Download Multiplication Properties

Name _____________________________________________________________________________________________________
Multiplication Properties
R 4-1
Commutative Property
Associative Property
The order of the factors does not
change the product.
Factors Product
The way factors are grouped does not
change the product. (Always complete
the work in parentheses first.)
7 ! 4 " 28
5 ! (2 ! 4) " 5 ! 8 " 40
4 ! 7 " 28
(5 ! 2) ! 4 " 10 ! 4 " 40
Identity Property
Zero Property
When 1 is one of two factors, then the
product is the other factor.
When zero is a factor, the product
is zero.
23 ! 1 " 23
243 ! 0 " 0
1 ! 23 " 23
0 ! 243 " 0
!
!
!
The distributive property combines multiplication and addition.
Distributive Property
Think of one factor as the sum of two addends. Then multiply each addend
by the other factor and add the product.
3 ! 11 " 3 ! (8 # 3)
" (3 ! 8) # (3 ! 3)
" 24 # 9
" 33
Write the name of the property shown.
1. 5 ! (7 ! 2) " (5 ! 7) ! 2
2. (2 ! 8) ! 5 " 2 ! (8 ! 5)
3. 5 ! 9 " 9 ! 5
4. 4 ! (1 ! 7) " (4 ! 1) ! 7
Find n. Name the property you used.
5. 3 ! 9 " n ! 3
© Scott Foresman, Gr. 5
(89)
6. 14 ! n " 14
Use with Chapter 4, Lesson 1.
Name _____________________________________________________________________________________________________
Multiplication Properties
H 4-1
Find each n. Name the property that you used.
1. 5 ! 3 " 3 ! n
2. 30 ! 1 " n
3. 12 ! 1 " n
4. 12 ! n ! 15 " 0
5. 3 ! (4 ! 2) " (n ! 4) ! 2
6. 5 ! 12 " 5 ! (10 # n)
7. 6 ! (10 # 5) " n
8. 13 ! n " 13
9. (3 ! 8) # (3 ! 7) " n ! (8 # 7)
10. 23 ! n " 0
11. (4 ! 7) ! 8 " 4 ! ( 7 ! n)
Compare. Write $, %, or " for each
!2!8!3
15. 5 ! 5 ! 6 ! 5
13. 3 ! 8 ! 2
12. n ! (4 # 5) " (6 ! 4) # (6 ! 5)
!.
! 100 ! 6 ! 0
16. 4 ! (10 # 6) ! 16 ! 4
14. 100 ! 5 ! 1
17. Math Reasoning
Sheelah gets paid $5 per dog walk, and she walks 7 dogs three
times a day. Malcom earns $7 per dog walk, and walks 5 dogs three times a day.
Who earns more each day?
Test Prep Circle the correct letter for each answer.
18. 16 ! 4 ! 7 "
A 16 ! (4 # 7)
C 7 ! 16 ! 4
B 16 ! (7 # 4)
D 16 ! (7 & 4)
19. 5 ! 27 "
F (5 ! 20) & (5 ! 7)
H (5 ! 20) # (5 ! 7)
G (5 ! 20) # (7 & 5)
J
© Scott Foresman, Gr. 5
(90)
(5 ! 20) ! 7
Use with Chapter 4, Lesson 1.
Name _____________________________________________________________________________________________________
Order of Operations
R 4-2
Evaluate 20 ! 4 " 2.
Example 1
20 ! 4 " 2
20 ! 4 " 2
To
•
•
•
If you add first, the problem becomes 24 " 2 # 48
If you multiply first, the problem becomes 20 ! 8 # 28
avoid having different answers, follow the order of operations below.
First, do all the operations inside parentheses.
Next, do all multiplication and division from left to right.
Last, do all addition and subtraction from left to right.
Example 2
Find n if 5 ! 12 " (3 " 4) $ 8 " 2 # n.
