test your knowledge of properties from chapters 1 & 2

Property Quiz

Test your knowledgeOf Properties from Chapters 1 & 2

Name the property demonstrated: If 3g = 4h, then 4h = 3g.

The Symmetric Property

The Symmetric Property gives the mirror image of

one equation.

Name the property demonstrated: If 3g = 4h and 4h = 5j, then 5j = 3g.

The Transitive PropertyOf Equality

Three equations that form a circular chain of steps.

An entire side of an equation was replaced.

Name the property demonstrated: If 3g ≥ 4h and 4h ≥ 5j, then 3g ≥ 5j .

The Transitive Property of Order

“order” is a synonym for “inequality”

Notice that the conclusion has to be in this left to

right ORDER.

Name the property demonstrated: If 3g = 4h and h = 5j, then 3g = 4(5j).

Substitution(Principle)

Only part of the right side was replaced!

Name the property demonstrated: If 3g = 4h, then 3g + 5j = 4h + 5j.

Addition Property(of Equality)

5j was added to both sides of the equation.

Name the property demonstrated: If 3g + 5j = 4h + 5j, then 3g = 4h.

Cancellation Property(of Addition) or Addition

Property of Equality

“+ 5j” was cancelled from both sides of the equation.

Name the property demonstrated: If 3g + 5j = 4h + 7j, then 3g = 4h + 2j.

Addition Property(of Equality)

You added the opposite of 5j to both sides, but it did

not cancel out all the j’s on the right hand side.

Name the property demonstrated: If 3g > 4h, then -6g < -8h.

Multiplication Prop. of Order(you must write “of order” since this is only true for

inequalities)

Reverse the inequality sign when you multiply or divide

by a negative value.

Name the property demonstrated: If 3g > 4h, then 3g > 4h .

Addition Property of Order(Subtraction Prop of Order is

OK with Ms. Hardtke)

Adding (or subtracting) the same constant from both

sides of an inequality does not change the inequality.

Name the property demonstrated: If g and h are real numbers, then either g = h or g < h or g > h.

Comparison Property(or Trichotomy Principle in some

textbooks)

Simply assures us that two unique numbers cannot be

placed on a real number line in more than one way in the same

problem.

Name the property demonstrated: or

Multiplicative Property of - 1

Multiplying by negative one produces the opposite value.

Name the property demonstrated: 3g ● 4 = 3 ● 4 ● g

Commutative Property(of Multiplication)

The “g” and “4” terms changed order. Remember:

you commute home to school and then school to

home.

Name the property demonstrated: 3(4h) = (3 ● 4) h

Associative Property(of Multiplication)

The order of the terms did not change; only the parentheses moved.

Remember: different terms are associating within the ( ).

Name the property demonstrated: (3g + 4h) + 5h= 3g + (4h + 5h)

Associative Property(of Addition)

The order of the terms did not change; only the parentheses moved.

Remember: different terms are associating within the ( ).

Name the property demonstrated: If 3g + 4h = 5j, then 4h + 3g = 5j

Commutative Property(of Addition)

The order of the terms changed. Remember: you commute home to school and then school to home.

Name the property demonstrated: If 3g + 4h = 5j, then 5j = 4h + 3g

Symmetric Property

(of Equality)

Symmetric Prop. gives the mirror image of the

equation.

Name the property demonstrated: 3g ● 1 = 3g

Identity Property of Mult.

Multiplying by the identity element keeps the term

“identical”

Name the property demonstrated: 3g + -3g = 0

Property of Opposites(or Inverse Property of

Addition)

Inverse property because it produced the identity

element of addition as the result.

Name the property demonstrated: -(g + h) = -g + -h

Property of Opposite of a Sum(Note that Distributive is OK, but not the best answer and

multiplication by -1 is not really shown here)

The opposite sign affects each term of the sum.

Name the property demonstrated: 3g + 0 = 3g

Identity Property of Addition

Adding the identity element keeps the term “identical”

Name the property demonstrated: -(g h) = -g ● h or -(g h) = g ● -h

Prop. of Opposite of a Product(Note that multiplication by -1

is not really shown here)

The opposite sign affects just one factor of the property.

Otherwise, two negatives would cancel each other.

Name the property demonstrated:

= 1 (Note: g ≠ 0, h ≠ 0.)

Property of Reciprocals

(or Inverse Property of Mult.)

Inverse property because it produced the identity

element of multiplication as the result.

Match the Property Nameto each statement.

1. ab + 0 = ab

2. 1ab = ab

3. ab = ba.

