions. Which statement is
correct? (Lesson 6.6)
3 __
A __
>1
8 2
2 __
<1
B __
5 2
1
7
C ___
< __
12 2
9
1
= __
D ___
10 2
© Houghton Mifflin Harcourt Publishing Company
3. Bethany has 9 pennies. What fraction of a
Lesson 9.6
Name
Add Fractional Parts of 10 and 100
Find the sum.
2
43
1. ___ 1 ____
10 100
100
Understand decimal notation for fractions, and
compare decimal fractions.
2
Think: Write __
10 as a fraction with a
denominator of 100:
20
43
63
__
1 __
5 __
100
COMMON CORE STANDARD MACC.4.NF.3.5
2 3 10 5 ____
20
_______
10 3 10 100
100
63
___
100
17
6
2. ____ 1 ___
9
4
3. ____ 1 ___
23
7
4. ___ 1 ____
5. \$0.48 1 \$0.30
6. \$0.25 1 \$0.34
7. \$0.66 1 \$0.06
© Houghton Mifflin Harcourt Publishing Company
100
100
10
10
38
8. Ned’s frog jumped ___
100 meter. Then his
4
frog jumped __
meter. How far did Ned’s
10
frog jump in all?
10
100
5
9. Keiko walks __
10 kilometer from school to
19
the park. Then she walks ___
kilometer
100
from the park to her home. How far does
Keiko walk in all?
Chapter 9
P181
Lesson Check (MACC.4.NF.3.5)
2
1. In a fish tank, __
10 of the fish were orange
5
and ___
of the fish were striped. What
100
fraction of the fish were orange or
striped?
7
A ___
10
52
B ____
100
25
C ____
100
7
D ____
100
2. Greg spends \$0.45 on an eraser and
\$0.30 on a pen. How much money does
Greg spend in all?
A \$3.45
B \$0.75
C \$0.48
D \$0.15
Spiral Review (MACC.4.NF.1.1, MACC.4.NF.2.3d, MACC.4.MD.1.2)
many months will it take him to save
at least \$60? (Lesson 9.5)
A 6 months
B 7 months
C 8 months
D 9 months
5. A carpenter has a board that is 8 feet
long. He cuts off two pieces. One piece is
3 1_2 feet long and the other is 2 1_3 feet long.
How much of the board is left? (Lesson 7.10)
4. Ursula and Yi share a submarine
sandwich. Ursula eats _28 of the sandwich.
Yi eats 3_ of the sandwich. How much
8
of the sandwich do the two friends eat?
(Lesson 7.5)
1
A __
8
__
B 4
8
__
C 5
8
__
D 6
8
6. Jeff drinks _23 of a glass of juice. Which
fraction is equivalent to 2_ ? (Lesson 6.2)
A
A 2 1_6 feet
B
B 2 5_6 feet
C
C 3 1_6 feet
D
D 3 5_6 feet
P182
1
__
3
3
__
2
3
__
6
8
___
12
3
© Houghton Mifflin Harcourt Publishing Company
3. Phillip saves \$8 each month. How
Lesson 9.7
Name
COMMON CORE STANDARDS MACC.4.NF.3.7
Compare Decimals
Understand decimal notation for fractions, and
compare decimal fractions.
Compare. Write ,, ., or 5.
1. 0.35
,
0.53
2. 0.6
0.60
3. 0.24
0.31
Think: 3 tenths is less
than 5 tenths.
So, 0.35 , 0.53
4. 0.94
0.9
5. 0.3
0.32
6. 0.45
0.28
7. 0.39
0.93
Use the number line to compare. Write true or false.
8. 0.8 . 0.78
9. 0.4 . 0.84
10. 0.7 , 0.70
11. 0.4 . 0.04
14. 0.17 , 0.32
15. 0.85 . 0.82
Compare. Write true or false.
© Houghton Mifflin Harcourt Publishing Company
12. 0.09 . 0.1
13. 0.24 5 0.42
16. Kelly walks 0.7 mile to school. Mary walks
0.49 mile to school. Write an inequality
using ,, ., or 5 to compare the distances
they walk to school.
17. Tyrone shades two decimal grids. He
shades 0.03 of the squares on one grid
blue. He shades 0.3 of another grid red.
Which grid has the greater part shaded?