• First, do operations inside parentheses: 5 ! 12 " (12) $ 8 " 2 # n.
• Next, do multiplication and division from left to right: 5 ! 144 $ 16 # n.
• Last, do all addition and subtraction from left to right: 133 # n.
Write which operation should be done first.
1. 3 " 4 ! 9
___________________________________________________
2. 12 $ 3 " 4
___________________________________________________
3. 12 % 3 " 4 $ 2
___________________________________________________
4. (12 $ 3) " 4 % 2
___________________________________________________
Write which operation should be done first. Then find each n.
5. 4 " 8 ! 6 # n
6. (3 ! 5) % 2 # n
7. 1 ! 8 " 7 # n
8. 12 % 2 " 3 # n
9. 1 " 7 ! (5 % 1) # n
10. (15 $ 5) ! 7 " 2 # n
11. 12 % (5 ! 1) " 2 # n
12. 12 $ (3 ! 2) % 5 # n
© Scott Foresman, Gr. 5
(92)
Use with Chapter 4, Lesson 2.
Name _____________________________________________________________________________________________________
Order of Operations
H 4-2
Use the box at the right for exercises
1–9. Choose a value from the box to
make each sentence true.
1. 3 ! 9 " 6 # n
n#
21
36
15
1
9
33
69
28
4
2. (10 " 8) $ 2 # n
n#
4. 18 $ 3 ! 6 # n
n=
n#
5. 0 ! 8 " (8 $ 8) # n
n#
7. 3 ! 3 ! 3 " 3 $ 3 # n
n#
3. 5 ! (3 " 2) % 4 # n
6. (13 % 5) ! 7 " 13 # n
n#
8. 16 % 5 " 4 $ (9 % 8) # n
n#
9. 9 $ (9 % 6) $ 3 ! 4 # n
n#
For a, write which operation should be done first. For b, find each n.
10. 32 $ (12 % 4) # n
11. 3 " 5 ! 6 % 2 # n
12. 40 % (2 ! 10) $ 5 # n
a.
a.
a.
b.
b.
b.
Find each n.
13. 16 % (5 ! 3) " 4 # n
n#
14. 16 $ (8 % 4) ! 2 # n
n#
15. 30 % (36 $ 3) $ 4 # n
n#
Test Prep Circle the correct letter for each answer.
16. Which number sentence is true?
17. Which number sentence is false?
A 7 ! 7 " 7 % 7 # 48
F (7 " 7 " 7) $ 7 # 13
B (7 " 7) " (7 $ 7) # 15
G 7 $ 7 " 7 ! 7 # 50
C (7 $ 7) " 7 " 7 # 13
D 7 $ 7 " 7 " 7 # 14
© Scott Foresman, Gr. 5
(93)
H (7 $ 7) " 7 % 7 # 1
J (7 " 7) " (7 $ 7) # 15
Use with Chapter 4, Lesson 2.
Name _____________________________________________________________________________________________________
Evaluating Expressions with Whole Numbers
R 4-3
If an expression contains more than one operation, you need to follow the order of
operations when you evaluate the expression.
Example 1
Evaluate 4n ! 6 when n " 2, n " 4, and n " 12.
When n " 2
When n " 4
When n " 12
4n ! 6 " 4 # 2 ! 6
"8!6
" 14
4n ! 6 " 4 # 4 ! 6
" 16 ! 6
" 22
4n ! 6 " 4 # 12 ! 6
" 48 ! 6
" 54
Example 2
Evaluate
x$
$3
! 6 when x " 3, x " 6, and x " 9.
When x " 3
x$
$3
3
$3$
!6" !6
"1!6
"7
When x " 6
x$
$3
6
$$
3
!6" !6
"2!6
"8
When x " 9
x$
$3
! 6 " 9$3 ! 6
"3!6
"9
Evaluate each expression for x " 4, x " 3, and x " 12.
