Chapter 2 Flashcards
equation
a mathematical sentence that shows that two expressions are equivalent
solution of an equation
a value of values that make the equation or inequality true
Additional Property of Equality
For real numbers a, be, and c, if a = b, then a+c=b+c
Subtraction Property of Equality
If a, b, and c are real numbers and a=b, then a-c=b-c
Opposites
The opposite of a number a, denoted -a, is the number that is the same distance from zero as a, on the opposite side of the number line. The sum of opposites is 0.
Additive Inverses
The opposite of a number. Two numbers are additive inverses if their sum is zero.
Identity element
An equation that is true for all values of the variables.
Multiplication Property of Equality
If a, b, and c are real numbers and a=b, then ac=bc.
Division Property of Equality
For real numbers a, b, and c, where c does not =0, if a =b, then a/c=b/c
Distributive Property
For all real numbers a, b, and c, a(b+c) = ab+ac, and: (b+c)a=ba+ca.
Least common denominator
The least common multiple of two or more given denominators
Greatest common factor
The product of the greatest integer and the greatest power of each variable that divides evenly into each term of the expression.
identity
An equation that is true for all values of the variables.
contradiction
An equation that has not solutions.
ratio
A comparison of two numbers by division
rate
A ratio that compares two quantities measured in different units.
scale
The ratio of any length in a drawing to the corresponding actual length.
unit rate
A rate in which the second quantity in the comparison is one unit.