6 Associative Property of Addition When three numbers are added, it makes no difference which two numbers are added first.Examples:a + (b + c) = (a + b) + c2 + (3 + 5) = (2 + 3) + 5(4 + 2) + 6 = 4 + (2 + 6)
7 Associative Property of Multiplication When three numbers are multiplied, it makes no difference which two numbers are multiplied first.Examples:a(bc) = (ab)c2 • (3 • 5) = (2 • 3) • 5(4 • 2) • 6 = 4 • (2 • 6)
18 Equality PropertyFor all operations: The property that states that if you perform an operation with the same number to both sides of an equation, the sides remain equal (i.e., the equation continues to be true.)2 Most Common:Multiplicative Property of EqualityAdditive Property of Equality
19 Multiplicative Property of Equality The two sides of an equation remain equal if they are multiplied by the same number. That is: for any real numbers a, b, and c, if a = b, then ac = bc.x = y; and x • 8 = y • 8m=20 ; and m • 2 = 20 • 2
20 Additive Property of Equality Additive Property of Equality: The two sides of an equation remain equal if they are increased by the same number.That is: for any real numbers a, b, and c, if a = b, then a + c = b + c.x = y; and x + 6 = y + 6m=15 ; and m + 5 =
51 RootsInverse operation of exponential form. Also used to isolate the variable and solve equations.
52 Combine Like TermsLike terms are monomials that are of the same category. That is they are both constants, or they contain the same variables raised to the same powers. They can be combined to form a single term or used to simplify expressions & equations.
53 Combine like terms to simplify the expression. 10 + 4x3 + 7x4 – x2 + 5x3 +4x2 – 2x4 – 6Hint: Remember to only combine terms that are all from the same number family (constants with constants, x2 with other x2, x3 with x3, and x4 with x4)
55 OppositesTwo real numbers that are the same distance from the origin of the real number line are opposites of each other.Examples of opposites:2 and and and
56 ReciprocalsTwo numbers whose product is 1 are reciprocals of each other.Examples of Reciprocals:and and
57 Absolute ValueThe absolute value of a number is its distance from 0 on the number line. The absolute value of x is written .Examples of absolute value:
58 Least Common Denominator The least common denominator (LCD) is the smallest number divisible by all the denominators.Example: The LCD of is 12 because 12 is the smallest number into which 3 and 4 will both divide.
59 Adding Two FractionsTo add two fractions you must first find the LCD. In the problem below the LCD is 12. Then rewrite the two addends as equivalent expressions with the LCD. Then add the numerators and keep the denominator.