1. 4x ! 10 "
12
$
2. 15 % $
x "
24
$
3. $
x !4"
4. 15 ! 3x "
Evaluate each expression for a " 5, a " 10, and a " 20.
5. 5a % 12 "
60
$
6. $
a !7"
7. 100 % 3a "
8. a ! 12 "
© Scott Foresman, Gr. 5
(95)
Use with Chapter 4, Lesson 3.
Name _____________________________________________________________________________________________________
Evaluating Expressions with Whole Numbers
H 4-3
1. At Sammy’s Sub Shop the cost of a regular sub sandwich is $5. Sammy’s has a Sunday
Sub Special: $2 off every order. Write an expression that represents the cost of an
order of n regular sub sandwiches on Sunday.
a. How much will one order of 3 regular subs cost on Sunday?
b. How much will one order of 5 regular subs cost on Sunday?
c. How much will one order of 8 regular subs cost on Sunday?
2. VideoVenture gives $3 off every purchase of 6 video tapes. If the price of one video
tape is p, write an expression for the cost of 6 video tapes.
a. Evaluate the expression if the price of each videotape is $5
b. Evaluate the expression if the price of each videotape is $7
c. Evaluate the expression if the price of each videotape is $8
3. DiscountTix sells half-price tickets to plays and musical performances.
There is a $2 fee for each purchase. If p is the regular cost of a ticket,
write an expression for the cost of a ticket bought at DiscountTix.
a. The ordinary price of a ticket for a Rick Cotta concert is $14.
What is the cost of a ticket purchased at DiscountTix?
b. The Vermy Celli concert tickets have a regular price of $22.
How much will one DiscountTix ticket to the concert cost?
c. How much will 3 DiscountTix tickets to Vermy Celli cost?
Test Prep Circle the correct letter for each answer.
Evaluate each expression for x = 12.
x
5. 20 ! 5 " #3# $ 18 % 2
A 105
B 29
C 55
D 95
G 4
H 16
J 0
48
6. #x# ! 8 % 8 $ 6
F 10
© Scott Foresman, Gr. 5
(96)
Use with Chapter 4, Lesson 3.
Name _____________________________________________________________________________________________________
Problem-Solving Skill
R 4-4
Choose the Operation
You add to combine groups, subtract to compare groups, multiply to combine equal
groups, and divide to separate into equal groups.
Jim and Sharon spend a week collecting bird feathers. Each day, Jim collects
8 feathers, and Sharon collects 2.
Addition
At the end of the first day, how many do they have in all?
(combine groups; add)
Subtraction
How many more feathers does Jim have than Sharon?
(compare groups; subtract)
Multiplication
How many feathers does Jim collect in 7 days?
(combine equal groups; multiply)
Division
How many groups of 2 feathers can Jim make?
(separate into equal groups; divide)
These notes show Andy’s research
on how fast some animals fly.
A pigeon flies 60 miles per hour.
1. How would you find how many
An eider duck flies 47 miles per hour.
more miles per hour an eider duck
flies than a monarch butterfly?
A monarch butterfly flies 20 miles per hour.
A hawk moth flies 33 miles per hour.
a. Add the miles per hour each flies,
then multiply by 2.
b. Subtract the number of miles per hour a monarch butterfly
flies from the number of miles per hour an eider duck flies.
c. Divide the number of miles per hour the eider duck flies by
the number of miles per hour a monarch butterfly flies.
2. Which number sentence would you use to find out how many
groups of two ducks there are in a larger group of 12 ducks?
a. n = 12 ! 2
© Scott Foresman, Gr. 5
b. n = 12 " 2
(98)
12
c. n = #2#
Use with Chapter 4, Lesson 4.
Name _____________________________________________________________________________________________________
Problem-Solving Skill
H 4-4
Choose the Operation
Use the table of mammal weights to solve the problems.
