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Level 209

Properties of Real Numbers & Inequalities


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a+b=b+a
Commutative Property of Addition
ab=ba
Commutative Property of Multiplication
(a+b)+c=a+(b+c)
Associative Property of Addition
(AB)C = A(BC)
Associative Property of Multiplication
a(b+c)=ab+ac
Distributive Property
Addition Property of Equality
For all real numbers x, y, and z, if x = y, then x + z = y + z.
Subtraction Property of Equality
For all real numbers x, y, and z, if x = y, then x - z = y - z.
Multiplication Property of Equality
For all real numbers x, y, and z, if x = y, then xz = yz.
Division Property of Equality
For all real numbers x, y, and z, if x = y, and z ≠ 0, then x/z = y/z. You can divide each side of an equation by the same non-zero number and not change its truth value.
Transitive Property of Equality
For all real numbers x, y, and z , if x = y and y = z, then x = z.
a=a
Reflexive Property of Equality
Symmetric Property
when two segments or two angles are congruent, you can flip them over and they will still be congruent
Substitution property
a(b) = (ab)
Equation to Inequality Property
If a > 0 and b > 0 and a+b=c then c>a and c>b
Trichotomy Property
For every x and y, one and only one of the following conditions holds: x < y, x=y, x > y
Transitive Property of Inequalities
If x > y and y < z, the x < z
Addition Property of Inequalities
If a < b and x ≤ y, then a + x < b + y
Multiplication Property of Inequalities
If x < y and a > 0 then ax < ay