ACT Math

A comprehensive course covering the essential math concepts and strategies needed to excel on the ACT.

Numbers, Operations, and Number PropertiesAlgebraic Expressions and EquationsGeometry Fundamentals
Functions and GraphsSystems of Equations and InequalitiesProbability, Statistics, and Data Interpretation
Math in Everyday LifeCareers That Use MathMath in Sports and Games
Time Management and PacingPlugging In and Answer Choice StrategiesReading and Translating Word Problems
Numbers, Operations,...Algebraic Expression...Geometry Fundamental...Functions and GraphsSystems of Equations...Probability, Statist...Math in Everyday Lif...Careers That Use Mat...Math in Sports and G...Time Management and ...Plugging In and Answ...Reading and Translat...
Basic Concepts

Numbers, Operations, and Number Properties

Understanding Numbers and How They Work

Numbers are the building blocks of all math problems on the ACT. You'll encounter whole numbers, decimals, fractions, and negative numbers in a variety of questions.

Types of Numbers

  • Whole Numbers: 0, 1, 2, 3, ...
  • Integers: ..., -2, -1, 0, 1, 2, ...
  • Rational Numbers: Numbers that can be written as a fraction
  • Irrational Numbers: Numbers that cannot be written as a simple fraction (like \( \sqrt{2} \) or \( \pi \))

Key Operations

You’ll need to be comfortable with:

  • Addition, subtraction, multiplication, and division
  • Working with exponents and roots
  • Understanding order of operations (PEMDAS/BODMAS)

Real-World Use

From calculating discounts while shopping to figuring out your average test score, being fluent with numbers helps in countless daily situations.

Common Mistakes

  • Forgetting negative signs
  • Mixing up order of operations
  • Misplacing decimals

Examples

  • Adding fractions: \( \frac{2}{3} + \frac{1}{4} = \frac{8}{12} + \frac{3}{12} = \frac{11}{12} \)

  • Applying order of operations: \( 3 + 6 \times (5 + 4) \div 3 = 3 + 6 \times 9 \div 3 = 3 + 54 \div 3 = 3 + 18 = 21 \)

In a Nutshell

Everything starts with numbers—mastering their properties and operations is the foundation of ACT Math.

Key Terms

Integer
A whole number that can be positive, negative, or zero.
Rational Number
A number that can be expressed as the quotient of two integers.
Order of Operations
The rules that state the sequence in which operations should be performed.
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Algebraic Expressions and Equations