Free Printable Order of Operations and Algebraic Properties

1.

(7 + 41) ÷ 2 – 15

a)

19

b)

9

c)

25

d)

3

2.

15 + 7 × 2 – 11 + 35=

a)

38

b)

251

c)

53

d)

50

3.

8²- 20 ÷ 2 x 5

a)

14

b)

10

4.

8(3 + 4) =

a)

24 + 32

b)

11 + 12

c)

123 + 124

d)

5 + 4

5.

12(3 + 4) =

a)

36 + 48

b)

15 + 16

c)

123 + 124

d)

0.84

6.

Solve 7 x 57 using the distributive property.

a)

499

b)

398

c)

399

d)

599

7.

Solve 89 x 6 using the distributive property.

a)

534

b)

434

c)

539

8.

Which is an example of Associative Property of Addition?

a)

(12+3)+8=12x(3x8)

b)

12x(3x8)=(12x3)x8

c)

(12+8)+3=12+(8+3)

d)

12 + 18 = 18 + 12

9.

What number fills in the blank?
5 + (7 + 6) = (5 + ___) + 6

a)

8

b)

6

c)

5

d)

7

10.

Which equations show the commutative property of multiplication?

a)

5 × 4 = 4 × 5

b)

4 × 2 + 7 = 4 × 9

c)

4 + 4 + 1 + 1 = 2 × 5

d)

6 + 6 + 6 + 6 + 6 + 6= 3 × 3 × 4

11.

Which one shows the numbers in order from biggest to smallest?

a)

3²,2³,6¹

b)

6¹,2³,3²

c)

2²,6¹,3²

12.

10 + 45 ÷ 9 -(14 ÷ 2) =

a)

9

b)

7

c)

53

d)

18

13.

Simplify:
[25-(13+4)+4] ÷ 3

a)

6

b)

2

c)

3

d)

4

14.

11²- 8 ⋅ 7 + 2

a)

100

b)

793

c)

67

d)

49

15.

7[12 − (6 − 2) ÷ 4]

a)

7

b)

77

c)

14

d)

0

16.

What property allows for two or more numbers to be added in any order without changing the sum?

a)

Associative Property of Addition

b)

Commutative Property of Multiplication

c)

Commutative Property of Addition

d)

Distributive Property

17.

What property allows for two or more numbers to be multiplied in any order without changing the sum?

a)

Associative Property of Multiplication

b)

Commutative Property of Multiplication

c)

Distributive Property

d)

Multiplicative Identity Property

18.

What property states that the sum of three or more numbers is always the same, regardless of how they are grouped together with parentheses?

a)

Associative Property of Addition

b)

Associative Property of Multiplication

c)

Commutative Property of Addition

d)

Additive Identity

19.

What property states that the product of three or more numbers is always the same, regardless of how they are grouped together with parentheses?

a)

Associative Property of Multiplication

b)

Associative Property of Addition

c)

Commutative Property of Multiplication

d)

Multiplicative Identity

20.

What property includes both addition and multiplication and allows you to rewrite an expression from a product of two numbers to the sum of two separate products?

Example: 3(4x+5) = 12x+15

a)

Associative Property of Multiplication

b)

Commutative Property of Addition

c)

Additive Inverse Property

d)

Distributive Property

21.

The following equation is representing what TWO properties?

3 + 0 = 3

a)

Addition Property of Zero

b)

Additive Identity Property

c)

Multiplicative Identity Property

d)

Commutative Property of Multiplication

22.

What property is represented by the following equation?
4 $\cdot$ 1 = 4

a)

Multiplicative Inverse Property

b)

Associative Property of Multiplication

c)

Multiplicative Identity Property

d)

Commutative Property of Multiplication

23.

What property states that the product of a number and its reciprocal is always 1?

a)

Multiplicative Identity Property

b)

Distributive Property

c)

Multiplicative Inverse Property

d)

Commutative Property of Multiplcation

24.