4. ab ● = 1

5. ab = ab

A. Reflexive Prop (of Equality)

B. Commutaive Property (of Mult.)

C. Identity Prop. of Addition

D. Identity Prop. of Mult.

E. Inverse Prop of Mult. Or Prop. of Reciprocals

TRUE or FALSE?TRUE or FALSE?

The set of integers is closedunder addition.

When you add two integers, the result is

always an integer.


The set of integers is closed under division.

A counter-example could be: 7 / 2 = 3.5


The set of natural numbers is closed under subtraction.

A counter-example could be: 5 – 7 = -2


The set of natural numbers is closedunder addition.

Adding two natural (or counting) numbers always

results in a natural number.


The set of real numbers is closed under the square root operation.

Counter-example: the square root of a negative real number is not a real

number.


The set of non-negative real numbers is closed under the square root operation.

The square root of zero or of a positive real number is

always a real number (either rational or irrational).


The set of even integers is closedunder multiplication.

Multiplying two even integers always results in

an even integer.


The set of even integers is closedunder addition.

Adding two even integers always results in an even integer.


The set of even integers is closedunder division.

One counter-example: division by zero does not produce an even integer.

A.

B.

C.

D.

E.

Which property is used below?If 3a(b + 7) = 0, then 3a = 0 or b + 7 = 0.

Property of Opposite of a Sum

Transitive Property

Distributive Property

Multiplicative Property of Zero

Zero Product Property

A.

B.

C.

D.

E.

Which property is used below? ½ + - ½ = 0

Addition Property of Equality

Transitive Property

Zero Product Property

Inverse Property of Multiplication

Property Of Opposites

A.

B.

C.

D.

E.

Which property is used below? ½ + ¼ = ¼ + ½

Addition Property (of Equality)

Transitive Property (of Equality)

Associative Property (of Addition)

Symmetric Property (of Equality)

Commutative Prop (of Addition)

A.

B.

C.

D.

E.

Which property is used below? =

Addition Property (of Equality)


Commutative Property (of Addition)


Associative Prop (of Addition)

A.

B.

C.

D.

E.

Which property is used below?

Multiplication Property (of Equality)

Transitive Property

Inverse Property (of Multiplication)


Cancellation Prop (of Addition)

Ms. H would accept Addition

Prop (of Equality) as well, but

it was not a choice here.


Subtraction of real numbers is commutative.

One counter-example: 5 – 9 ≠ 9 - 5

A.

B.

C.

D.

E.


Transitive Property of Order




Reflexive Property (of Equality)


For real numbers a and b, it is possible that 2a < 2b and 2a = 2b.

This would contradict the Comparison or Trichotomy

Principle.

Note that this is different than 2a ≤ 2b which has the infinite

solution set {a: a ≤ b}

A.

B.

C.

D.

E.


Transitive Property of Order






1. ¼ + 7 + ¾ = ¼ + ¾ + 7

2. For 2 unique real numbers a and b,Exactly one of these is true: a = b or a > b or a < b.

3. For 2 real numbers p and q,pq is a real number.

4. -(ab) = (- a) ● b or a ● (- b)

5. (7 + ¼) + ¾ = 7 + (¼ + ¾ )

A. Associative Prop (of Add.)

B. Closure Property (of Mult.)

C. Commutative Prop (of Add.)

D. Comparison or Trichotomy Principle

E. Opposite of a Product Prop.


If a < b and b < c, then c < a .

The conclusion is out of order. This is a good

reminder why Properties of Inequalities are called Properties of ORDER.


For any real numbers a, b and c, if a < b, then a + c < b +c .

This is the Addition Prop of Order and it works whether

c is positive, negative or zero.


For any real numbers a, b and c, if a < b, then ac < bc.

This is true if c is positive, but it is false if c is zero or

if c is negative.


1. If xy = 0, then x = 0 or y = 0

2. 0x = 0

3. 0 + x = x

4. x + -x = 0

5. 0x = 0x

A. Reflexive Prop (of Equality)

B. Identity Prop of Addition

C. Zero Product Prop

D. Multiplication Prop of Zero

E. Inverse Prop of Addition or Prop of Opposites


By the Distributive Property14xy – 7xz + 7x = 7x(2y – z)

The right hand side should read 7x(2y – z + 1).

If you factor a monomial from a trinomial, there should still be a trinomial in the parentheses.

A.

B.

C.

D.

E.

Name the property demonstrated: +2y = +2y

Property of Reciprocals

Multiplication Property (of Equality)


Inverse Property (of Multiplication)

Multiplicative Identity Property

test your knowledge of properties from chapters 1 & 2

Documents

g h note

g of multiplication

h of addition

g multiplying

h of multiplication

symmetric property

j of addition

addition property of