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Alg. 1 Properties,Rules, Signs, and other stuff
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Here are the properties and rules for Algebra 1.
Terms in this set (26)
Commutative Property
A+B=B+A, AB=BA, it doesn't matter which order it is put as long as the answer is the same.
Associative Property
Changing the grouping of numbers will NOT change the value. For example: (7 + 4) + 8 = 7 + (4 + 8) also works with multiplication.
Identity Property
A poroperty in addition where when you add zero to a number it doesn't change, in multiplication its when you multiply a number by one.
Closure Property
a+b and ab are unique real numbers.
Property of Opposities
(-a)(b)=-ab, a(-b)=-ab, (-a)(-b)=ab
Multiplicative Property of Zero
The product of any number and zero is zero (a x 0=0)
Rules of Multiplication
1. If two numbers have the same sign, their product is positive.
If two numbers have opposite signs, their product is negative.
2. The product of an even number of negative numbers is positive.
The product of an odd number is negative numbers is negative.
Reflexive Property
Any quantity that is equal to itself: a = a
Symmetric Property
Each side of the equal sign looks different but they are equivalent a=b, b=a
Transitive Property
If one quantity equals a second quantity, and the second quantity equals a third quantity, then the first quantity equals the third quantity. If a=b and b=c, then a=c
Property of Reciprocals
Any non-zero number multiplies by its multiplicative inverse (reciprocal) is 1, 2 x 1/2 = 1
Greater Than
>, When a number is larger than the other number. Example 65 > 56
Less Than
<, When a number is less than the other number.
Example 56 < 65
Greater Than or Equal to
describes a comparison in which the first number or quantity is the same as or more than the second number or quantity.
2 ≥ 1
Less Than or Equal to
describes a comparison in which the first number or quantity is the same as or smaller than the second number or quantity.
1 ≤ 2
Substitution Property
If a=b, then a can be substituted for b in any equation or expression.
x-y=7
2x+y=13
Proportion
an equation that shows that two ratios are equivalent
1/2 3/5
x=7
Undefined
y=6
0
Ratio
the relative magnitudes of two quantities (usually expressed as a quotient)
2:1
2 to 1
2/1
Adding and Subtracting Rule for Fractions
Denominators must be the same
Reciprocal
one of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2
Percent
a proportion multiplied by 100
33%= 33/100
Functions
An input-output relationship that has exactly one output for each input
Domain
The set of x-coordinates of the set of points on a graph; the set of x-coordinates of a given set of ordered pairs. The value that is the input in a function or relation.
Range
the difference between the greatest and least numbers in a set
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