Properties of Equality Worksheet
Explore and apply the fundamental properties of equality to solve algebraic equations.
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Properties of Equality
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Read each question carefully and apply the correct property of equality to solve or answer the problem. Show all your work where space is provided.
1. The Property of Equality states that if you add the same number to both sides of an equation, the equation remains balanced.
2. If a = b, then b = a. This is an example of the Property of Equality.
3. The Property of Equality allows you to replace one expression with an equivalent expression in an equation.
Match each equation with the property of equality it demonstrates.
1. If x = y and y = 5, then x = 5.
a. Addition Property of Equality
2. If a = b, then a - c = b - c.
b. Subtraction Property of Equality
3. 3x = 15; x = 5.
c. Multiplication Property of Equality
4. If 4 = 4, then 4 = 4.
d. Division Property of Equality
5. If x = 7, then 7 = x.
e. Reflexive Property of Equality
6. If 2x = 10, then 2x/2 = 10/2.
f. Symmetric Property of Equality
7. If a = b and b = c, then a = c.
g. Transitive Property of Equality
8. Solve the equation x - 8 = 15 using the Addition Property of Equality. Show your steps.
9. If 4x = 20, what property of equality would you use to find the value of x? Explain.
10. The image below represents a balanced equation. If you add 2 units to the left side, what must you do to the right side to keep the scale balanced? What property of equality does this demonstrate?
11. The Reflexive Property of Equality states that a number is equal to itself (e.g., 7 = 7).
True
False
12. If a = b, then a + 5 = b - 5 is an example of a property of equality.
True
False
13. Which property of equality is demonstrated by the statement: If 2x = 10, then x = 5?
Addition Property
Subtraction Property
Multiplication Property
Division Property
14. If a = b and b = c, which property allows us to say a = c?
Symmetric Property
Transitive Property
Reflexive Property
Substitution Property