properties of equality
In mathematics, the properties of equality refer to a set of rules or principles that govern the manipulation and relationship between two equal expressions or equations
In mathematics, the properties of equality refer to a set of rules or principles that govern the manipulation and relationship between two equal expressions or equations. These properties allow us to perform various operations and transformations, while ensuring that the equality remains true.
The main properties of equality are:
1. Reflexive Property: This property states that any quantity is equal to itself. In other words, for any number or expression ‘a’, a = a.
2. Symmetric Property: This property states that if two quantities are equal, then their order can be reversed. In other words, if a = b, then b = a.
3. Transitive Property: This property states that if a quantity ‘a’ is equal to another quantity ‘b’, and ‘b’ is equal to a third quantity ‘c’, then ‘a’ is also equal to ‘c’. In symbolic form, if a = b and b = c, then a = c.
4. Addition Property of Equality: This property states that if we add the same quantity to both sides of an equation, the equality is still preserved. In other words, if a = b, then a + c = b + c.
5. Subtraction Property of Equality: This property states that if we subtract the same quantity from both sides of an equation, the equality is still preserved. In other words, if a = b, then a – c = b – c.
6. Multiplication Property of Equality: This property states that if we multiply both sides of an equation by the same non-zero quantity, the equality is still preserved. In other words, if a = b and c ≠ 0, then a * c = b * c.
7. Division Property of Equality: This property states that if we divide both sides of an equation by the same non-zero quantity, the equality is still preserved. In other words, if a = b and c ≠ 0, then a / c = b / c.
These properties of equality allow us to manipulate equations and solve for unknowns. They are fundamental in algebraic manipulations and reasoning, and serve as the foundation for solving mathematical problems involving equations or expressions.
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