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Pre-Algebra | Free Practice Problems & Explanations

I. Integers, Decimals, and Fractions

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?

II. Beginning Algebra

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)

III. Equations

Lesson: One-Step Equations

Example: Solve for x.

Two-Step Equations

Example: Solve for x.

Lesson: Multi-Step Equations

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

IV. Factors and Exponents


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

Lesson: Properties of Exponents

Example: Simplify. Your answer should contain only positive exponents.
5x^3 \times 3x^2

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

V. Proportions and Similarity

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}

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

Example: Write \dfrac{3}{20} 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

    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 y=2x-5.

Lesson: Graphing Systems of Equations

Example: Choose the graph that corresponds to the function y=2x-5.

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 120^o.

Angle Relationships

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


Example: Classify each triangle by its angles and sides.


Classify each quadrilateral by its angles its sides.

Area of Triangles and Quadrilaterals

Example: Find the area of the figure below.


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 \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).

XII. Statistics

Visualizing Data

Lesson: Dot Plot

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.

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.