Mammal
Average Weight
elephant
10,000 lb
gorilla
400 lb
meerkat
3 lb
Bengal tiger
500 lb
giant panda
265 lb
polar bear
880 lb
1. How would you find the difference between a giant panda’s weight
and a polar bear’s weight?
a. Multiply the panda’s weight by the polar bear’s weight.
b. Subtract the panda’s weight from the polar bear’s weight.
c. Add the weights of the panda and the polar bear.
2. How would you estimate how much 5 meerkats weigh?
a. Multiply the average weight of a meerkat by 5.
b. Subtract the average weight of a meerkat from 5.
c. Add the average weight of a meerkat to 5.
3. Suppose you know that a group of meerkats weighs 85 lb in all.
How would you find the number of meerkats in this group?
a. Multiply 85 by the average weight of a meerkat.
b. Divide 85 by the average weight of a meerkat.
c. Subtract the average weight of a meerkat from 85.
4. Which number sentence represents the combined weights
of a Bengal tiger and a gorilla?
a. 500 ! 400 " w
b. 500 # 400 " w
c. 500 $ 400 " w
5. Write a number sentence to show about how much a herd of 9 elephants weighs.
© Scott Foresman, Gr. 5
(99)
Use with Chapter 4, Lesson 4.
Name _____________________________________________________________________________________________________
Mental Math:
Multiplication Patterns Using 10, 100, and 1,000
R 4-5
You can use basic facts and patterns with zeros to multiply by 10, 100, and 1,000.
Example 1 2 ! 4,000 " ?
Example 2 50 ! 30 " ?
2!4
"8
5!3
2 ! 40
" 8 ! 10
50 ! 30 " 5 ! 10 ! 3 ! 10
2 ! 400
" 8 ! 100
50 ! 30 " 5 ! 3 ! 10 ! 10
2 ! 4,000
" 8,000
50 ! 30 " 15 ! 100
" 15
50 ! 30 " 1,500
Continue, using the pattern with zeros.
5!3
" 15
5 ! 30
" 5 ! 3 ! 10 " 150
50 ! 30 " 5 ! 10 ! 3 ! 10 " 1,500
50 ! 300 " 5 ! 10 ! 3 ! 100 " 15,000
Find each product. Use patterns to help you.
1. 5 ! 5 " 25
2. 6 ! 4 " 24
5 ! 50 " 25 !
5 ! 500 " 25 !
5 ! 5,000 " 25 !
3. 40 ! 2
© Scott Foresman, Gr. 5
" 250
" 2,500
" 25,000
4. 9,000 ! 3
(101)
6 ! 40 " 24 !
" 240
6 ! 400 " 24 !
" 2,400
6 ! 4,000 " 24 !
5. 400 ! 9
" 24,000
6. 60 ! 50
Use with Chapter 4, Lesson 5.
Name _____________________________________________________________________________________________________
Mental Math:
Multiplication Patterns Using 10, 100, and 1,000
H 4-5
Find each product. Use patterns with zeros to help you. Then match the products
to the numbers below the blanks and write the letter on the line.
1.
700
! 20
2.
!
"""
200
5
!
"""
E
5.
3.
3,000
90
""""
R
260
! 10
6.
!
"""
7.
""""
"""
N
70
! 70
8.
!
""
T
9. 25 ! 20
400
! 30
D
4,000
40
B
4.
""""
I
10. 600 ! 70
W
2,500
4
H
11. 700 ! 3
S
12. 50 ! 50
A
C
What gift did Albert Einstein leave to science?
10,000
4,900
42,000
2,600
1,000
2,100
4,900
12,000
Test Prep Circle the correct letter for each answer.
13. Which expression gives the same product as 2,400 ! 50?
A 2,400 ! 500
C 240 ! 5,000
B 24,000 ! 500
D 24,000 ! 5
14. Which expression gives the same product as 450 ! 5,000?
F 45 ! 5,000
H 45 ! 500,000
G 4,500 ! 5,000
J 4,500 ! 500
© Scott Foresman, Gr. 5
(102)
Use with Chapter 4, Lesson 5.
