Two values are equal if they have the same value. For example, a = 15, states that the variable a has the same value as 15. The symbol '=' is called the equal sign /ˈikwəl saɪn/ and is used to show that the expression on the left is equal to the expression on the right. The equation x + 2 = 5 states that when 2 is added to an unknown value x, the sum is equal to 5.
|Addition property of equality||If a = b then a + c = b + c|
|Subtraction property of equality||If a = b then a - c = b - c|
|Multiplication property of equality||If a = b then a · c = b · c|
|Division property of equality||If a = b and c ≠ 0 then a ÷ c = b ÷ c|
|Table 1: Operative properties of equality|
The reflexive property of equality states that: a = a. This means that every value is equal to itself.
The symmetric property of equality states that: If a = b then b = a. A mnemonic for this property is the meaning of symmetric. A object has binary symmetry if both sides are the same. if a = b, a is the same as b, so b = a.
The transitive property of equality states; if a = b and b = c, then a = c. For example, if y = x+2 and y = x - 4, then x + 2 = z - 4. A mnemonic for this property is taken from the root word 'transit'. A transit is a mode of movement. For example, a mass transit system is a system to move masses of people. Since equality is transitive, given a = b and b = c the value of a 'transits' or moves to c.
An equality that is reflexive, symmetrical and transitive is called an equivalence relation.
The substitution property of equality states that; if two values are equal, then one can be substituted for the other in equations.
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