Download Using Fractions and Decimals

Name _____________________________________________________________________________________________________
Problem-Solving Application
H 4-10
Using Fractions and Decimals
Use the table below for Exercises 1–4.
Agua Caliente County Park Trails
Trail
Distance
Pond Trail
0.7 mi (each way)
Desert Overlook Trail
0.25 mi (each way)
Ocotillo Ridge Nature Trail 0.6 mi (loop)
Moonlight Canyon Trail
2.5 mi (loop)
1. Which is the shortest trail?
1
2
2. Dana doesn’t want to walk more than 1 miles round trip. Could she walk the Pond
Trail? Explain.
1
2
3. Brian walked all the trails at Agua Caliente. Did he walk more than 3 miles? Explain.
4. Agua Caliente County Park is 25.6 miles from the town of Ocotillo. If your trip meter read
147.6 miles when you left Agua Caliente, what would it read when you got to Ocotillo?
Use the prices to the right for Exercises 5 and 6.
5. Which different items could you buy and
spend exactly $16.00?
Items
Prices
Guide to Desert Plants
$3.25
Desert wildlife poster
$1.75
Sun hat
$7.50
Sunglasses
6. You have $40.00. Could you buy 2 sun hats,
2 pairs of sunglasses, and a canteen? Explain.
© Scott Foresman, Gr. 6
(125)
$12.25
Cactus candy
$0.75
Canteen
$4.50
Map
$0.75
Use with Chapter 4, Lesson 10.
Name _____________________________________________________________________________________________________
Relating Fractions and Decimals
H 4-9
Use a ruler to connect equivalent fractions and decimals. Then rearrange
the letters that have not been crossed out to answer the riddle below.
1
4
•
19
20
•
1
8
•
9
10
•
4
8
•
3
5
•
35
100
•
12
16
•
4
5
•
7
8
•
11. 3
20
•
12. 3
40
•
17
20
•
87
100
•
5
50
•
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 13. 14. 15. W
Q
R
P
T
V
Z
E
H
G
L
K
F
N
A
J
M
O
C
•
0.6
•
0.5
•
0.75
•
0.1
•
0.35
•
0.85
•
0.875
•
0.25
•
0.125
•
0.9
•
0.15
•
0.8
•
0.95
•
0.075
•
0.87
Two wrongs don’t make a right, but three rights make
.
1
16. Mental Math Joe drank 73 ounces of milk.
Bo drank 7.35 ounces. Who drank more milk?
Test Prep Circle the correct letter for the answer.
2
17. Josh started out with 75.66 pounds of grain. He purchased 135 pounds more.
5
How many pounds of grain does Josh have altogether?
A 210.86 pounds
© Scott Foresman, Gr. 6
(122)
B 211.06 pounds
C 211.26 pounds
D 210.06 pounds
Use with Chapter 4, Lesson 9.
Name _____________________________________________________________________________________________________
Comparing and Ordering Fractions
and Mixed Numbers
H 4-8
How can you tell when the guy sitting next to you in a diner is a math teacher?
To find out, compare the fractions and mixed numbers. Write >, <, or = in each blank.
Then circle the letter next to the lesser number. If you wrote =, don’t circle either letter.
2
3
3
4
1. H 7
10
9
20
2. H S
11. G
225
E
12. R
7
3
10
3
2
10
F
345
I
3. E
1
6
1
8
O
13. F
9
12
6
9
A
4. T
2
4
5
10
P
14. L
17
9
189
P
5. R
1
4
1
3
E
15. C
123
7
3
W
3
5
5
8
R
16. T
318
27
8
O
5
9
45
81
N
17. H
14
14
7
8
I
8. A 5
6
1
4
E
18. O 21
5
515
A
2
5
1
2
S
19. N
712
23
3
U
4
5
15
20
S
20. C
535
5
5
10
S
6. D 7. M 9. R
10. V To solve the riddle, write the circled letters in numerical order in the blanks below.
.
Test Prep
Circle the correct letter for the answer.
3
of the cookies and
21. Four friends baked a batch of cookies. Penelope ate 20
Simon ate 11
of the cookies. Gina consumed
0
Who ate the most cookies?
A Penelope
© Scott Foresman, Gr. 6
B Simon
(119)
1
4
and Ted consumed
C Gina
2
5
of the cookies.
D Ted
Use with Chapter 4, Lesson 8.
Name _____________________________________________________________________________________________________
Equivalent Fractions
H 4-7
Write each fraction in simplest form.