Name _____________________________________________________________________________________________________
Estimating Products
R 4-6
You can use what you know about rounding numbers to help you estimate products.
Example 1
469
Estimate 469 ! 32.
Round each number to its greatest place so that
you can multiply mentally. Round 469 to the
nearest hundred, and round 32 to the nearest ten.
Example 2
Estimate $7.65 ! 73.
Round each number to its greatest place.
Round 7.65 to the nearest ones, and round
560 to the nearest hundred.
32
!
rounds
rounds
to
to
500
!
7.65
!
30 " 1,500
73
rounds
rounds
to
to
8
70 " 560
!
Remember:
Round up if the digit to the right of the greatest place is 5, 6, 7, 8, or 9.
Round down if the digit to the right of the greatest place is 0, 1, 2, 3, or 4.
Estimate each product. Round to the greatest place.
1. 32 ! 7 "
2. 38 ! 2 "
3. 5 ! 29 "
4. 8 ! 79 "
5. 41 ! 39 "
6. 53 ! 82 "
7. 13 ! 27 "
8. 73 ! 66 "
9. 92 ! 23 "
10.
57
11.
! 14
© Scott Foresman, Gr. 5
81
! 28
(104)
12.
62
! 45
13.
76
! 34
Use with Chapter 4, Lesson 6.
Name _____________________________________________________________________________________________________
Estimating Products
H 4-6
Estimate each product. Round to the greatest place.
1.
21
! 3
2.
59
! 41
6.
""
5.
3.
72
! 62
7.
""
""
9.
68
! 7
10.
"""
645
! 7
"""
4.
83
! 28
8.
""
""
927
! 4
19
! 5
""
""
11.
421
! 19
84
! 6
16
! 19
""
12.
"""
452
! 35
"""
13. 6 ! 58
14. 4 ! 96
15. 17 ! 34
16. 93 ! 82
17. 141 ! 8
18. 3 ! 285
19. 33 ! 192
20. 77 ! 506
21. 45 ! 96
22. 18 ! 89
23. 19 ! 9
24. 23 ! 11
Test Prep Circle the correct letter for each answer.
25. In which of the following is an exact answer more useful than an estimate?
A counting change for a purchase
C predicting the number of people in the
B the number of jelly beans in a jar
D describing the number of geese in a flock
for a contest
park on a given day
26. In which of the following is an estimate more useful than an exact answer?
F number of presidents of the
H time it takes to travel from home to
G teaspoons of salt in a recipe
J amount of medicine in a dose
United States
© Scott Foresman, Gr. 5
(105)
grandmother’s house
Use with Chapter 4, Lesson 6.
Name _____________________________________________________________________________________________________
Multiplying by One-Digit and Two-Digit Numbers
R 4-7
Find 52 ! 38.
Step 2
!"""
Multiply by the
ones. Regroup
if necessary.
!"""
Step 1
Place a zero in the ones
place. Multiply by the
tens. Regroup if
necessary.
1
52
! 38
""
416 !"" 52 ! 8
Step 3
Add the products.
52
! 38
""
416
1560 !"" 52 ! 30
52
! 38
""
416
# 1,560
""""
1,976
Check by estimating. 50 ! 40 $ 2,000.
The answer is reasonable because 1,976 is close to 2,000.
Here’s WHY it works
52 ! 38
1.
$
$
$
$
52 ! (30 # 8)
(52 ! 30) # (52 ! 8)
1560 # 416
1,976
52
! 24
2.
44
! 22
6.
""
5.
33
! 13
3.
91
! 46
7.
""
""
""
32
! 14
4.
56
! 11
8.
