Properties of Equality Worksheet
Explore and apply the fundamental properties of equality including reflexive, symmetric, transitive, addition, subtraction, multiplication, and division properties with algebraic expressions.
Includes
Standards
Topics
Properties of Equality
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Read each question carefully and provide your answer. Show all your work for short answer questions.
1. If a = b and b = c, then a = c. This statement demonstrates which property of equality?
Reflexive Property
Symmetric Property
Transitive Property
Substitution Property
2. Which property allows us to say that if 5x + 2 = 12, then 5x = 10?
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
3. The Property of Equality states that if a = b, then a + c = b + c.
4. According to the Property of Equality, if a = b, then b = a.
5. Any quantity is equal to itself, which is the definition of the Property of Equality.
6. Solve the equation 3x - 7 = 11. Justify each step using the properties of equality.
7. The Division Property of Equality states that if a = b, then a/c = b/c for any real number c.
True
False
8. The Multiplication Property of Equality allows you to multiply both sides of an equation by zero.
True
False
Match each property with its algebraic representation.
9. Reflexive Property
a. If a = b, then ac = bc
10. Symmetric Property
b. a = a
11. Transitive Property
c. If a = b, then b = a
12. Multiplication Property
d. If a = b and b = c, then a = c
Consider the following image of a balance scale. If the left side has a weight 'x' and the right side has a weight of '5', what property of equality is demonstrated if we add '2' to both sides to maintain balance?
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