Multiplication

1
Multiplication Related Concepts

• PRACTICE TEST

2
1.) Find the product mentally.300 x 500
3
Find the product mentally.300 x 500
150,000 The number of zeros in the factors
equals the number of zeros in the product.
4
2.) There are only a few exceptions to this
rule.For example, what is the following
product?40 x 500
5
Extra Zero
40 x 500 20,000
3 zeros
3 zeros
6
3.) Find the product mentally..2 x .3
7
Find the product mentally..2 x .3 .06 The
number of digits to the right of the decimal
point in the factors must equal the number of
digits to the right of the decimal point in the
product.
8
4.) Use pencil and paper to find the following
product.
5.16 x .45
9
Use pencil and paper to find the following
product.
5.16 x .45 2580 20640 2.3220
Remember to use a placeholder on this row.
10
5.) What number belongs on the third row of this
problem?
291 x413 873 2910 ______ 120,183
11
What number belongs on the third row of this
problem?
291 x413 873 2,910 116,400 120,183
You need 2 place-holders on this row.
12
6.) What is the standard form of53
13
What is the standard form of53
5 x 5 x 5 125
14
7.) The area of this rectangle can be expressed
as (4 x5) (4 x 6)
4
5 6

• What property does this show?
• Commutative
• Associative
• Distributive

15
The area of this rectangle can be expressed as (4
x5) (4 x 6)
4
5 6

• What property does this show?
• Commutative
• Associative
• Distributive

16
The area of this rectangle can be expressed as (4
x5) (4 x 6)
4
4 x 5
4 x 6
4
5 6
C) Distributive
17
8) Which expression uses the distributive
property to find the product of 4 and 32?A) 4 x
(30 x 2)B) 40 x (3 2)C) 4 (30 x 2)D) 4 x
(30 2)
18
Which expression uses the distributive property
to find the product of 4 and 32?A) 4 x (30 x
2)B) 40 x (3 2)C) 4 (30 x 2)D) 4 x (30 2)
19
9) Which expression does NOT show how to
calculate the perimeter of the rectangle?
3

• 3 x 8
• 3 8 3 8
• 2 x (3 8)
• 3 x 2 8 x 2

8
20
Which expression does NOT show how to calculate
the perimeter of the rectangle?
3

• 3 x 8 24
• 3 8 3 8 22
• 2 x (3 8) 22
• 3 x 2 8 x 2 22

8
21
Remember, perimeter is the total distance around
the shape.
8
3
3
8
22
10) Evaluate the following expression3 x 4 5 x
6
23
Evaluate the following expression3 x 4 5 x 6
12 30 42 Remember,
multiplication comes before addition in the order
of operations.
24
11.) Evaluate the following expression(2 5)2
(2 3)2
25
Evaluate the following expression(2 5)2 (2
3)2
72 - 52
Remember, parentheses come first in the order of
operations.
26
Evaluate the following expression(2 5)2 (2
3)2
72 - 52
49 - 25 24
Remember, exponents come before subtraction in
the order of operations.
27
12.) Evaluate the following expression3 x 10 ? 2
x 4
28
Evaluate the following expression3 x 10 ? 2 x 4
30 ? 2 x 4
29
Evaluate the following expression3 x 10 ? 2 x 4
30 ? 2 x 4
15 x 4 60
Remember, if there is only multiplication
division in the expression, then work left to
right.
30
Order of Operations

• Please
• Excuse
• My Dear
• Aunt Sally

31
Order of Operations

• Parentheses
• Excuse
• My Dear
• Aunt Sally

32
Order of Operations

• Parentheses
• Exponents
• My Dear
• Aunt Sally

33
Order of Operations

• Parentheses
• Exponents
• Multiplication Division
• Aunt Sally

34
Order of Operations

• Parentheses
• Exponents
• Multiplication Division
• Addition Subtraction

35
13.) After you press the following keys on your
calculator, you see 17 on the display.2 3 x 5
You press another sequence of keys and see 36
on the display. Which of the following key
sequences might you have used?

• 3 x 10 3 x 5
• 3 x 5 3 x 5
• 4 x 8 2 x 2
• 3 x 10 x 5

36
After you press the following keys on your
calculator, you see 17 on the display.2 3 x 5
You press another sequence of keys and see 36
on the display. Which of the following key
sequences might you have used?

• 3 x 10 3 x 5 45
• 3 x 5 3 x 5 30
• 4 x 8 2 x 2 36
• 3 x 10 x 5 150

37
14.) Which of the following key sequences would
produce the same display on a calculator using
algebraic logic or a calculator using arithmetic
logic?

• 40 3 x 5
• 100 25 ? 5
• 4 x 8 20
• 4 x 5 3 x 2

38
Which of the following key sequences would
produce the same display on a calculator using
algebraic logic or a calculator using arithmetic
logic?
Algebraic Arithmetic

• 40 3 x 5 25 185
• 100 25 ? 5
• 4 x 8 20
• 4 x 5 3 x 2

39
Which of the following key sequences would
produce the same display on a calculator using
algebraic logic or a calculator using arithmetic
logic?
Algebraic Arithmetic

• 40 3 x 5 25 185
• 100 25 ? 5 105 25
• 4 x 8 20
• 4 x 5 3 x 2

40
Which of the following key sequences would
produce the same display on a calculator using
algebraic logic or a calculator using arithmetic
logic?
Algebraic Arithmetic

• 40 3 x 5 25 185
• 100 25 ? 5 105 25
• 4 x 8 20 52 52
• 4 x 5 3 x 2

41
Which of the following key sequences would
produce the same display on a calculator using
algebraic logic or a calculator using arithmetic
logic?
Algebraic Arithmetic

• 40 3 x 5 25 185
• 100 25 ? 5 105 25
• 4 x 8 20 52 52
• 4 x 5 3 x 2 26 46

42
Which of the following key sequences would
produce the same display on a calculator using
algebraic logic or a calculator using arithmetic
logic?
Algebraic Arithmetic

• 40 3 x 5 25 185
• 100 25 ? 5 105 25
• 4 x 8 20 52 52
• 4 x 5 3 x 2 26 46

43
Multiplication must be done before addition using
the correct order of operations. However, if you
work this problem from left to right, you will
still do the multiplication first.
Algebraic Arithmetic

• C) 4 x 8 20 52 52

44
15.) Which of the following key sequences would
produce a different display on a calculator using
algebraic logic than on a calculator using
arithmetic logic?

