# Ch 2: Basic Arithmetic & Algebra

### About This Chapter

## Basic Arithmetic & Algebra - Chapter Summary

In this chapter, you'll learn about basic arithmetic and algebra, including adding, subtracting, multiplying and dividing rational numbers. Our lessons cover arithmetic using decimal numbers and the processes involved in changing between fractions and decimals. Topics also include using quadratic surds to solve equations, the powers and roots of numbers and how to solve inequalities using addition, subtraction, multiplication and division. After you complete this chapter, you should be able to:

- Convert numbers to scientific notation
- Explain what an inequality is
- Give an example of an absolute-value inequality
- Simplify practice algebraic expressions
- Use the substitution method to solve equations
- Solve algebra problems containing fractions

Each one of our video and text lessons is followed by a short multiple-choice quiz you can use to test your understanding before moving on to another lesson or in preparation for an exam. All of our learning materials are accessible 24 hours a day on your mobile device or computer. Or, if you like to study offline, our printable lesson transcripts highlight key concepts and terms. If at any time you need help, reach out to one of our instructors for assistance.

### 1. Adding & Subtracting Rational Numbers

After watching this video lesson, you will be able to add and subtract rational numbers like a pro. Learn what is involved in adding and subtracting these types of numbers.

### 2. Multiplying & Dividing Rational Numbers

After watching this video lesson, you will know how to multiply and divide rational numbers. You will know when you need to flip your number and when you don't.

### 3. Arithmetic with Decimal Numbers

Watch this video lesson and see how our little professor goes about adding, subtracting, multiplying, and dividing decimal numbers all without the use of a calculator!

### 4. Changing Between Decimals and Fractions

In this video lesson, you will learn about the usefulness of knowing how to change quickly between decimals and fractions. You will also learn how changing from a decimal to a fraction is different than changing from a fraction to a decimal.

### 5. Solving Equations with Quadratic Surds

This lesson will define quadratic surds. We will look at simplifying quadratic surds, and at how to add, subtract, multiply and divide these types of expressions. We will then use operations on quadratic surds to solve various equations.

### 6. Powers & Roots of Numbers

This lesson will go over the definitions of powers and roots of numbers. We will also look at some basic properties of each of these and how we can use these properties to work with and simplify these types of expressions.

### 7. Converting Numbers to Scientific Notation

After watching this video lesson, you will be able to convert any number you come across into scientific notation. You will also learn why scientific notation is used and where you are most likely to see it.

### 8. What is an Inequality?

Deciding how to spend your money can be a tricky thing. Should you save it, invest it, or enjoy it? Learn how inequalities can help you make your decision!

### 9. Solving Inequalities Using Addition, Subtraction, Multiplication & Division

Solving inequalities is almost identical to solving equations. By using the inverse operation for the inequality, variables are quickly isolated to find solutions.

### 10. The Absolute-Value Inequality: Definition & Example

After watching this video lesson, you will be able to solve absolute value inequalities. Learn how you can easily set up your problem to successfully solve your problem each and every time.

### 11. Practice Simplifying Algebraic Expressions

In this lesson, we'll practice simplifying a variety of algebraic expressions. We'll use two key concepts, combining like terms and the distributive property, to help us simplify.

### 12. Solving Equations with the Substitution Method: Algebra Examples & Overview

What does the substitution method have to do with substitute teachers? Learn why you should love substitutes. Also learn how substitutes make your life easier when it comes to solving sets of equations.

### 13. How to Solve Algebra Problems with Fractions

This lesson will explain how to solve algebra problems that include fractions by modifying the problems to make them easier. It will explain two methods that are closely related to one another.

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### Other Chapters

Other chapters within the HSC Mathematics: Exam Prep & Syllabus course

- Mathematical Proofs & Reasoning
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Integration
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards