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Classification/Properties of Real Numbers & Equality/Expressions

Total questions: 60

Worksheet time: 10hrs 0mins

Name
Class
Date
1.
a)
A
b)
B
c)
C
d)
D
2.
a)
A
b)
B
c)
C
d)
D
3.
The distance a value is from zero is
a)
Distance
b)
Absolute Value
c)
Integer
d)
origin
4.

Select ALL TRUE statements about negative numbers.

a)

Negative numbers have a value less than zero.

b)

Negative numbers are located to the right of zero on a horizontal number line.

c)

Negative numbers are located below zero on a vertical number line.

d)

Negative numbers sometimes have a negative sign in front of them.

5.

A rational number can be written as a fraction.

a)

True

b)

False

6.

Identify the sets to which the following real number belongs.  Check all that apply.


0.54‾0.\overline{54}  

a)

Natural Numbers

b)

Whole Numbers

c)

Integers

d)

Rational Numbers

e)

Irrational Numbers

7.

Identify the sets to which the following real number belongs.  Check all that apply.


π\pi  

a)

Natural Numbers

b)

Whole Numbers

c)

Integers

d)

Rational Numbers

e)

Irrational Numbers

8.
0.8 is a rational number
a)
True
b)
False
9.

Identify the sets to which the following real number belongs.  Check all that apply.


630630  

a)

Natural Numbers

b)

Whole Numbers

c)

Integers

d)

Rational Numbers

e)

Irrational Numbers

10.
Classify the Number: -23
a)
Rational
b)
Real, rational, integer
c)
integer
d)
Real, irrational, whole
11.
Classify √35.
a)
Rational, Integer
b)
Whole, Integer, Rational 
c)
Irrational, Integer
d)
Irrational
12.
What number below is a natural, whole, integer, rational, and real number ?
a)
-4
b)
5.1
c)
0.7
d)
3
13.
Which statement is NOT true?
a)
Every rational number is a real number.
b)
Every counting number is a whole number.
c)
Every integer is a rational number.
d)
Every decimal number is an irrational number.
14.
Say 'TRUE' or 'FALSE'
Every irrational number is a real number
a)
TRUE
b)
FALSE
15.
Decimal representation of a rational number cannot be_____
a)
Terminating
b)
Non-terminating
c)
Non-terminating and repeating
d)
Non-terminating and non-repeating
16.
A repeating decimal or decimal that terminates is called a 
a)
Natural Number
b)
Irrational Number
c)
Rational Number
d)
Whole Number
17.

3(w + 4) = 3w + 12 is an example of...

a)

Inverse Property

b)

Distributive Property

c)

Multiplicative Inverse

d)

Associative Property

18.

(5 + 3) + 2 = 5 + (3 + 2)

a)

Commutative  Addition

b)

Commutative Multiplication

c)

Associative Addition

d)

Associative Multiplication

19.

3 + (12 + 8) = 3 + (8 + 12) 

a)

Associative Addition 

b)

Associative Multiplication 

c)

Commutative Addition 

d)

Commutative Multiplication 

20.

Identify the property you would use to solve this equation:
4x = 72

a)

Addition Property of Equality

b)

Subtraction Property of Equality

c)

Multiplication Property of Equality

d)

Division Property of Equality

21.

Identify the property you would use to solve this equation:
y – 7 = 28

a)

Additive Property of Equality

b)

Subtraction Property of Equality

c)

Multiplicative Property of Equality

d)

Division Property of Equality

22.

Name the first property you will use to solve this equation:
3(x – 7) = 42

a)

Multiplication Property of Equality

b)

Commutative property

c)

Associative Property

d)

Distributive Property

23.

Name the property you will first use to solve this equation:
4x – 5 = 17

a)

Addition Property of Equality

b)

Subtraction Property of Equality

c)

Multiplication Property of Equality

d)

Division Property of Equality

24.

Which equation shows the commutative property of addition?

a)

m + n = n + m

b)

a + (b + c) = (a + b) + c

c)

r + y = m + v

d)

v + r + p = t

25.

Which equation shows the associative property of addition?

a)

m + n = n + m

b)

a + (b + c) = (a + b) + c

c)

r + y = m + v

d)

v + r + p = t

26.

If y/4 = 5, then y = 20

a)

Multiplication Property of Equality

b)

Division Property of Equality

c)

Addition Property of Equality

d)

Subtraction Property of Equality

27.

If 3x + 4x - 5 = 10, then 7x - 5 = 10

a)

Addition Property of Equality

b)

Combine Like Terms or Simplify

c)

Subtraction Property of Equality

d)

Transitive Property of Equality

28.

Which property is shown below?
__________________________
4(x+6) = 4x + 4(6)

a)

Reflexive

b)

Distributive

c)

Transitive

d)

Substitution

29.

12⋅112=112\cdot\frac{1}{12}=1  

a)

Identity Property of Multiplication

b)

Associative Property of Multiplication

c)

Commutative Property of Multiplication

d)

Inverse Property of Multiplication

30.

What property is this?

a)

Multiplicative Inverse

b)

Multiplicative Identity

c)

Commutative

d)

Associative

31.

What is the ADDITIVE INVERSE of
-7

a)

-7

b)

-1/7

c)

1/7

d)

7

32.

What is the MULTIPLICATIVE INVERSE of
8

a)

-8

b)

-1/8

c)

1/8

d)

1

33.

What property is this?
1a = a

a)

Commutative Property of Multiplication

b)

Multiplicative Inverse

c)

Multiplicative Identity

d)

Distributive Property

34.