What property states that the sum of a number and its opposite always equals zero?

a)

Additive Inverse Property

b)

Additive Identity Property

c)

Commutative Property of Addition

d)

Distributive Property

25.

What is an expression that contains at least one variable called?

a)

operational expression

b)

constant expression

c)

numerical expression

d)

algebraic expression

26.

A lower case letter or symbol used to represent an unknown value is called a what?

a)

term

b)

variable

c)

constant

d)

operation

27.

A numerical value in an expression that does not change its value is called a what?

a)

constant

b)

variable

c)

operation

d)

symbol

28.

The number (in front of a variable) that is multiplied by the variable in an algebraic expression is called a what?

a)

constant

b)

operator

c)

coefficient

d)

term

29.

What are the parts of an algebraic expression called that are added or subtracted?

a)

terms

b)

operations

c)

coefficients

30.

Addition, subtraction, multiplication, and division are called the four basic what?

a)

commands

b)

equations

c)

terms

d)

operations

31.

The process of finding the value of a numerical or algebraic EXPRESSION is called what?

a)

identifying

b)

graphing

c)

evaluating

d)

solving

32.

True or False: Terms that have the same variables and can be combined through addition and subtraction are called "like terms."

a)

true

b)

false

33.

True or False: Expressions that are written differently but have the same value are called "equivalent expressions."

a)

true

b)

false

34.

In the order of operations, which operation is simplified first?

a)

mulitplication

b)

subtraction

c)

exponents

d)

division

35.

Which key word/phrase DOES NOT apply to subtraction?

a)

less than

b)

quotient

c)

difference

d)

subtracted from

36.

Which expression best describes the statement "the product of a number and 5"?

a)

$\frac{p}{5}$

b)

$p+5$

c)

$5-p$

d)

$5p$

37.

Are these expressions equivalent? $8n+12\ =\ 4\left(2n+6\right)$

a)

yes

b)

no

38.

Are these expressions equivalent? $7\left(3x+5\right)=21x+35$

a)

yes

b)

no

39.

Which is an example of the Associative Property of Addition?

a)

7+(6+3)=7+(3x6)

b)

3x4 = 4x3

c)

7 + 3 = 13 + 7

d)

2+(3+4)=(2+3)+4

40.

Which of these illustrates the Associative Property of Multiplication?

a)

4x(5x6)=(4x5)x6

b)

6+(9+1)=(6x9)+1)

c)

4 x (56) = (45) x 6

d)

5 + 0 = 0 + 5

41.

Adding zero to any number does not change the number. The sum will be that number. Which property is this?

a)

Commutative Property

b)

Identity Property

42.

2 + 5 + 6 = 6 + 2 + 5

a)

Associative

b)

Commutative

c)

Identity

43.

What property of addition can change order, but stay the same? Hint: looks like a mirror

a)

Associative

b)

Commutative

c)

Identity

44.

Simplify the expression:
8(5 + w)

a)

40 + w

b)

40+8w

c)

85 + 8w

d)

13+8w

45.

9x-21 is equivalent to which of the following expressions?

a)

3(3x-7)

b)

3(x-2)

c)

3x

d)

Potatoes

46.

Which operation would you do first in the following equation?
10 - 4 ÷ 1 · 5

a)

Subtraction

b)

Division

c)

Multiplication

d)

Addition

47.

(52 ÷ 4) + 5³

a)

28

b)

38

c)

138

48.

27 ÷ 3 x 2 + 4²

a)

34

b)

20.5

c)

26

49.

How do you write 2 x 2 x 2 x 2 with an exponent?

a)

4²

b)

2⁴

c)

2²

50.

The exponent equivalent of 20 x 20 x 20 is

a)

20 x 3

b)

20³

c)

3²⁰

51.

What does the term "squared" mean?

a)

raised to the power of 3

b)

raised to the power of 4

c)

raised to the power of 2

52.