45
!9
""
""
""
35
! 72
""
9. 63 ! 7
10. 86 ! 12
11. 43 ! 37
12. 58 ! 5
13. 67 ! 22
14. 71 ! 8
© Scott Foresman, Gr. 5
(107)
Use with Chapter 4, Lesson 7
Name _____________________________________________________________________________________________________
Multiplying by One-Digit and Two-Digit Numbers
1.
24
! 27
I
55
! 14
O
31
! 27
I
37
! 49
M
2.
""
5.
6.
51
! 33
A
88
! 54
R
78
! 23
B
3.
10.
7.
""
R
42
! 43
T
96
! 55
E
51
! 19
L
4.
11.
8.
""
S
98
! 37
S
42
! 36
U
49
! 22
Y
""
12.
""
15.
96
! 11
""
""
""
14.
45
! 16
""
""
""
13.
N
""
""
9.
14
! 24
H 4-7
""
16.
""
""
Match the products in Exercises 1 – 16
to the numbers below the blanks and
write the appropriate letter on the blank.
You are my brother, but I am not your brother. Who am I?
______ ______
1,078 770
______
1,512
______
4,752
______
1,056
______
648
______
3,626
______
1,806
______ ______
5,280 720
Test Prep Circle the correct letter for each answer.
17. Southbank School recycles about 37 pounds of paper each week. How many pounds
will they recycle in 43 weeks?
A 1,410 pounds
B 430 pounds
C 1,591 pounds
D 148 pounds
18. Southbank School earns $1.19 for each 100 pounds of paper they recycle. Last year
they recycled about 17,000 pounds of paper. How much did they earn for their
recycling efforts?
F $20,230
© Scott Foresman, Gr. 5
G $202.30
(108)
H $833
J $119
Use with Chapter 4, Lesson 7.
Name _____________________________________________________________________________________________________
Problem-Solving Strategy
R 4-8
Solve a Simpler Problem
Ms. Tchou needs to teach 30 students how to use a new computer drawing program.
She has decided to teach the program to two students. Then each of those students
will teach 2 others and so on. No one will teach more than once. It takes 15 minutes to
learn the program. How long will it take all 30 students to learn the program?
Understand
What information do you have? What do you need to find? You
know how long it takes students—2 at a time—to learn the
program. You need to know how long it will take for 30 students to
learn the new program.
Plan
You can solve a simpler problem. Look for a pattern. Then
continue the pattern to find the answer to your problem.
Solve
How long will it take for 2 students to learn the program?
How long will it take 6 students to learn the program?
How many students will have learned the program after
Ms. Tchou has taught 2 students and 6 students have
each taught 2 students?
So it will take 30 students
program.
Look Back
minutes to learn the drawing
What other strategy did you use to discover the pattern?
Use the information above for Exercises 1–2.
1. If 62 students needed to learn the program, how long would using
Ms. Tchou’s method take?
2. How long will Ms. Tchou’s method take to teach 126 students
the new program?
© Scott Foresman, Gr. 5
(110)
Use with Chapter 4, Lesson 8.
Name _____________________________________________________________________________________________________
Problem-Solving Strategy
H 4-8
Solve a Simpler Problem
Use the information in the table at the right for Exercises 1–2.
1. Janeen is making sandwiches for her Round the
World study club. She will use one kind of bread
and only one kind of filling for each sandwich.
How many different sandwiches can she make?
2. Jorge decides that he will make sandwiches using
Bread
Filling
pita
turkey
bagel
cheese
tortilla
veggie
wheat bread
one kind of bread for each sandwich but either
one or two fillings. How many different sandwiches can he make?
3. Four students are sitting along one side of a bench as they eat lunch.
How many different seating arrangements can they make?
4. Four students are sitting at a circular table eating lunch.
How many different seating arrangements can the students make?
Hint: Because the table is circular, ABCD arrangement is the same
as BCDA, CDAB, and DABC.
5. Fifteen students decide to play musical chairs after lunch.
They will remove one chair each time the music stops. How many
times will the music have to stop for someone to win the game?
