Properties of Equality

• Addition Property of Equality
• If a = b and c = d, then a + c = b + d
• If the value of a is equal to b, and c is similar to the value of d, then adding a and c is equal to the sum of b and d.
• Example:
• a = 1 and b = 1 therefore we can say that a = b ;  c = 2 and d = 2 so we can say that c = d
• a + c = b + d
• 1 + 2 = 1 + 2
• 3 = 3

• Subtraction Property of Equality
• If a = b and c = d, then a - c = d - b
• It's just like how the Addition Property of Equality works except, only this time with this property, you're going to subtract instead of add.
• Example:
• a = 1 and b = 1, a = b ;  c = 2 and d = 2, c = d
• a - c = b - d
• 1 - 2 = 1 - 2
• -1 = -1

• Multiplication Property of Equality
• If a = b and c = d, then ac = bd
• Example:
• a = 1 and b = 1, a = b ;  c = 2 and d = 2, c = d
• ac = bd
• 1 · 2 = 1 · 2
• 2 = 2
• Division Property of Equality
• If a = b and c = d, then a/c = b/d and a/b = c/d
• This property is kinda the same with the other properties previously mentioned since it says that if the value of a is equal to b, and c is similar to the value of d, then a divided by c is equal to b over d. The extra thing that this property has is the a/b = c/d equation. What does that part say? Well, since a = b and c = d, a/b would be equal to 1, and so would c/d. Therefore, since both are equal to 1, a/b = c/d.
• Example:
• a = 1 and b = 1, a = b ;  c = 2 and d = 2, c = d
• a/c = b/d
• ½
   = ½
• 0.5 = 0.5
• a/b = c/d
• 1/1 = 2/2
• 1 = 2
• Reflexive Property of Equality
• This property states that a = a
• Well, this property speaks for itself. If it's a, then it's a. It's kinda like how you are you. a = a. 1 = 1.
• Example:
• a = a
• 1 = 1
• Symmetric Property of Equality
• If a = b, then b = a
• Since a is similar to b, then b is also similar to a.
• Example:
• a = 1 and b = 1
• a = b and b = a
• Transitive Property of Equality
• If a = b and b = c, then a = c
• Example:
• a = 1 and b = 1, a = b ;  c = 1, b = c
• a = 1
• b = 1
• c = 1
• a = b
• a = c
• Substitution Property
• If a = b, neither can be substituted for the other to find the value of the other.
• This one's kinda tricky to explain with just words, so look at this example to understand the property more.
• Example:
• x = y + 5
• If: y = 7
• x = (7) + 5
• x = 12
• Zero Product Property
• If ab = 0, then either a = 0, b = 0 or both a and b = 0
• This property says that if you multiply two variables together and their product is zero, then that means that either one of those variables are equal to zero (since they yielded a product of zero), or both of their values are zero.
• Example:
• ab = 0
• If: a = 9
• b = 0
• If: b = 6
• a = 0