What does the term"cubed" mean?

a)

raised to the power of 2

b)

raised to the power of 3

c)

raised to the power of 4

53.

Which operation would you do first in the following equation?
10 - 4 ÷ 1 · 5

a)

Subtraction

b)

Division

c)

Multiplication

d)

Addition

54.

Which operation would you do first?
( 12 + 10) ÷ 10 · 14 - 6

a)

Division

b)

Multiplication

c)

Addition

d)

Subtraction

55.

What does 3² mean?

a)

3 x 2

b)

3 x 3

c)

2 x 2 x 2

56.

4²- 6

a)

16

b)

8

c)

2

d)

10

57.

What would be my first step? 3 + 4 x 6 - 4 =

a)

addition

b)

multiplication

c)

subtraction

d)

exponents

58.

(8 + 5) + 8 ÷ 4

a)

5 R 1

b)

16

c)

6 r 1

d)

15

59.

Which expression equals 9.

a)

(4 - 1) x (2 + 1)

b)

(3 x 4) - 1

c)

12 - 9 x 3

d)

7 x 2 - 6

60.

a)

8y+5

b)

3y+3

c)

7y+5

d)

7y+4

61.

a)

24z+8

b)

22z+6

c)

23z+8

d)

24z+2

62.

a)

10x+16

b)

12x+18

c)

16x+18

d)

15x+18

63.

a)

6x-1

b)

10x+7

c)

6x+1

d)

8x+1

64.

a)

5x+5y+18

b)

6x+6y+10

c)

5x+2y+18

d)

5x +6y+10

65.

a)

9x+6

b)

3x+4

c)

3x-4

d)

6x+4

66.

a)

13x+11

b)

2x-1

c)

x-1

d)

2x+1

67.

a)

2x²+13y+5

b)

2x²+13y-5

c)

x²-y-5

d)

4x²-13y-5

68.

a)

2y-2

b)

x²+2y-2

c)

2x²-2y+2

d)

-2y+2

69.

a)

2y-2

b)

x²+2y-2

c)

2x²-2y+2

d)

-2y+2

70.

a)

x²+2y+8

b)

2x²+y+4

c)

2x²+2y+4

d)

2y+4

71.

a)

x+y+1

b)

15x+19y+11

c)

-x-y-1

d)

-15x-19y-11

72.

a)

x+y+1

b)

-15x-19y-11

c)

-x+y+1

d)

-x-y-1

73.

a)

2x²-2y-2

b)

-3x²-2y-2

c)

-2x²-4y-2

d)

-2x²-2y+2

74.

2x - 5x =

a)

-3x

b)

3x

c)

-3

d)

3

75.

-4x - 10x

a)

-14

b)

6x

c)

-6x

d)

-14x

76.

Simplify:
-8x + 4x

a)

-12x

b)

-4x

c)

4x

d)

12x

77.

Simplify:
2x + 1 + 7x

a)

10x

b)

10

c)

9x + 1

d)

9 + 1x

78.

Simplify:
2x + 1 + 7x

a)

10x

b)

10

c)

9x + 1

d)

9 + 1x

79.

-2x + 11 + 6x

a)

8x+11

b)

4x +11

c)

4x

d)

15x

80.

Distribute
5(a + 6)

a)

5a + 6

b)

a + 30

c)

5a + 30

d)

5a - 30

81.

Distribute
(b + 8)5

a)

b + 40

b)

5b - 40

c)

5b + 40

d)

5b + 8

82.

-r -10r

a)

11r

b)

-11r

c)

9r

d)

-11

83.

Distribute
-(2x - 7)

a)

-2x + 7

b)

2x

c)

2x - 7

d)

9x

84.

-4x - 10x

a)

-14

b)

6x

c)

-6x

d)

-14x

85.

Simplify the following expression:
3 + 5x + 8 - 2x

a)

-3x² - 11

b)

3x² + 11

c)

11 - 3x

d)

11 + 3x

86.

