# Ch 1: GACE Middle Grades Math: Basic Arithmetic Operations

### About This Chapter

## GACE Middle Grades Math: Basic Arithmetic Operations - Chapter Summary

Watch these video lessons to review basic arithmetic operations including steps to solving various arithmetic problems and examples of each. The following topics are covered in this chapter:

- Defining different types of numbers
- Identifying the properties of real numbers
- Exploring the order of operations
- Discussing the order of real numbers and inequalities
- Showing the steps for performing addition and subtraction problems
- Solving multiplication problems, including multiplication of large numbers
- Performing division problems and long division with large numbers
- Calculating arithmetic problems with signed numbers

Our experienced instructors present content-rich lessons and engaging visuals to make studying fun. Each video lesson is less than 10 minutes long and can be watched any number of times. If you wish to re-watch a main point in a lesson, use a tag to jump to that part of the video. Transcripts of each lesson are also available.

### GACE Middle Grades Math: Basic Arithmetic Operations Chapter Objectives

The state of Georgia requires educators to pass the GACE Middle Grades Mathematics test to teach math to 4th through 8th graders. The test is organized into two content subareas: (1) arithmetic and algebra and (2) geometry and data. Questions on arithmetic and algebra, which includes basic arithmetic operations, comprise 65% of the test. Use these videos and lesson quizzes to prepare to answer these types of questions on the test.

The test is computer delivered and consists of 45 selected-response questions. Selected-response questions include formats such as typing in an entry box, clicking on check boxes and clicking on options from a drop down menu. You will have 2 hours to complete the test.

### 1. What are the Different Types of Numbers?

Learn all of the different types of numbers: natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. This video lesson teaches you how to classify any numbers you come across.

### 2. What are Real Numbers? - Definition & Properties

There are many definitions of real numbers, but they all lead to the same conclusion. Real numbers are numbers that have a measurable value. Learn more about real numbers with some examples and a quiz to test your knowledge.

### 3. What Is The Order of Operations in Math? - Definition & Examples

The order of operations is the steps used to simplify any mathematical expression. In this video, learn how to solve problems using these steps and easy tricks to remember them.

### 4. The Order of Real Numbers: Inequalities

An inequality is an operation describing how one number can be compared to another. This lesson will describe and define inequalities and the symbols used to represent them. It will also give some examples on how to work with inequalities.

### 5. How to Perform Addition: Steps & Examples

Addition is one of the basic operations of math. You can say that the whole of mathematics is based on addition. Without addition, we wouldn't have higher math. Watch this video to learn how to add.

### 6. How to Perform Subtraction: Steps & Examples

Subtraction is one of the basic operations in math. Watch this video lesson to learn how you can view and understand subtraction so that you can easily perform it.

### 7. How to Perform Multiplication: Steps & Examples

Multiplication, one of the basic operations of math, is important not just in elementary math but also in higher math. Watch this video lesson to learn how you can multiply with ease.

### 8. How to Multiply Large Numbers: Steps and Examples

After watching this video lesson you will be able to multiply any two numbers together. You will learn how to use your knowledge of multiplying smaller numbers together to multiply larger numbers with ease.

### 9. How to Perform Division: Steps & Examples

Watch this video lesson to learn how you can divide. Division is one of the basic operations of math. It is one of the fundamental operations that all higher mathematics depends upon.

### 10. Performing Long Division with Large Numbers: Steps and Examples

After watching this video lesson, you will be able to divide larger numbers. You'll learn an easy to follow procedure that you can use to divide any two numbers.

### 11. Arithmetic Calculations with Signed Numbers

Signed numbers are often referred to as integers. Integers include both positive and negative numbers. In this lesson, you will learn how to add, subtract, multiply, and divide integers.

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### Other Chapters

Other chapters within the GACE Middle Grades Mathematics (013): Practice & Study Guide course

- GACE Middle Grades Math: Solving Math Word Problems
- GACE Middle Grades Math: Properties of Numbers
- GACE Middle Grades Math: Roots & Radical Expressions
- GACE Middle Grades Math: Exponents & Exponential Expressions
- GACE Middle Grades Math: Scientific Notation
- GACE Middle Grades Math: Simplifying Expressions
- GACE Middle Grades Math: Integers
- GACE Middle Grades Math: Rational Numbers
- GACE Middle Grades Math: Introduction to Fractions
- GACE Middle Grades Math: Operations with Fractions
- GACE Middle Grades Math: Introduction to Decimals
- GACE Middle Grades Math: Operations with Decimals
- GACE Middle Grades Math: Percents
- GACE Middle Grades Math: Rates, Ratios & Proportions
- GACE Middle Grades Math: Number Theory
- GACE Middle Grades Math: Factoring
- GACE Middle Grades Math: Estimating & Rounding
- GACE Middle Grades Math: Monomials & Polynomials
- GACE Middle Grades Math: Writing Algebraic Expressions
- GACE Middle Grades Math: Basic Algebraic Expressions
- GACE Middle Grades Math: Algebraic Distribution
- GACE Middle Grades Math: One-Step Equations
- GACE Middle Grades Math: Two-Step Equations
- GACE Middle Grades Math: Rational Expressions
- GACE Middle Grades Math: The Coordinate Graph
- GACE Middle Grades Math: Linear Equations
- GACE Middle Grades Math: Systems of Linear Equations
- GACE Middle Grades Math: Negative Numbers
- GACE Middle Grades Math: Absolute Value
- GACE Middle Grades Math: Inequalities
- GACE Middle Grades Math: Number Patterns & Sequences
- GACE Middle Grades Math: Properties of Functions
- GACE Middle Grades Math: Graphing Functions
- GACE Middle Grades Math: Perimeter & Area
- GACE Middle Grades Math: Polyhedrons & Geometric Solids
- GACE Middle Grades Math: Symmetry, Similarity & Congruence
- GACE Middle Grades Math: Properties of Lines
- GACE Middle Grades Math: Angles
- GACE Middle Grades Math: Triangles
- GACE Middle Grades Math: Triangle Theorems & Proofs
- GACE Middle Grades Math: Similar Polygons
- GACE Middle Grades Math: The Pythagorean Theorem
- GACE Middle Grades Math: Quadrilaterals
- GACE Middle Grades Math: Circles
- GACE Middle Grades Math: Circular Arcs & Measurement
- GACE Middle Grades Math: Transformations
- GACE Middle Grades Math: Measurement
- GACE Middle Grades Math: Data & Graphs
- GACE Middle Grades Math: Sets
- GACE Middle Grades Math: Statistics
- GACE Middle Grades Math: Data Collection
- GACE Middle Grades Math: Samples & Populations
- GACE Middle Grades Math: Probability
- GACE Middle Grades Mathematics Flashcards