6. Crates of apples are labeled on each of four sides of a crate.
How many labels can you see when 16 boxes are lined up side-by-side?
7. Your school district’s basketball tournament includes 8 teams.
A team leaves the tournament as soon as it loses one game.
What is the greatest number of games one team will play?
© Scott Foresman, Gr. 5
(111)
Use with Chapter 4, Lesson 8.
Name _____________________________________________________________________________________________________
Multiplying Greater Numbers
R 4-9
Example
Find 452 ! 231.
!"""
!"""
Multiply by the
ones.
Step 2
Multiply by the tens.
Move to the left one
place or use one zero
as a placeholder.
Regroup if necessary.
1
Step 3
!"""
Step 1
Multiply by the
hundreds. Move to
the left two places
or use two zeros
as placeholders.
Step 4
Add the partial
products.
452
! 231
452
! 231
452
! 231
452
! 231
452
452
13560
452
13560
90400
452
13560
# 90400
""""
104,412
""
""
""
""
Check by estimating. 500 ! 200 $ 100,000.
The answer is reasonable because 104,412 is close to 100,000.
1.
355
! 221
2.
815
! 256
5.
"""
4.
3.
313
! 111
6.
"""
"""
"""
7. 601 ! 554
© Scott Foresman, Gr. 5
846
! 963
8. 715 ! 341
(113)
274
! 470
"""
921
! 402
"""
9. 127 ! 518
Use with Chapter 4, Lesson 9.
Name _____________________________________________________________________________________________________
Multiplying Greater Numbers
H 4-9
1.
745
! 853
2.
894
! 129
3.
479
! 392
4.
872
! 396
5.
517
! 312
6.
721
! 612
7.
455
!$3.14
8.
9.
815
! 325
12.
888
! 987
10.
689
! 212
11.
640
! 126
513
! 378
Test Prep Circle the correct letter for each answer.
13. Scrub-A-Pup charges $24.49 to wash and groom dogs weighing more than 60
pounds. During the last seven days, they washed and groomed 132 large dogs. How
much money did the store take in?
A $1,469.40
B $792.00
C $3,232.68
D $7,920.00
14. Scrub-A-Pup has a small dog special. On weekdays, dogs under 20 pounds are
washed and groomed for $19.49. Last week they washed and groomed 112 small
dogs. How much money did the store earn?
F $584.70
© Scott Foresman, Gr. 5
G $2,240.00
(114)
H $5,487.00
J $2,182.88
Use with Chapter 4, Lesson 9.
Name _____________________________________________________________________________________________________
Exponents
R 4-10
You can represent repeated multiplication of the same number by using
exponential notation.
3 ! 3 ! 3 ! 3 ! 3 can be written as 35
The base is the number to be multiplied. The exponent is the number that tells
how many times the base is used as a factor.
3 ! 3 ! 3 ! 3 ! 3 " 35
5 factors
5 is the exponent
3 is the base
Numbers involving exponents can be written in three different forms.
Exponential notation:
35
Expanded form:
3!3!3!3!3
Standard form:
243
An exponent is also called a power. Read 35 as “3 raised to the fifth power” or “3
to the fifth power.” Read 32 as “3 to the second power,” or “3 squared.” Read 33
as “3 to the third power,” or “3 cubed.”
Write using exponents.
1. 2 ! 2 ! 2 ! 2
2. 10 ! 10 ! 10 ! 10
3. 15 ! 15 ! 15
4. 11 ! 11 ! 11 ! 11 ! 11
5. 12 ! 12
6. 6 ! 6 ! 6 ! 6 ! 6 ! 6
2. 72
3. 55
2. 62
3. 25
Write in expanded form.
1. 43
Write in standard form.
1. 53
© Scott Foresman, Gr. 5
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Use with Chapter 4, Lesson 10.
Name _____________________________________________________________________________________________________
Exponents
H 4-10
Write using exponents.