What property is this?
9(b + 0.5) = 9b + 4.5

a)

Commutative

b)

Associative

c)

Distributive

d)

Additive Inverse

35.

What is the additive inverse of 2/3?

a)

-2/3

b)

3/2

c)

2/3

d)

-3/2

36.

If you multiply a number and its multiplicative inverse, what do you get?

a)

0

b)

1

c)

Not enough information

d)

None of these

37.

What property of real numbers was used to go from Step 3 to Step 4?

a)

Property of equality of sum

b)

Property of equality of subtraction

c)

Combine similar terms

d)

Property of equality of multiplication

38.

What property justifies the work in solving this equation?

a)

Addition equality property

b)

Multiplication equality property

c)

Addition identity property

d)

Subtraction equality property

39.

If 2x + 4 = 10 and x = 3, then 2(3)+4=10

a)

Symmetric Property

b)

Substitution Property

c)

Transitive Property

d)

Distributive Property

40.

Match the property to the statement.

a)

If 4m+n=74m+n=7 and n=3n=3 , then 4m+3=74m+3=7 .

1.

Substitution

b)

If a=−5a=-5 , then 2a=−102a=-10 .

2.

Multiplication

c)

If 3x=y3x=y , then y=3xy=3x .

3.

Symmetric

d)

If 4w−1=124w-1=12 , then 4w=114w=11 .

4.

Addition

e)

If a+b=ca+b=c and c=d2c=d^2 , then a+b=d2a+b=d^2 .

5.

Transitive

41.

Identify the property:

39 = 39

a)
Reflexive
b)
Symmetric
c)
Transitive
d)
Substitution
42.
Translate this phrase into an algebraic expression.
8 less than the product of 4 and a number
Use the variable m to represent the unknown number.
a)
4m + 8
b)
8m - 4
c)
8m + 4
d)
4m - 8
43.

What word phrase can you use to represent "5x + 2"?

a)

5 times a number plus 2

b)

2 more than the product of 5 and a number

c)

a number times the sum of 5 and 2

d)

the sum of 5 times a number and 2

44.
Nate has 6 fewer CDs than Emily.  If c represents the number of CDs Emily has, which expression tells how many CDs Nate has?
a)
6-c
b)
6+c
c)
c-6
d)
c+6
45.
Students brought in 300 canned goods for the food drive on Monday. On Tuesday students brought in x more than the day before. Write an expression for how many canned goods students brought on Tuesday.
a)
300 + x
b)
300 - x
c)
300x
d)
x - 300
46.
Matthew is 3 times older than Brian. If x represents Brian’s age, which expression represents the combined age of Matthew and Brian?
a)
3x
b)
3x + x
c)
x + 3
d)
x + x + 3
47.

For a walk-a-thon a sponsor committed to give you a flat fee of $5 plus $2 for every mile m you walk. Write an expression for the total amount you will collect from your sponsor at the end of the walk-athon.

a)

5+2

b)

5+2m

c)

5m+2

d)

5-2m

e)

2m-5

48.

You and four friends plan a surprise party. Each of you contributes the same amount of money m for food. Write an algebraic expression for the total amount of money contributed for food.

a)

m+4

b)

4m

c)

m/4

d)

m-4

e)

4-m

49.

Identify the constant of the algebraic expression:

3x + 5

a)

3

b)

x

c)

5

d)

3x and 5

50.
What are the terms in the expression?
4 + 16v
a)
4, 16v
b)
4
c)
v
d)
+16
51.

How many terms are there in this expression below?

2m + 3n - 7

a)

3

b)

5

c)

2

d)

1

52.
Kendra’s math teacher assigned math homework, but Kendra decided to do 5 extra problems. Which algebraic expression shows how many problems Kendra completed? 
a)
5x
b)
x-5
c)
x+5
d)
x5
53.

Rhonda was organizing photos in a photo album. She took 60 photos and divided them evenly among p pages. Which algebraic expression represents the number of photos on each page? What are the important parts of this problem that can help you write an algebraic expression?

a)

60 photos

b)

This is an algebra problem

c)

The phrase, "divided them evenly" lets me know which operation to use.

d)

Her name is Rhonda

e)

p stands for the pages

54.

Tyrell has a sister that is y years younger than him. If Tyrell is 12 years old, how old is his sister? Which algebraic expression could be used to find the age of Tyrell's sister?

a)

y - 12

b)

12 / y

c)

12 + y

d)

12 - y

55.

Kelly has some money she has already saved. After mowing two lawns on Saturday, she adds $40 to her savings. How much money has Kelly saved altogether? Let s represent the amount of money she already has in savings.

a)

s + 40

b)

40s

c)

40 - s

d)

40/s

56.
Pizzazz Publications is having some books printed. The printer charges $800 plus $5 per book. What equation could help me find how many books can be printed for $4,000?
a)
800 + 5x = 4000
b)
800x + 5 = 4000
c)
4000 + 5x= 800
d)
800 + 5 = 4000
57.
Mr. Piper's plumbing needed repairs. The plumber charged $98 for parts plus $45 per hour for labor. If the bill totaled $458, how could I find out the hours of labored required?
a)
98x + 45 = 458
b)
98 + 45x = 458
c)
45 + 98 = 458
d)
45x - 98 = 458
58.
a)
A
b)
B
c)
C
d)
D
59.
a)
A and B
b)
B, C, D
c)
B and E
d)
A, C, D, E
60.
Half of your baseball card collection got wet and was ruined.  Bought 11 cards to replace some that were lost.  How many did you begin with if you now have 31?
a)
40
b)
51
c)
73
d)
62

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