Chapter 9 1 How can you rewrite a subtraction of integers problem

Exam

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Answer the question.

1)

Choose the expression that is equivalent to the following: (4x + 2y)(9y + 8x)

1)

A)

(4x +2y)(8x +9y)

B)

(4x +8y)(2x +9y)

C)

12x +11y

D)

(4x +2y)(8y +9x)

Provide an appropriate response.

2)

Give one number between –10 and 10 that is a real number but not not an integer.

2)

A)

3.60555128

B)

–9

C)

9

D)

Not possible

A

Answer the question.

3)

Choose the expression that is equivalent to the following: 5(3a) + 5(6b)

3)

A)

5(9ab)

B)

5(3a +6b)

C)

10(9ab)

D)

10(3a +6b)

B

4)

Choose the expression that is equivalent to the following: 1(9y2)

4)

A)

10y2

B)

1

C)

9y2

D)

9y3

C

Provide an appropriate response.

5)

Give one number between –8 and 8 that is a negative real number but not an integer.

5)

A)

5

B)

Not possible

C)

5.38516481

D)

–5.3851648

D

A

Answer the question.

6)

Which one of the following is the correct method for evaluating the expression 2x2– 5 for x =6?

6)

A)

2 · 62– 5 = (12 – 5)2= 7 = 49

B)

2 · 62– 5 = 2 · 36 – 5 = 72 – 5 = 67

C)

2 · 62– 5 = 2 · 12= 2 · 1 = 2

D)

2 · 62– 5 = 122– 5 = 144 – 5 = 139

7)

Which phrase correctly translates the expression 13 – x?

7)

A)

x less than 13

B)

x take away 13

C)

x minus 13

D)

13 subtracted from x

8)

Choose the expression that is equivalent to the following: (4x + 8y)(6y2)

8)

A)

(4x) + (8y)(6y2)

B)

(6y2)(4x+8y)

C)

(4x +6y2)(8y)

D)

4x + (8y +6y2)

9)

Which pair of values of x and y makes 4x + y equal 10?

9)

A)

x = 5 and y = 10

B)

x = 10 and y = 5

C)

x = 1 and y = 6

D)

x = 6 and y = 1

10)

Which pair of values of x and y makes x – 3y equal 5?

10)

A)

x = 3 and y = 4

B)

x = 11 and y = 2

C)

x = 4 and y = 3

D)

x = 2 and y = 11

Provide an appropriate response.

11)

Give one number between –8 and 8 that is a negative real number but not an integer.

11)

A)

–3.67

B)

3.67

C)

7

D)

Not possible

Answer the question.

12)

Choose the expression that is equivalent to the following: 3– 3

12)

A)

(3)(3)

B)

3+ (–3)

C)

(–2)(3)

D)

2(3)

13)

Choose the expression that is equivalent to the following: 0 + 2b

13)

A)

–2b

B)

0

C)

2b

D)

2+b

14)

Choose the expression that is equivalent to the following: 6x + 2y

14)

A)

2(3x + y)

B)

2(4x + y)

C)

2(3x +2y)

D)

8xy

15)

Choose the expression that is equivalent to the following: 9( 1

9)

15)

A)

91

9

B)

9+1

9

C)

9

D)

1

81

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Give a number that satisfies the given condition.

16)

A whole number greater than 3.5

16)

Write the statement in words and decide whether it is true or false.

17)

65

17)

Provide an appropriate response.

18)

A whole number less than 4.8.

18)

19)

How can you rewrite a subtraction of integers problem to make it easier to solve? Give an

example.

19)

Write the statement in words and decide whether it is true or false.

20)

11

20)

Provide an appropriate response.

21)

Make up a subtraction problem in which the difference between two negative numbers

results in a positive number.

21)

22)

A positive number multiplied by two negative numbers and then divided by a positive

number is .

22)

Answer the question or complete the sentence to make a true statement.

23)

Under what condition will the sum of a positive number and a negative number be

positive?

23)

Provide an appropriate response.

24)

What is the additive inverse of 0?

24)

25)

How is the order of operations applied to integers?

25)

26)

What values of a and b make the result negative? –(a – b)

26)

27)

Is this statement true or false? Why? (9– 9) – 9 =9– (9– 9)

27)

28)

If x and y are both replaced by negative numbers, is the value of 5x – 4y positive or

negative?

28)

Give a number that satisfies the given condition.

29)

A whole number less than 3.5

29)

Write the statement in words and decide whether it is true or false.

30)

13

85

4

30)

Provide an appropriate response.

31)

The only real number that does not have a reciprocal is .

31)

32)

Fill in the blanks with the correct numbers.

The opposite of –4 is _____.

The absolute value of –4 is _____.

The opposite of the absolute value of –4 is _____.

The absolute value of the opposite of –4 is _____.

32)

Write the statement in words and decide whether it is true or false.

33)

12 >6+ 5

33)

Provide an appropriate response.

34)

The average of a group of positive numbers is a number.

34)

Answer the question or complete the sentence to make a true statement.

35)

Under what condition will the sum of a positive number and a negative number be

negative?

35)

Provide an appropriate response.

36)

Is the integer 0 positive or negative? Explain.

36)

37)

Explain what happens when an integer is multiplied by 1, –1, and 0.

37)

Write the statement in words and decide whether it is true or false.

38)

2

53

10

38)

Give a number that satisfies the given condition.

39)

An integer greater than –2.3 and less than –1.3

39)

Provide an appropriate response.

