Transitive, Reflexive and Symmetric Properties of Equality

The properties of equality are fundamental rules that allow us to manipulate equations while maintaining equality. These properties are used extensively in algebra to solve for unknown variables.

The following diagram gives the properties of equality: reflexive, symmetric, transitive, addition, subtraction, multiplication, division, and substitution. Scroll down the page for more examples and solutions on equality properties.

 

1. Reflexive Property:
   For any real number a, a = a.
   A quantity is equal to itself.
   
2. Symmetric Property:
   For any real numbers a and b, if a = b, then b = a.
   The order in which an equality is stated does not matter.
   
3. Transitive Property:
   For any real numbers a, b, and c, if a = b and b = c, then a = c.
   If two quantities are equal to the same quantity, then they are equal to each other.
   
4. Addition Property of Equality:
   For any real numbers a, b, and c, if a = b, then a + c = b + c.
   You can add the same quantity to both sides of an equation.
   
5. Subtraction Property of Equality:
   For any real numbers a, b, and c, if a = b, then a - c = b - c.
   You can subtract the same quantity from both sides of an equation.
   
6. Multiplication Property of Equality:
   For any real numbers a, b, and c, if a = b, then a * c = b * c.
   You can multiply both sides of an equation by the same quantity.
   
7. Division Property of Equality:
   For any real numbers a, b, and c, if a = b and c ≠ 0, then a / c = b / c.
   You can divide both sides of an equation by the same non-zero quantity.
   
8. Substitution Property of Equality:
   If a = b, then b can be substituted for a in any expression.
   If two quantities are equal, one can be replaced by the other in any expression without changing the value of the expression.

Explanations on the Properties of Equality

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Examples of Addition, Subtraction, Multiplication, and Division Properties of Equality

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Transitive Property of Equality - Math Help
Students learn the following properties of equality: reflexive, symmetric, addition, subtraction, multiplication, division, substitution, and transitive.

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Algebra1 2.01c - The Transitive Property

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Reflexive Property and Symmetric Property
Students learn the following properties of equality: reflexive, symmetric, addition, subtraction, multiplication, division, substitution, and transitive.

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