1. 4 ! 4 ! 4 ! 4 ! 4
2. 9 ! 9 ! 9 ! 9
3. n ! n ! n ! n ! n ! n
5. 29
6. n5
8. 83
9. 132
11. 45
12. 252
Write in expanded form.
4. 63
Write in standard form.
7. 54
10. 202
13. Math Reasoning What is the value of the expression n1? Explain.
14. Evaluate n1 when n " 10, 14, 127.
15. In a fable, a poor man received a reward of 2 grains of rice on one day. On the
second day he received 22 grains of rice. On the third day he received 23 grains
as a reward. If the pattern continues, how many grains of rice did the man receive
on the tenth day? Give your answer using exponents and in standard form.
16. What was the total amount of rice the poor man had received by the end
of 10 days? Explain.
Test Prep Circle the correct letter for each answer.
17. This number squared equals 1,000,000.
A 10
B 100
C 1,000
D 10,000
H 3
J 27
18. This number cubed equals 729.
F 9
© Scott Foresman
G 81
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Use with Chapter 4, Lesson 10.
Name _____________________________________________________________________________________________________
Problem-Solving Applications
R 4-11
Using Money
Two families go to a movie together. The group
consists of 2 children who are 11 years old, 4 children
between the ages of 12 and 18, and 3 adults. How
much will the group have to pay altogether?
Understand You need to find the total cost
for the group.
Plan
Solve
Movie Admission
Children under 12
$3.00
Students 12–18
$5.00
Adults
$7.00
Use a multistep approach. First, multiply the number of tickets
needed for each age group by the admission cost. Then add to
find the total cost.
Step 1
Children
under 12
Step 2
Students
12 – 18
Step 3
Adults
Step 4
Everyone
$3.00
!
2
$5.00
!
4
$7.00
!
3
Students $20.00
$47.00
Children
"""
"""
"""
$6.00
$20.00
$21.00
Adults
$6.00
$21.00
The cost of admission to the movies is $47.00 for this group.
Look Back
Did you use the correct data from the Movie Admission chart?
Did you multiply and add correctly?
Use the data in the Movie Admission chart to solve Exercises 1–2.
1. The Maynard family went to a movie. They bought 2 adult tickets
and tickets for their children who are 8, 11, and 14 years old.
How much did they spend in all?
2. The Gonzalez family has three adults and one child 7 years old. Will it cost
them more or less than the Maynards to go to the movies? Explain.
© Scott Foresman, Gr. 5
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Use with Chapter 4, Lesson 11
Name _____________________________________________________________________________________________________
Problem-Solving Applications
H 4-11
Using Money
You will need to use the table for some problems.
1. The Hashimoto family went to a play. They bought
2 adult tickets, 3 student tickets, and 1 senior
citizen ticket. How much did they spend?
Play Tickets
Students under 18
$4.00
Adults
$7.50
Senior Citizens
$4.50
2. The fifth-grade class plans to take a field trip to a play. There are 23 students
and 3 adults. How much will the tickets cost?
3. Nick plans to take his grandmother to a play. He has saved $10. Does he have
enough money to buy 1 student ticket and 1 senior citizen ticket? Explain.
4. The Cooper family spent $23 for tickets to a play, $11.50 for snacks at intermission,
and $12.75 for souvenirs. How much did they spend in all?
5. The theater offers discounts to student groups of more than 100. They charge $3.50
per student for large groups. If 105 students go to a play, how much will they save
using the discount? Explain.
6. A restaurant near the theater has a special rate for groups. Any child 12 and under
can have soup and a sandwich for $4.50. For everyone else, the price is $5.25 per
person. Suppose four adults take five 10-year-olds to the restaurant. What is the total
cost of their meal?
7. Which group will pay more for a meal at this restaurant: 6 adults or 7 children under 12?
© Scott Foresman, Gr. 5
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Use with Chapter 4, Lesson 11.