8
2. 21
9
5. 10
5
6. 36
21
10. 60
1. 20
9. 28
8
6
3. 12
12
7. 9
15
11. 81
4. 42
6
12
8. 16
63
56
12. 88
Use the LCD to write each set of fractions as fractions with the same denominator.
1 4
13. 3, 5
5
3 1
15. 7, 28
4 15
2 3 5
, 19. 8, 10 20
14. 5, 4
7
, 17. 11 22
3
18. 3, 4, 6
3
3
1
9
,
16. 2, 15
1
7 1 2
20. 9, 2, 6
2
21. Jordan ate 6 of the spaghetti. Kim ate 8 of the spaghetti and Carlos ate
the rest. Who ate more spaghetti, Jordan by himself, or Kim and Carlos together?
Explain your answer.
22. Of the 120 raviolis that Amy baked, 48 of them were spinach.
In simplest form, what fraction of the raviolis were spinach?
12
6
6
and are equivalent fractions. Is in simplest form? Explain.
23. Math Reasoning 10
10
20
Test Prep Circle the correct letter for each answer.
5
55
13
24. What is in simplest form?
25. What is the LCD of and ?
12
80
14
5
11
A C F 84
H 26
8
12
11
3
B D G 60
J 168
16
4
© Scott Foresman, Gr. 6
(116)
Use with Chapter 4, Lesson 7.
Name _____________________________________________________________________________________________________
Least Common Multiple
H 4-6
When he was 24 years old, Levi Strauss moved to San Francisco to sell dry goods. He
eventually obtained a patent for the sturdy work pants that were known at the time as
“waist overalls.” These waist overalls made Levi Strauss famous and are better known
today as “jeans.” May 20, 1998, marked a big anniversary of the invention of jeans.
To discover how many years old jeans were on that day, find the least common multiple
(LCM) of the numbers on the left and cross them off in the numbers on the right.
The number you have left over is your answer.
1. 3, 21
51
2. 9, 5
210
3. 17, 3
76
4. 5, 7
125
5. 15, 14
120
6. 36, 45
45
7. 15, 8
84
8. 11, 15
90
9. 4, 19
180
10. 9, 10
21
11. 10, 14
70
12. 7, 12
165
35
May 20, 1998 marked the
th birthday of blue jeans.
13. Mental Math What is the least common multiple
of 2 and 6,089,246?
Test Prep Circle the correct letter for the answer.
14. Mandy wears jeans every 2 days. She wears her white tennis shoes every 3 days.
If Mandy wears jeans and white tennis shoes on October 19, what is the next date
on which she will wear both jeans and white tennis shoes?
A October 26
© Scott Foresman, Gr. 6
(113)
B October 24
C November 2
D October 25
Use with Chapter 4, Lesson 6.
Name _____________________________________________________________________________________________________
Problem-Solving Strategy
H 4-5
Using Logical Reasoning
Make a table on a separate sheet of paper and use logical reasoning to find the missing
digits of each telephone number for Exercises 1–3.
1. 222-abcd.
2. 333-efgh.
Clue 1: All the digits are different.
Clue 2: a and c are the only odd
numbers.
Clue 3: a and d are the only
prime numbers.
Clue 4: c is neither prime nor
composite.
Clue 5: b d 4
Clue 6: a c d
Clue 1: All the digits are different.
Clue 2: f h f
Clue 3: e and g are the only
prime numbers.
Clue 4: e e f
Clue 5: f 6
Clue 6: g 5
The phone number is
.
The phone number is
.
3. 444-jkmn.
Clue
Clue
Clue
Clue
Clue
Clue
1:
2:
3:
4:
5:
6:
The only even numbers are j and k.
The only prime numbers are k and m.
m5
jm
jmn
j2k
The phone number is
.
Use logical reasoning for Exercise 4.
4. Mrs. Burke can order boxes of 6, 8, or 10 cupcakes from the bakery.
How many of each size of box should she order so that she can send
full boxes to each classroom and have no extras?
•
•
•
Room 17 has 36 students.
Room 15 has 40 students.
Room 21 has 52 students.
© Scott Foresman, Gr. 6
(110)
Use with Chapter 4, Lesson 5.
Name _____________________________________________________________________________________________________
Greatest Common Factor
H 4-4
Find the greatest common factor (GCF).
1. 15, 42
2. 9, 45
3. 26, 64
4. 22, 33, 121
5. 32, 80
6. 27, 72
7. 42, 70, 84
8. 18, 30, 45
9. 28, 50
10. 6, 18, 72
11. 12, 48, 96
12. 21, 63, 84
Use the Venn diagram at the right to answer Exercises 13–14.
