Pre-Algebra Help | Free Pre Algebra Lessons & Practice Problems

Go through the lessons and practice problems below to help you learn Pre-Algebra and excel in school. We’ll track your progress and help you identify your strengths and weaknesses. Our Free Pre-Algebra Lessons is available to everyone, but you need to create an account in order to access the practice questions and track your progress.

Lesson: Adding and Subtracting Real Numbers

Example: Evaluate $5 - (-3)$

Lesson: Factors

Example: What are the factors of 28?

Lesson: Greatest Common Factor (GCF)

Example: What is the greatest common factor of 48 and 32?

Lesson: Least Common Multiple (LCM)

Example: What is the least common multiple of 6 and 8?

Simplifying Fractions

Example: Simplify. Write your answer as a mixed number when possible. $\dfrac{18}{27}$

Converting Fractions and Decimals

Example: Write $8\dfrac{3}{8}$ as a decimal

Writing Numbers with Words

Example: Write two hundred forty five million, three hundred six, seventy five as a number.

Lesson: Multiplying and Dividing

Example: What is $9 \times -3$?

Lesson: Writing Algebraic Expressions

Example: Write the sum of nine and eighteen mathematically.

Lesson: Order of Operations

Example: Evaluate $3 + 3 + 3 \div 3$

Combining Like Terms

Example: Simplify $2x - 9 + 5x -3$

Lesson: Using the Distributive Property

Example: Distribute $5(x - 9)$

Lesson: One-Step Equations

Example: Solve for $x$.
$4x=24$

Two-Step Equations

Example: Solve for $x$.
$3x-4=17$

Lesson: Multi-Step Equations

Example: Solve for $x$.
$5(2x-4) = 10$

Divisibility

Example: 9,432 is divisible by which of the following?

Lesson: Properties of Exponents

$5x^3 \times 3x^2$

Lesson: Writing Scientific Notation

Example: Write 82,300,000 in scientific notation.

Lesson: Operations with Scientific Notation

$(5.4 \times 10^8) \times (3 \times 10^{-2})$

Checking for a Proportion

Example: State if the pair of ratios forms a proportion.
$\dfrac{5}{8}$ and $\dfrac{10}{13}$

Lesson: Solving Proportions

Example: Solve for $x$.
$\dfrac{5}{x} = \dfrac{12}{14}$

Drawing and Measuring Angles

Example: Select the angle that measures $120^o$.

Angle Relationships

Example: Name the relationship between the two labeled angles: complementary, supplementary, vertical, adjacent, alternate interior, corresponding, or alternate exterior.

Triangles

Example: Classify each triangle by its angles and sides.

Classify each quadrilateral by its angles its sides.
Example:

Example: Find the area of the figure below.

Circles

Example: Find the area of the circle below.

Classifying Solid Figures, Volume, and Surface Area

Example: Calculate the surface area of the figure below.

Squares and Square Roots

Example: Evaluate $\sqrt{121}$

Lesson: The Pythagorean Theorem

Example: Find the missing length to the nearest tenth.

Lesson: The Distance Formula

Example: Find the distance between the points (-2, 4) and (5, 12).

XI. Beginning Polynomials

Example: Simplify $(3x^2 + 4x - 9) + (-2x^2 - 12x + 18)$

Lesson: Multiplying Binomials

Example: Simplify $(5x +7)(3x - 8)$

Lesson: Box-and-Whisker Plot

Example: Draw a dot plot for the data set below.
Example: Draw a box-and-whisker plot for the data set below.