Simplify the following expression:
-8x + 4x

a)

-12x

b)

-4x

c)

4x

d)

12x

87.

Simplify the following expression:
(5 + 4x) + (2x - 8)

a)

13 + 6x

b)

6x - 3

c)

6x - 13

d)

6x + 3

88.

Simplify
6(x + -2)

a)

6x + -2

b)

6x + -12

c)

4x

d)

6x - 2

89.

Simplify by combining like terms:
5a + 2b - 3a + 4

a)

8a + 2b + 4

b)

2a + 2b + 4

c)

8ab

d)

4ab + 4

90.

3x-5x

a)

2x

b)

8x

c)

-2x

d)

15x²

91.

-r -10r

a)

11r

b)

-11r

c)

9r

d)

-11

92.

-6k + 7k=

a)

k

b)

-k

c)

12k

d)

-12k

93.

n -10 +9n -3=

a)

-3

b)

9n-3

c)

n

d)

10n -13

94.

-4x - 10x

a)

-14

b)

6x

c)

-6x

d)

-14x

95.

Combine like terms
3x + 2x + 3y - 7y

a)

5x + 10y

b)

5x + 4y

c)

5x - 4y

d)

5x -10y

96.

-2x + 11 + 6x

a)

8x+11

b)

4x +11

c)

4x

d)

15x

97.

-6k + 7k=

a)

k

b)

-k

c)

12k

d)

-12k

98.

-2x + 11 + 6x

a)

8x+11

b)

4x +11

c)

4x

d)

15x

99.

Simplify the expression:
n -10 +9n -3

a)

-3

b)

9n-3

c)

n

d)

10n -13

100.

-2x + 11 + 6x

a)

8x+11

b)

4x +11

c)

4x

d)

15x

101.

-v +12v

a)

11v

b)

-9v

c)

0

d)

11

102.

Simplify the expression: 2x + 1 + 7x

a)

10x

b)

10

c)

9x + 1

d)

9 + 1x

103.

Simplify the expression: 7v + 2 + 12 + 2v

a)

23

b)

23v

c)

9 + 14v

d)

9v + 14

104.

Simplify: 2x+3+9x+2

a)

16x

b)

11x+5

c)

5x+11

d)

16+x

105.

Simplify: -2x+8y+10x

a)

12x+8y

b)

-20xy

c)

8x+8y

d)

10xy+10x

106.

Simplify: -7+25x-9

a)

-16+25x

b)

-2+25x

c)

2+25x

d)

16+25x

107.

A prime number...

a)

has one factor.

b)

has more than 2 factors.

c)

has 100 factors.

d)

has exactly 2 factors: 1 and the itself.

108.

A composite number ...

a)

has more than 2 factors.

b)

has one factor.

c)

has at least 10 factors.

d)

is always a really big number.

109.

One is...

a)

prime

b)

composite

c)

not prime or composite

d)

the loneliest number

110.

Which of the following is NOT prime?

a)

29

b)

23

c)

17

d)

39

111.

Is 5, a prime or composite number?

a)

Prime

b)

Composite

112.

Is 12, a prime or composite number?

a)

Prime

b)

Composite

113.

Is 17, a prime or composite number?

a)

Prime

b)

Composite

114.

Is 34, a prime or composite number?

a)

Prime

b)

Composite

115.

All of these are prime except

a)

3

b)

9

c)

2

d)

13

116.

2 x 2 x 2 is the prime factorization of...

a)

6

b)

12

c)

22

d)

8

117.

If the expanded form is 2⋅2⋅2⋅3⋅3⋅5⋅7 what would the exponential form be?

a)

2⋅3⋅5⋅7

b)

2³⋅3²⋅5⋅7

c)

2²⋅3²⋅5⋅7

d)

8⋅9⋅35

118.

