Distributive Property Practice Test

About This Distributive Property Practice Test

The distributive property connects multiplication with addition and subtraction. It is used to remove parentheses, multiply monomials by polynomials, factor common terms, simplify expressions, and solve equations.

Questions include positive and negative factors, fractions, decimals, multiple variables, reverse distribution, equations with one, no, or infinitely many solutions, and short geometry or cost applications.

Skills Covered

You will distribute signs and coefficients, combine like terms, extract a greatest common factor, solve equations after expansion, and identify identities or contradictions.

How to Approach the Questions

1. Multiply the outside factor by every term inside the grouping symbol.
2. Track negative signs before combining like terms.
3. When factoring, identify the greatest common numerical and variable factor.
4. For equations, simplify both sides before classifying the number of solutions.

Common Mistakes to Avoid

Typical mistakes include multiplying only the first term, losing a negative sign, combining unlike terms, using a common factor that is not greatest, and trying to solve an identity or contradiction as an ordinary one-solution equation.

Practice Format

Use this free 20-question test for classroom review, tutoring, homework support, exam preparation, or independent practice. Each response is followed by an explanation, and the test can be repeated without registration.