Test your knowledge Of Properties from Chapters 1 & 2.
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Transcript of Test your knowledge Of Properties from Chapters 1 & 2.
![Page 1: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/1.jpg)
Property Quiz
Test your knowledgeOf Properties from Chapters 1 & 2
![Page 2: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/2.jpg)
Name the property demonstrated: If 3g = 4h, then 4h = 3g.
The Symmetric Property
The Symmetric Property gives the mirror image of
one equation.
![Page 3: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/3.jpg)
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.
![Page 4: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/4.jpg)
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.
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Name the property demonstrated: If 3g = 4h and h = 5j, then 3g = 4(5j).
Substitution(Principle)
Only part of the right side was replaced!
![Page 6: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/6.jpg)
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.
![Page 7: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/7.jpg)
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.
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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.
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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.
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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.
![Page 11: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/11.jpg)
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.
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Name the property demonstrated: or
Multiplicative Property of - 1
Multiplying by negative one produces the opposite value.
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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.
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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 ( ).
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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 ( ).
![Page 16: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/16.jpg)
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.
![Page 17: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/17.jpg)
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.
![Page 18: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/18.jpg)
Name the property demonstrated: 3g ● 1 = 3g
Identity Property of Mult.
Multiplying by the identity element keeps the term
“identical”
![Page 19: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/19.jpg)
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.
![Page 20: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/20.jpg)
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.
![Page 21: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/21.jpg)
Name the property demonstrated: 3g + 0 = 3g
Identity Property of Addition
Adding the identity element keeps the term “identical”
![Page 22: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/22.jpg)
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.
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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.
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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
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TRUE or FALSE?TRUE or FALSE?
The set of integers is closedunder addition.
When you add two integers, the result is
always an integer.
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TRUE or FALSE?TRUE or FALSE?
The set of integers is closed under division.
A counter-example could be: 7 / 2 = 3.5
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TRUE or FALSE?TRUE or FALSE?
The set of natural numbers is closed under subtraction.
A counter-example could be: 5 – 7 = -2
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TRUE or FALSE?TRUE or FALSE?
The set of natural numbers is closedunder addition.
Adding two natural (or counting) numbers always
results in a natural number.
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TRUE or FALSE?TRUE or FALSE?
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.
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TRUE or FALSE?TRUE or FALSE?
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).
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TRUE or FALSE?TRUE or FALSE?
The set of even integers is closedunder multiplication.
Multiplying two even integers always results in
an even integer.
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TRUE or FALSE?TRUE or FALSE?
The set of even integers is closedunder addition.
Adding two even integers always results in an even integer.
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TRUE or FALSE?TRUE or FALSE?
The set of even integers is closedunder division.
One counter-example: division by zero does not produce an even integer.
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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
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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
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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)
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A.
B.
C.
D.
E.
Which property is used below? =
Addition Property (of Equality)
Transitive Property (of Equality)
Commutative Property (of Addition)
Symmetric Property (of Equality)
Associative Prop (of Addition)
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A.
B.
C.
D.
E.
Which property is used below?
Multiplication Property (of Equality)
Transitive Property
Inverse Property (of Multiplication)
Symmetric Property (of Equality)
Cancellation Prop (of Addition)
Ms. H would accept Addition
Prop (of Equality) as well, but
it was not a choice here.
![Page 39: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/39.jpg)
TRUE or FALSE?TRUE or FALSE?
Subtraction of real numbers is commutative.
One counter-example: 5 – 9 ≠ 9 - 5
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A.
B.
C.
D.
E.
Which property is used below?
Transitive Property of Order
Transitive Property (of Equality)
Commutative Property (of Addition)
Symmetric Property (of Equality)
Reflexive Property (of Equality)
![Page 41: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/41.jpg)
TRUE or FALSE?TRUE or FALSE?
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}
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A.
B.
C.
D.
E.
Which property is used below?
Transitive Property of Order
Transitive Property (of Equality)
Reflexive Property (of Equality)
Symmetric Property (of Equality)
Commutative Property (of Addition)
![Page 43: Test your knowledge Of Properties from Chapters 1 & 2.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649daf5503460f94a9cdb5/html5/thumbnails/43.jpg)
Match the Property Nameto each statement.
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.
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TRUE or FALSE?TRUE or FALSE?
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.
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TRUE or FALSE?TRUE or FALSE?
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.
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TRUE or FALSE?TRUE or FALSE?
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.
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Match the Property Nameto each statement.
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
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TRUE or FALSE?TRUE or FALSE?
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.
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A.
B.
C.
D.
E.
Name the property demonstrated: +2y = +2y
Property of Reciprocals
Multiplication Property (of Equality)
Reflexive Property (of Equality)
Inverse Property (of Multiplication)
Multiplicative Identity Property