Properties refer to rules that indicate a standard procedure or method to be followed. A proof is a demonstration of the truth of a statement in mathematics. Properties or rules in mathematics are the result from testing the truth or validity of something by experiment or trial to establish a proof. Therefore every mathematical problem from the easiest to the more complex can be solved by following step by step procedures that are identified as mathematical properties.

Additive Identity Property Multiplicative Identity Property Multiplicative Identity Property of Zero Multiplicative Inverse Property

Additive Identity Property For any number a, a + 0 = 0 + a = a. If a = 5 then = = 5 The sum of any number and zero is equal to that number. The number zero is called the additive identity. The sum of any number and zero is equal to that number. The number zero is called the additive identity.

Multiplicative identity Property For any number a, a  1 = 1  a = a. If a = 6 then 6  1 = 1  6 = 6 The product of any number and one is equal to that number. The number one is called the multiplicative identity. The product of any number and one is equal to that number. The number one is called the multiplicative identity.

Multiplicative Property of Zero For any number a, a  0 = 0  a = 0. If a = 6 then 6  1 = 1  6 = 6 The product of any number and zero is equal to zero.

Multiplicative Inverse Property Two numbers whose product is 1 are called multiplicative inverses or reciprocals. Zero has no reciprocal because any number times 0 is 0. Two numbers whose product is 1 are called multiplicative inverses or reciprocals. Zero has no reciprocal because any number times 0 is 0.

Equality Properties allow you to compute with expressions on both sides of an equation by performing identical operations on both sides of the equation. This creates a balance to the mathematical problem and allows you to keep the equation true and thus be referred to as a property. The basic rules to solving equations is based on these properties. Whatever you do to one side of an equation; You must perform the same operation(s) with the same number or expression on the other side of the equals sign. Reflexive Property of Equality Symmetric Property of Equality Transitive Property of Equality Substitution Property of Equality Addition Property of Equality

Reflexive Property of Equality For any number a, a = a. If a = a ; then 7 = 7; then 5.2 = 5.2 If a = a ; then 7 = 7; then 5.2 = 5.2 The reflexive property of equality says that any real number is equal to itself. Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. The hypothesis is the part following if, and the conclusion is the part following then. The reflexive property of equality says that any real number is equal to itself. Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. The hypothesis is the part following if, and the conclusion is the part following then.

Symmetric Property of Equality For any numbers a and b, if a = b, then b = a. If 10 = 7 + 3; then 7 +3 = 10 If a = b then b = a If 10 = 7 + 3; then 7 +3 = 10 If a = b then b = a The symmetric property of equality says that if one quantity equals a second quantity, then the second quantity also equals the first. Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. The hypothesis is the part following if, and the conclusion is the part following then. The symmetric property of equality says that if one quantity equals a second quantity, then the second quantity also equals the first. Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. The hypothesis is the part following if, and the conclusion is the part following then.

Transitive Property of Equality For any numbers a, b and c, if a = b and b = c, then a = c. If = 12 and 12 = 7 + 5, then = If a = b and b = c, then a = c If = 12 and 12 = 7 + 5, then = If a = b and b = c, then a = c The transitive property of equality says that if one quantity equals a second quantity, and the second quantity equals a third quantity, then the first and third quantities are equal. Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. The hypothesis is the part following if, and the conclusion is the part following then. The transitive property of equality says that if one quantity equals a second quantity, and the second quantity equals a third quantity, then the first and third quantities are equal. Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. The hypothesis is the part following if, and the conclusion is the part following then.

Substitution Property of Equality If a = b, then a may be replaced by b in any expression. If = 7 + 5; since = 12 or = 12; Then we can substitute either simplification into the original mathematical statement. If = 7 + 5; since = 12 or = 12; Then we can substitute either simplification into the original mathematical statement. The substitution property of equality says that a quantity may be substituted by its equal in any expression. Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. The hypothesis is the part following if, and the conclusion is the part following then. The substitution property of equality says that a quantity may be substituted by its equal in any expression. Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. The hypothesis is the part following if, and the conclusion is the part following then.

Addition Property of Equality If a = b, then a + c = b + c or a – c = b - c If 6 = 6 ; then 6 +3 = or 6 – 3 = If a = b ; then a + c = b + c or a – c = b - c If 6 = 6 ; then 6 +3 = or 6 – 3 = If a = b ; then a + c = b + c or a – c = b - c The addition property of equality says that if you add or subtract equal quantities to each side of the equation you get equal quantities. Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. The hypothesis is the part following if, and the conclusion is the part following then. The addition property of equality says that if you add or subtract equal quantities to each side of the equation you get equal quantities. Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. The hypothesis is the part following if, and the conclusion is the part following then.