13. The prime factors of what two numbers are being shown?
2
7
2
2
3
14. What is their greatest common factor?
15. Find two other numbers whose greatest common factor is 14.
Test Prep Circle the correct letter for the answer.
16. Kiki was hired by the museum to create displays of photographs taken from the
recent space shuttle mission. There are 18 photos of the Moon, 42 photos of Earth,
and 36 photos of the Milky Way. Kiki will display photos from each group together.
She will hang the same number of photos on each wall. What is the greatest number
of photos she can hang on a wall?
A 18
© Scott Foresman, Gr. 6
B 6
(107)
C 3
D 9
Use with Chapter 4, Lesson 4.
Name _____________________________________________________________________________________________________
Problem-Solving Skill
H 4-3
Reasonable Answers
Answer each question. Give a reason for each choice.
Roofers from Kleinschmidt Roofing are going to put a new roof on an apartment building.
The roof of the building measures 40 feet wide by 60 feet long. They need to order
sheets of plywood and bundles of shingles for the roof. A sheet of plywood covers
32 square feet. A bundle of shingles covers 30 square feet.
1. Which of the following is a reasonable conclusion?
a. They will need more sheets of plywood than bundles of shingles.
b. They will need more bundles of shingles than sheets of plywood.
c. They will need 32 sheets of plywood and 30 bundles of shingles.
2. Which expression describes the approximate number of sheets of plywood that
will be needed?
a. (40 60) 32
b. (40 60) 30
c. (40 60) 32
3. Which of the following is not a reasonable conclusion?
a. They should underestimate the number of bundles of shingles they will need.
b. They should overestimate the number of sheets of plywood they will need.
c. When they cut the plywood, there may be some wasted.
4. Which of the following would be the most reasonable conclusion?
a. order 80 sheets of plywood and 85 bundles of shingles
b. order 70 sheets of plywood and 75 bundles of shingles
c. order 95 sheets of plywood and 90 bundles of shingles
© Scott Foresman, Gr. 6
(104)
Use with Chapter 4, Lesson 3.
Name _____________________________________________________________________________________________________
Prime Factorization
H 4-2
Follow the divisibility clues to find the mystery number in each box.
33
20
1. Clues
The mystery number . . .
is divisible by 5,
is divisible by 2,
is not divisible by 3.
45
60
30
95
The mystery number is
5,1
5
7
21
2,4
13,2
75
4,322
2. Clues
The mystery number . . .
is not divisible by 6,
is divisible by 9,
is not divisible by 5.
.
4
1
1,91
86
The mystery number is
.
0 2,480
167,360
1,12
0 47,328
00
8
,86
,
5
2
5
3
7
3. Clues
The mystery number . . .
is divisible by 4,
is divisible by 10,
is divisible by 6.
The mystery number is
.
Use exponents to write the prime factorization of each number.
4. 24
5. 56
6. 80
7. 180
8. 225
9. 240
10. Is 3,117 a prime number?
Explain your answer.
Test Prep Circle the correct letter for the answer.
11. Shandra, Antonio, Betsy, Melissa, Joe, and Lynae have been earning extra money
raking leaves for their neighbors. So far they have collected $314. How many more
dollars do they need to earn in order to be able to divide the money equally?
A $6
© Scott Foresman, Gr. 6
B $2
(101)
C $4
D $11
Use with Chapter 4, Lesson 2.
Name _____________________________________________________________________________________________________
Exponents
H 4-1
Complete the chart.
Word Form
Exponent
Form
Factor
Form
Product
42
44
16
four to the second power
10 10 10
1.
25
2.
3. five to the fourth power
49
4.
83
5.
6. six to the fourth power
Evaulate each expression when a 3.
7. a3 10
8. 4a2 16
9. 75 3a2
10. 10a4
11. 35 6a2
12. (a 2)2
13. (12 a)4
14. 25a2 127
15. (4 a)3
16. The volume of the cube at the right
can be found with the expression s3.
Find the volume when s 9 in.
17. Mental Math If f 2 100, then f Test Prep Circle the correct letter for the answer.
18. David forwarded an e-mail to 7 friends. Each of those people sent it to
7 more friends, who in turn each forwarded the e-mail to 7 more friends.
How many friends received the e-mail?
A 343 friends
© Scott Foresman, Gr. 6
(98)
B 49 friends
C 2,401 friends
D 21 friends
Use with Chapter 4, Lesson 1.