Algebra Worksheets
Free algebra worksheets with answer key. No login or account needed. Below are a variety of topics from simplifying expressions or identifying coefficients to solving inequalities, graphing lines, and finding combinations. A grading column and quick grade scale maker grading a breeze and a modified pages help with lower level learners or when just introducing a topic. Great for teachers or for homeschool.
About these worksheets
These worksheets introduce students to the concept of variables and algebraic thinking. Activities include using substitution to evaluate expressions, writing and graphing inequalities on a number line, identifying numerical coefficients, solving for unknown values using all four operations, and exploring powers, bases, and slope. Aligned with sixth through eighth grade standards, these resources build the foundation for pre-algebra and algebra.
About these worksheets
These worksheets cover a wide range of algebraic expression skills, from simplifying and expanding to factoring. Students practice combining like terms, using the distributive property, rewriting expressions as multiples of a sum, solving linear equations with variables on both sides, and expanding polynomials using the box method. Topics also include perfect square trinomials and matching equivalent expressions, making these resources ideal for sixth through eighth grade algebra.
Rewriting Expressions as Multiples of a Sum
- Rewrite an expression like 3x + 6 as a multiplication problem with parentheses, like 3(x + 2).
- Find the greatest common factor of the terms so you know what number or variable can be factored out.
- Keep expressions equivalent while working with coefficients and variables.
Linear Equations with Variables on Both Sides
- Solve linear equations where the variable shows up on both sides of the equals sign.
- Combine like terms to simplify each side before solving.
- Use the distributive property to clear parentheses in an equation.
- Move terms across the equals sign using addition, subtraction, and multiplication to isolate the variable.
- Handle equations that need more than one step to get the variable alone.
About these worksheets
These worksheets explore number concepts essential for middle school math, including square roots, cube roots, rational and irrational numbers, laws of exponents, scientific notation, radicals, and powers of ten. Students practice estimating radical values, simplifying expressions with exponents, and performing operations in scientific notation. Aligned with eighth grade Common Core standards, these resources build a strong number sense foundation for high school math.
Rewriting Using the Laws of Exponents
- Rewrite expressions with exponents using the product and quotient rules.
- Simplify powers raised to powers by multiplying exponents.
- Rewrite expressions with zero and negative exponents using reciprocals.
Solving Using the Laws of Exponents
- Practice rewriting negative exponents as fractions (e.g., 3⁻² becomes 1/3²)
- Multiply powers with the same base by adding their exponents, even when some exponents are negative
- Raise fractions to a power by applying the exponent to both the numerator and denominator
- Simplify expressions step by step to reach a final whole number or fraction
Rewriting Factors as Squares
- Break a number into factors and spot pairs that make a perfect square.
- Use exponents to write repeated factors more simply, like 3×3 as 3^2.
Finding Relative Value with Powers of Ten
- Compare two powers of ten and decide which one is larger or smaller.
- Figure out how many times bigger one power of ten is than another.
- Connect powers of ten to place value shifts, like moving the decimal left or right.
Multiplying with Scientific Notation
- Multiply two numbers written in scientific notation.
- Multiply the coefficients and combine the powers of 10 using exponent rules.
- Rewrite answers in proper scientific notation by shifting the decimal and adjusting the exponent.