Chapter 9
P183
Lesson Check (MACC.4.NF.3.7)
1. Bob, Cal, and Pete each made a stack
of baseball cards. Bob’s stack was 0.2
meter high. Cal’s stack was 0.24 meter
high. Pete’s stack was 0.18 meter high.
Which statement is true?
2. Three classmates spent money at the
school supplies store. Mark spent
0.5 dollar, Andre spent 0.45 dollar,
and Raquel spent 0.52 dollar. Which
statement is true?
A 0.2 . 0.24
A 0.45 . 0.5
B 0.24 . 0.18
B 0.52 , 0.45
C 0.18 . 0.2
C 0.5 5 0.52
D 0.24 5 0.2
D 0.45 , 0.5
Spiral Review (MACC.4.NF.2.3c, MACC.4.NF.2.4c, MACC4.NF.3.5)
\$0.40 in her pocket. How much money
do Pedro and Alice have in their pockets
altogether? (Lesson 9.6)
A \$0.05
B \$0.39
C \$0.75
D \$0.79
5. Joel has 24 sports trophies. Of the
trophies, _1 are soccer trophies. How
8
many soccer trophies does Joel have?
(Lesson 8.4)
A 2
B 3
C 4
D 6
P184
4. The measure 62 centimeters is equivalent
62
to ___
meter. What is this measure written
100
as a decimal? (Lesson 9.3)
A 62.0 meters
B
6.2 meters
C
0.62 meter
D
0.6 meter
6. Molly’s jump rope is 6 _13 feet long. Gail’s
jump rope is 4 _2 feet long. How much
3
longer is Molly’s jump rope? (Lesson 7.8)
A 1 1_3 feet
B 1 2_3 feet
C 2 1_3 feet
D 2 2_3 feet
© Houghton Mifflin Harcourt Publishing Company
3. Pedro has \$0.35 in his pocket. Alice has
COMMON CORE STANDARDS MACC.4.NF.3.5,
MACC.4.NF.3.6, MACC.4.NF.3.7, MACC.4.MD.1.2
Name
Chapter 9 Extra Practice
Lessons 9.1–9.2
Write the fraction or mixed number and the decimal shown by the model.
1.
2.
3.
'
'%,
(%'
(%,
)%'
Lesson 9.3
Write the number as hundredths in fraction form and decimal form.
8
1. ___
10
2. 0.1
3
3. ___
10
Write the number as tenths in fraction form and decimal form.
60
4. ____
100
70
5. ____
100
6. 0.20
Lesson 9.4
© Houghton Mifflin Harcourt Publishing Company
Write as a money amount and as a decimal in terms of dollars.
30
1. ____
100
91
2. ____
100
5
3. ____
100
Write the total money amount. Then write the amount as a fraction
and as a decimal in terms of dollars.
4. 4 dimes, 9 pennies
5. 3 quarters, 1 dime
6. 7 nickels, 2 pennies
Chapter 9
P185
Lesson 9.5
1. Camila, Jocelyn, and Audrey each earned
2. Elijah, Xavier, and Adrian earned a total
3. Anthony saves \$7 each week. In how many
4. Brianna has \$2 less than Victoria. Victoria
\$2.55. How much did the three girls earn
altogether?
weeks will he have saved at least \$40?
of \$8.34. The boys shared the earnings
equally. How much did each boy get?
has \$11 more than Damian. Damian has
\$6. How much money do they have in all?
Lesson 9.6
Find the sum.
6
39
1. ___ 1 ____
10
100
14
8
2. ____ 1 ___
100
10
4
18
3. ___ 1 ____
10
100
5
16
4. ___ 1 ____
10
100
5. \$0.43 1 \$0.20
6. \$0.07 1 \$0.35
7. \$0.80 1 \$0.15
8. \$0.52 1 \$0.28
3. 0.54
4. 0.04
0.06
8. 0.63
0.48
Lesson 9.7
1. 0.3
0.39
2. 0.9
5. 0.7
0.70
6. 0.36
0.90
0.51
7. 0.8
0.45
0.67
Compare. Write true or false.
9. 0.32 . 0.23
P186
10. 0.86 5 0.9
11. 0.68 , 0.83
12. 0.97 . 0.94
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Compare. Write ,, ., or 5.
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