40)

Is the following expression undefined? 7+7

7+7

40)

41)

Is this statement true or false? Why? (4+ 4) – 4 =4+ (4– 4)

41)

42)

The reciprocal of a positive number is a number.

42)

Write the statement in words and decide whether it is true or false.

43)

10 8+ 3

43)

6

44)

28

44)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the indicated property to provide a new expression equal to the given expression. Simplify, if possible.

45)

5(k – 5); distributive

45)

A)

5k + 25

B)

k – 25

C)

5k – 5

D)

5k – 25

D)

Find the numerical value of the expression for a) x = 4 and b) x = 18.

46)

4x – 9

4x

46)

A)

a) 7

72 b) 7

8

B)

a) 25

72 b) 9

8

C)

a) 7

16 b) 7

8

D)

a) 7

8 b) 7

16

D)

Find the sum.

47)

5+ [2+ (–3)]

47)

A)

4

B)

0

C)

10

D)

6

D)

Solve the problem.

48)

The ocean surface is at 0 feet elevation. A diver is underwater at an elevation of –228 feet near a

rock formation. In this area, the ocean floor has an elevation of –174 feet. The rock formation rises

to a peak 126 feet above the ocean floor. How many feet below the top of the rock formation is the

diver?

48)

A)

48 feet

B)

102 feet

C)

180 feet

D)

–54 feet

D)

Write a numerical expression for the phrase and simplify it.

49)

The product of –4 and 4, added to 7

49)

A)

(–4)(4)(7); –112

B)

(7)(–4+ 4); 0

C)

(–4+ 7)(4); 12

D)

7+ (–4)(4); –9

Use the indicated property to provide a new expression equal to the given expression. Simplify, if possible.

50)

10(r + k); distributive

50)

A)

10r – 10k

B)

r(10 + k)

C)

10r + k

D)

10r + 10k

Find the product.

51)

–5(17)

51)

A)

50

B)

–35

C)

12

D)

–85

State the phrase as a mathematical expression. Use x to represent the variable.

52)

The product of five and eight more than a number

52)

A)

5·8+ x

B)

5(x + 8)

C)

5+ 8 · x

D)

(5 + 8)x

Decide whether the problem is an equation or an expression.

53)

6x – 5

x + 5 –x

4+ 6

53)

A)

Equation

B)

Expression

Decide whether the statement is an example of the commutative, associative, identity, inverse, or distributive property.

54)

4+ 4 =4+ 4

54)

A)

Identity

B)

Associative

C)

Distributive

D)

Commutative

D)

Write a numerical expression for the phrase and simplify it.

55)

The sum of 1 and –5, divided by the product of 1 and –2

55)

A)

1+

–5

1+ (–2) ; 3

B)

1+ (–5)

1(–2) ; 2

C)

1+ (–5)

1– (–2) ; –4

3

D)

1+

–5

1(–2) ; –3

4

D)

Determine whether the statement is true or false.

56)

20 17

56)

A)

True

B)

False

Simplify the expression by combining like terms.

57)

–11

12 + 20y +13

12 y – 9 +17

12 y

57)

A)

45

2y –119

12

B)

61

3y + 2

C)

68

3y

D)

45

2– 2

D)

Use the indicated property to provide a new expression equal to the given expression. Simplify, if possible.

58)

–3+ 0; identity

58)

A)

1

B)

–3

C)

0

D)

3

D)

9

Decide if the given number is a solution to the given equation.

59)

6m + 5 =31; 4

59)

A)

No

B)

Yes

Find the sum.

60)

–24 + (–20)

60)

A)

–4

B)

4

C)

44

D)

–44

State the phrase as a mathematical expression. Use x to represent the variable.

61)

The difference between eleven times a number and three

61)

A)

11 – x + 3

B)

11x – 3

C)

3+ 11x

D)

3– 11x

Select the lesser of the two given numbers.

62)

–12, –10

62)

A)

–12

B)

–10

Change the word statement to an equation. Use x as the variable.

63)

50 divided by a number equals 1

2 times that number.”

63)

A)

50

x=2x

B)

x

50 =x

2

C)

50

x=1

2x

State the phrase as a mathematical expression. Use x to represent the variable.

64)

Two divided by a number

64)

A)

2+ x

B)

2

x

C)

2x

D)

2– x

Find the quotient.

65)

110

–5

65)

A)

–22

B)

–1

22

C)

–32

D)

22

A

Write the phrase as a mathematical expression. Use x to represent the number. Combine like terms if possible.

66)

Seven times a number, added to the sum of the number and eight.

66)

A)

15x

B)

8x

C)

7x +8

D)

(x +8) +7x; 8x +8

D

Write a numerical expression for the phrase and simplify it.

67)

4 more than the sum of –14 and 10

67)

A)

[14 + 10] + 4; 28

B)

–14 – [10 – 4]; –28

C)

[–14 + 10] + 4; 0

D)

10 + [4– 14]; 20

C

List all numbers from the set that are of the type indicated.

68)

{14, 7, –4, 0}

Real numbers

68)

A)

14, –4, 0

B)

14, 7, –4, 0

C)

14

D)

14, 0

B

Simplify.

69)

240 ÷5–3

69)

A)

45

B)

238

C)

232

D)

120

Provide an appropriate response.

70)

If a, b, and c are real numbers, is this statement true or false? –(–a) = – a

70)

A)

True

B)

False

B

Decide whether the statement is an example of the commutative, associative, identity, inverse, or distributive property.

71)

6(8f) –6(2g) =6(8f –2g)

71)

A)

Distributive

B)

Associative

C)

Commutative

D)

Identity

A

Refer to the table to answer the question.

Production