Transcript cow cry

Algebraic
Reasoning
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Addition Property of Equality- Add (+) the same thing to both sides of the
equation
Subtraction Property of Equality- Subtract (-)the same thing to both sides
of the equation
Multiplication Property of Equality- Multiply (x) the same thing to both
sides of the equation
Division Property of Equality- Divide (/)the same thing to both sides of the
equation
Distributive Property of Equality- Multiplying the number outside of the
parenthesis to each individual number in the group (in the parenthesis)
Substitution Property of Equality- Replacing a variable with a
value/number
Reflexive Property of Equality- A value that is equal/congruent to itself;
a=a
Symmetric Property of Equality- The values being compared are equal
to each other and order doesn’t matter; a=b, b=a
Transitive Property of Equality- If a=b, and b=c, then a=c
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Equation- a mathematical statement that proves that two
expressions are equal to one another (ex: 20+4=24
Expression- The side of the equation that is grouped with numbers,
operators, and/or variables (the side that needs to be solved)
(ex: 20x+40-30 = 90)
Coefficient- a number that is used to multiply a variable (ex: 4 x)
Variable- a symbol for a number that is unknown (needs to be
solved) (ex: 2m)
Sum- the answer for addition (ex: 6+4= 10
Difference- the answer for subtraction (ex: 20-18= 2)
Product- the answer for multiplication (14x10= 140)
Quotient- the answer for division (ex: 20/4= 5)
Operation- a mathematical process used to solve equations using
symbols (addition +, subtraction -, multiplication x, and division / )
Add the same thing to both
sides
Subtract the same thing to
both sides
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Addition Property of Equality
If a = b,
Then
a + c= b + c
The same thing is being added to both sides of the
equation.
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Subtraction Property of Equality
If a = b,
Then
a–c=b–c
The same thing is being subtracted from both sides of
the equation.
Multiply the same thing to both
sides
Divide the same thing to both
sides
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Multiplication Property of Equality
Multiply both sides by the same thing.
If a = b,
Then
ac=bc
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Division Property of Equality
Divide both sides by the same thing
If a = b AND c is NOT 0,
Then
a/c = b/c
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Distributive Property of
Equality
Multiplying the number outside of
the parenthesis to each individual
number in the group (in the
parenthesis)
When distributing, keep in mind that the
signs also matter!
For example:
5(x-4)
4*x= 4x
5+(-4)= -20
(notice how the -4 in the original
equation makes it a negative)
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Substitution Property of
Equality
Replacing a variable with a
value/number
This property allows us to use any
given information to solve an
equation.
For example:
Find the value of x using the given
information:
Y=8
6+y=x
6+8=x
X=14
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Reflexive Property of
Equality
A value that is
equal/congruent to itself;
Ex: a = a
*One way to remember this is
by remembering that the
word “Reflexive” is a little
similar to the word “reflect”
(like reflecting from a mirror)
Mirror images are the same,
so you can remember that a
= a (equals itself).
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Symmetric Property of
Equality
The values being compared
are equal to each other and
order doesn’t matter; a=b,
b=a
*Check to make sure that if
the solution is flipped around,
that is actually still equals the
same thing.
For example:
K=9
9=K
Even though it is flipped, they
still equal the same thing.
Transitive Property of
Equality
If a=b, and b=c, then a=c
The Transitive Property of
Equality is similar to one of
the laws of logic- The Law of
Syllogism
If the measure of angle PIG
equals the measure of angle
DOG, and the measure of angle
DOG equals the measure of
angle COW, then the measure
of angle PIG equals the
measure of angle COW
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Congruent
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1)
W=64; The Division Property of Equality was used to find the value of w
2)
1. The variable “k” randomly appears, and has nothing to do with the
statements above; Correct Answer: Then, the measure of angle b equals the
measure of angle h
2. There are no errors, therefore everything is correct
3. The order of the letters of the angles are mixed up, so the angles are not the
same;
Correct Answer: Angle BYE, is congruent to angle YUM
3)
The measure of angle z is congruent to the measure of angle z, therefore, the
measure of the reflexive property of equality is also 36 degrees.
4)
Line Segment AB is equal to Line Segment YZ and Line Segment YZ is equal to
Line Segment AB
5)
H= 1039; Properties Used: The Substitution Property of Equality and the
Distributive Property of Equality
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Conditional Statement- If (Hypothesis), then (Conclusion); “If, then” statement
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Hypothesis- The “If” of a conditional statement (p)
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Conclusion- The “Then” of a conditional statement (q)
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Law of Detachment-If a conditional statement is true and the hypothesis is
true, then the conclusion is also true; “If p then q, p is true, therefore q is true.”
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Law of Syllogism- The conclusion becomes another conditional statement; “If
p then q, if q then r, therefore if p then r.”
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Venn Diagram- A diagram to show the relationship between the hypothesis
and conclusion
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-“Therefore”
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If p, then q.
P is true.
Therefore, q is also true.
The conclusion for the Law of Detachment is just a con.
If it is a dog, then it barks.
Venn Diagram: Marshmallow
Marshmallow is a dog.
Therefore, Marshmallow barks.
Barks
Hypothesis: If it is a dog
Dogs
.
Conclusion: Then it barks
If p, then q.
 If q, then r.
Therefore, if p then r.
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For the Law of Syllogism, the conclusion is another
conditional statement.
If you cry, then you will have wet eyes.
If you have wet eyes, then you need a tissue.
Therefore, if you cry, then you will need a tissue.
1)
The Law of Syllogism
2)
The Law of Detachment
3)
Therefore, Santa will come
4)
1. The “therefore” statement is incorrect because crying never showed
up until the end. It did not relate to the conclusion or hypothesis.
The correct statement is: Therefore, if you do not eat, your tummy
will growl.
2. In this case, both the hypothesis and conclusion in the “therefore”
statement did not relate to the conditional statement. The
information that is given is what the “therefore” statement will be
based on. Correct Statement: Therefore, you will get a cavity.
5)
If it is snowing, then it is cold. If it is cold, then you need a jacket.
Therefore, If it is snowing, you need a jacket.
Thank You for reviewing:
Algebraic Reasoning and the Laws of Logic