1.1 Properties of Real Numbers.pdf

Properties of Real Numbers Ella Fontaine  Associative Property Addition - this property states that you can add no matter how the numbers are grouped or where the parenthesis are Ex. (6+2) +5=13, (5+2) + 6 =13 Multiplication - this property states that you can multiply no...

Properties of Real Numbers Ella Fontaine  Associative Property Addition - this property states that you can add no matter how the numbers are grouped or where the parenthesis are Ex. (6+2) +5=13, (5+2) + 6 =13 Multiplication - this property states that you can multiply no matter how the numbers are grouped or where the parenthesis are Ex. (2*2) * 3= 12, 2(3*2)= 12  Commutative Property Addition - this property states that you can add the numbers in any order Ex. 6+3=9, 3+6=9 Multiplication - this property states that you can multiply the numbers in any order Ex. 5*4=20, 4*5=20  Identity Additive Identity - this property states that if you add zero to a real number, that that real number will stay the same Ex. 5 +0 =5, 0 +5=5 Multiplicative Identity - this property states that if you multiply a real number by one then that real number will not change Ex. 6 x 1 = 6, 1 x 6 = 6  Distributive Property Over Addition - this property states that multiplying a sum by a number gives the same answer as multiplying each addend by the number, and then adding the two products together Ex. 4(5+2) = 28, 4x5 + 4x2 = 28 Over Subtraction - this property states that multiplying a difference by a number gives the same result as multiplying each difference by that same number and then subtracting them Ex. 4(3-2)=4, 4x3 - 4x2 =4  The Properties of Equality Addition - this property states that adding the same number to both sides of an equation gives you an equivalent equation Ex. If 20+2=22, then 20+2+5=22+5 Subtraction - this property states that subtracting the same number on both sides of an equation gives you an equivalent equation Ex. If 5-2=3, then 5-2-1=3-1  Properties of Equality Multiplication - this property says that if you multiply both sides of an equation by the same number, it will give you an equivalent equation Ex. If 2x4=8, then 2x4x3=8x3 Division - this property says that if you divide both sides of an equation by the same non-zero number, you will get an equivalent equation Ex. If 12/3=4, then 12/3/2=4/2  Properties Reflexive Property - this property states that any real number equals itself Ex. 6=6 Symmetric Property - this property states that the order to the equality doesn’t change the answer Ex. g=n, so this means that n=g  Properties Transitive Property - this property states that if two values are equal to each other, and the second one is equal to a third one, then the first is equal to the third Ex. If a=b and b=c, then a=c Substitution Property - this property states that if two values equal one another, then they both can be substituted in for each other in any equation Ex. If x=y, then x can be substituted for y and y can be substituted for x in any equation  Flow Chart Whole Real world Numbers Numbers Irrational number Rational Integers Numbers Negative Non - Integers Numbers  Sources http://study.com/ www.mathgoodies.com www.mathwords.com