Go through the lessons and practice problems below to help you learn PreAlgebra and excel in school. We’ll track your progress and help you identify your strengths and weaknesses. Our Free PreAlgebra Lessons is available to everyone, but you need to create an account in order to access the practice questions and track your progress.
I. Integers, Decimals, and Fractions
Lesson: Adding and Subtracting Real Numbers
Example: Evaluate
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.
Converting Fractions and Decimals
Example: Write 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 ?
II. Beginning Algebra
Lesson: Writing Algebraic Expressions
Example: Write the sum of nine and eighteen mathematically.
Lesson: Order of Operations
Example: Evaluate
Combining Like Terms
Example: Simplify
Lesson: Using the Distributive Property
Example: Distribute
III. Equations
Lesson: OneStep Equations
Example: Solve for .
TwoStep Equations
Example: Solve for .
Lesson: MultiStep Equations
Example: Solve for .
IV. Factors and Exponents
Divisibility
Example: 9,432 is divisible by which of the following?
Lesson: Properties of Exponents
Example: Simplify. Your answer should contain only positive exponents.
Lesson: Writing Scientific Notation
Example: Write 82,300,000 in scientific notation.
Lesson: Operations with Scientific Notation
Example: Evaluate. Write your answer in scientific notation.
V. Proportions and Similarity
Checking for a Proportion
Example: State if the pair of ratios forms a proportion.
and
Lesson: Solving Proportions
Example: Solve for .
Proportions Word Problems
Example: A bag of 12 oranges is $5.40. At this rate, how much would a bag of 14 oranges be?
Similar Figures
Example: The two figures below are similar. Find the missing side.
Similar Figures Word Problems
Example: The scale of a map is 1 inch : 5 miles. If two cities are 4.5 inches apart on the map, how far apart are the real cities?
VI. Percents
Fractions, Decimals, and Percents
Lesson: Percents and Fractions
Lesson: Representing a Percent as a Decimal
Example: Write as a percent.
Lesson: Percents
Example: What percent of 240 is 185?
Lesson: Percent of Change
Example: What is the percent change from 22 to 35?
Markup, Discount, and Tax
Lesson: Discount & Tax
Lesson: Markup
Example:

 A bike was originally $440. The bike is on sale with a 30% discount. What is the sale price of the bike?
Simple and Compound Interest
Example: If you deposit $12,000 in the bank at a simple annual interest rate of 5%, how much would you have in the account after 5 years?
VII. Linear Equations and Inequalities
Plotting Points
Example: Which point is at (10, 7)?
Lesson: The Midpoint Formula
Example: What is the midpoint of the line segment with endpoints (2, 5) and (8, 12)?
Lesson: Slope
Example: Find the slope of each line.
Lesson: Graphing Linear Equations
Example: Choose the graph that corresponds to the function .
Lesson: Graphing Systems of Equations
Example: Choose the graph that corresponds to the function .
Lesson: Solving a System of Equations by Substitution
Example: Solve the following system of equations by graphing:
Lesson: System of Equations Word Problems
Example: Shaun bought a total of 24 muffins. Blueberry muffins are $2.25 each and chocolate chip muffins are $2.75 each. If the total cost of the 24 muffins is $56, how many of each muffin did he buy?
VIII. Plane Figures
Drawing and Measuring Angles
Example: Select the angle that measures .
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.
Quadrilaterals
Classify each quadrilateral by its angles its sides.
Example:
Area of Triangles and Quadrilaterals
Example: Find the area of the figure below.
Circles
Example: Find the area of the circle below.
IX. Solid Figures
Classifying Solid Figures, Volume, and Surface Area
Example: Calculate the surface area of the figure below.
X. Right Triangles
Squares and Square Roots
Example: Evaluate
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
Lesson: Adding and Subtracting Polynomials
Example: Simplify
Multiplying Polynomials
Lesson: Multiplying a Polynomial by a Monomial
Lesson: Multiplying Binomials
Example: Simplify
XII. Statistics
Visualizing Data
Lesson: Dot Plot
Lesson: BoxandWhisker Plot
Example: Draw a dot plot for the data set below.
Example: Draw a boxandwhisker plot for the data set below.
Center and Spread
Example: Find the median, mean, and mean absolute deviation for the data set below.
Lesson: Scatter Plots
Example: Construct a scatter plot from the data set below. Determine if there appears to be a positive correlation, negative correlation, or no correlation. When there is a correlation, identify the relationship as linear or nonlinear.
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