Which is the prime factorization of 12 ?

a)

2 x 6

b)

2 + 2 + 2 + 2 + 2 + 2

c)

2²x 3

d)

1 x 2²x 3

119.

What is the prime factorization of 16 ?

a)

1 x 16

b)

2²x 4

c)

2⁴

d)

2² + 2²

120.

Find the prime factorization of 72

a)

2³x 3²

b)

2 x 3² x 4

c)

2⁴ x 3³

d)

2² x 6²

121.

Find the prime factorization of 105

a)

7x5x3

b)

11x5x3

c)

7x5x2x1

d)

7x5x3x2

122.

Find the prime factorization of 111

a)

33³

b)

3² x 11

c)

3 x 37

d)

2² x 3 x 11

123.

What is the prime factorization of 192 ?

a)

3⋅ 6²

b)

2⁶⋅ 3

c)

2⁸⋅ 3

d)

3 ⋅ 8²

124.

What are the prime factors of 30?

a)

3, 2, 5

b)

1, 2, 3, 5, 6, 15, 30

c)

3, 30

d)

10, 3

125.

Stickers come in packs of 12. Notebooks come in packs of 10. What is the fewest number of packs of each item that Lindsay can buy in order to have the same number of each item.

a)

10 packs of stickers; 12 packs of notebooks

b)

5 packs of stickers; 6 packs of notebooks

c)

6 packs of stickers; 5 packs of notebooks

d)

60 packs of each

126.

Use a number tree to find the prime factorization of 32

a)

2x2x2x4

b)

2x2x2x2x2

c)

4x4x2

d)

2x2x2x2x1

127.

Use a number tree to find the prime factorization of 60

a)

5x3x2x2

b)

7x6x5

c)

5x3x3x2

d)

7x5x4

128.

Use a number tree to find the prime factorization of 42

a)

4x4x3

b)

6x7

c)

7x3x2

d)

5x4x2

129.

Use a number tree to find the prime factorization of 64

a)

4x4x4

b)

4x4x2x2

c)

2x2x2x2x2x2

d)

4x4x2x1

130.

Use a number tree to find the prime factorization of 33

a)

33

b)

11x3

c)

10x3

d)

3x3x3x2

131.

Use a number tree to find the prime factorization of 72

a)

2x2x2x3x3

b)

4x3x3x2

c)

4x2x2x2x2

132.

Use a number tree to find the prime factorization of 48

a)

4x2x6

b)

4x2x2x3

c)

3x2x2x2x2

d)

12x4

133.

You spend $40 on 5 pounds of concrete. What is the unit rate in dollars per pound?

a)

$8 per pound

b)

$5 per pound

c)

$35 per pound

d)

0.125 pounds per dollar

134.

A store sees 120 customers in 8 hours. What is the unit rate (in customers per hour)?

a)

16 customers per hour

b)

15 customers per hour

c)

12 customers per hour

d)

20 customers per hour

135.

Solve for x

a)

x = 19.6

b)

x = 5/98

c)

x = 101/5

136.

Solve for x

a)

x = 6

b)

x = 25

c)

x = 28

d)

x = 17

137.

Solve for x

a)

x = 16

b)

x = 28

c)

x = 1/26

d)

x = 26

138.

What is a proportion?

a)

When two ratios can be simplified

b)

When two ratios are equivalent and show the same value

c)

When two ratios have the exact same numbers

d)

When two ratios can be multiplied by 2

139.

Solve the proportion.

a)

10.8

b)

7.5

140.

There were 5 ice cream cones for every 3 brownies sold at the ice cream shop. If there were 24 brownies sold, how many ice cream cones were sold?

a)

8

b)

15

c)

40

d)

29

141.

Solve for x

a)

x = 15

b)

x = 11

c)

x = 1/11

d)

x = 20

142.

Explain your answer.

a)

1

b)

3

c)

9

d)

8

Order of Operations and Algebraic Properties

Total questions: 142

Worksheet time: 4hrs 0mins

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