• 5 x 6 ?? 2
• 20 10 5
• 5 x 6 5
• 3 4 x 5

45
Which of the following key sequences would
produce a different display on a calculator using
algebraic logic than on a calculator using
arithmetic logic?
Algebraic Arithmetic

• 5 x 6 ?? 2 15 15
• 20 10 5
• 5 x 6 5
• 3 4 x 5

46
Which of the following key sequences would
produce a different display on a calculator using
algebraic logic than on a calculator using
arithmetic logic?
Algebraic Arithmetic

• 5 x 6 ?? 2 15 15
• 20 10 5 15 15
• 5 x 6 5
• 3 4 x 5

47
Which of the following key sequences would
produce a different display on a calculator using
algebraic logic than on a calculator using
arithmetic logic?
Algebraic Arithmetic

• 5 x 6 ?? 2 15 15
• 20 10 5 15 15
• 5 x 6 5 25 25
• 3 4 x 5

48
Which of the following key sequences would
produce a different display on a calculator using
algebraic logic than on a calculator using
arithmetic logic?
Algebraic Arithmetic

• 5 x 6 ?? 2 15 15
• 20 10 5 15 15
• 5 x 6 5 25 25
• 3 4 x 5 23 35

49
Which of the following key sequences would
produce a different display on a calculator using
algebraic logic than on a calculator using
arithmetic logic?
Algebraic Arithmetic

• 5 x 6 ?? 2 15 15
• 20 10 5 15 15
• 5 x 6 5 25 25
• 3 4 x 5 23 35

50
16.) Which of the following numbers is a square
number?

• 2
• 9
• 12
• 20

51
Which of the following numbers is a square number?

• 2
• 9
• 12
• 20

3
3
Area 32 3 x 3 9
52
17) Which of the following numbers is a cubic
number?

• 3
• 6
• 8
• 15

53
Which of the following numbers is a cubic number?

• 3
• 6
• 8
• 15

2
2
2
Volume 23 2 x 2 x 2 8
54
18.) Draw the factor tree for the number 40.
Then write the prime factorization of 40 using
exponents when appropriate.
55
40

56
40
5 8
57
40
5 8
58
40
5 8
2 4
59
40
5 8
2 4
60
40
5 8
2 4
2 2
61
40
5 8
2 4
2 2
62
40
5 8
2 4
2 2
40 23 x 5
63
19.) Draw the factor tree for 60. Then write the
prime factorization of 60 using exponents when
appropriate.
64
60
65
60
6 10
66
60
6 10
3 2 2 5
67
60
6 10
3 2 2 5
68
60
6 10
3 2 2 5
60 22 x 3 x 5
69
20.) Use a Venn diagram to find the greatest
common factor of 20 and 16.
70
16 20
71
16 20

• 16
• 8
• 4

72
16 20

• 20
• 10
• 4 5

• 16
• 8
• 4

73
16 20

• 20
• 10
• 4 5

• 16
• 8
• 4

74
16 20
20 10 5
1 2 4
16 8
75
16 20
20 10 5
1 2 4
16 8
4 is the greatest common factor of 16 and 20.
76
21.) Use a Venn diagram to find the least common
multiple of 4 and 6
77
4 6
78
4 6

• 8
• 16
• 20 24

79
4 6

• 8
• 16
• 20 24

• 12
• 24
• 30

80
4 6

• 8
• 16
• 20 24

• 12
• 24
• 30

81
4 6

• 8
• 16
• 20

12 24
6 18 30
82
12 is the least common multiple of 4 and 6.
4 6

• 8
• 16
• 20

12 24
6 18 30
83
22.) Which of the following numbers is a prime
number?

• 4
• 5
• 8
• 9

84
Which of the following numbers is a prime number?

• 4 2 x 2
• 5 1 x 5
• 8 2 x 2 x 2
• 9 3 x 3

The only way to make 5 is to do 1 times 5.
85
23.) Which of the following numbers is composite?

• 7
• 11
• 15
• 19

86
Which of the following numbers is composite?

• 7 1 x 7
• 11 1 x 11
• 15 3 x 5
• 19 1 x 19

87
24.) At the amusement park, Mike and his 5
friends each rode the bumper cars twice. The
total cost of their rides was 9.00. Write a
numerical expression that would help you find the
cost of each ride.
88
Possible answer9.00 ? (6 people x 2 rides
each)
89
25.) Write an expression to find the area of the
outer rectangle. Use the distributive property.
6
10
5
90
Possible answers 6 x (10 5) or (6 x 10) (6 x
5)
6
10
5
91
What you need to know for this test

• Multiply with whole numbers and decimals
• Distributive property
• Order of operations
• Exponents (square cubic numbers)
• Greatest Common Factor Least Common Multiple
• Factor Trees Prime Factorization (prime
  composite numbers)
• Writing numerical expressions

92
Study Hard!