# Pre-Algebra | Free Practice Problems & Explanations

#### 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: One-Step Equations

*Example:* Solve for .

### Two-Step Equations

*Example:* Solve for .

### Lesson: Multi-Step 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: 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.

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