Pre-Algebra and Elementary Algebra - Complete Interactive Lesson
Part 1: Number Properties
๐ข Number Properties
Part 1 of 7 โ Factors, Multiples, Primes & Divisibility Rules
Pre-Algebra questions make up roughly 20โ25 % of the ACT Math section. Mastering basic number properties gives you quick, reliable points.
| Concept | Definition |
|---|---|
| Factor | A number that divides evenly into another |
| Multiple | The product of a number and any positive integer |
| Prime | A number greater than 1 with exactly two factors: 1 and itself |
| Composite | A number greater than 1 that is not prime |
First 10 primes:
Remember: is neither prime nor composite, and is the only even prime.
Divisibility Rules
Quick divisibility tests save time on the ACT:
| Divisor | Rule | Example |
|---|---|---|
| 2 | Last digit is even | โ last digit โ |
| 3 | Sum of digits divisible by 3 | : โ |
Factors & Primes ๐ฏ
LCM & GCF
Greatest Common Factor (GCF): the largest number that divides two or more numbers evenly.
Least Common Multiple (LCM): the smallest positive number that is a multiple of two or more numbers.
Example 2 โ GCF: Find .
Number Properties Practice ๐งฎ
- What is ?
- What is ?
- How many prime numbers are between 10 and 30?
Concept Check ๐
ACT-Style Questions ๐
Part 2: Fractions & Decimals
๐ Fractions & Decimals
Part 2 of 7 โ Operations, Converting & Ordering
Fraction and decimal arithmetic appears on virtually every ACT. You need to add, subtract, multiply, and divide with confidence.
Key fraction rules:
| Operation | Rule |
|---|---|
| Add / Subtract | Common denominator: |
Part 3: Ratios & Proportions
๐ฏ Percents
Part 3 of 7 โ Percent of a Number, Increase/Decrease, Tax/Tip/Discount
"Percent" means "per hundred." So means .
Core conversions:
| From | To |
|---|
Part 4: Percentages
โ๏ธ Ratios & Proportions
Part 4 of 7 โ Setting Up, Cross-Multiplying, Scaling & Unit Rates
A ratio compares two quantities: or .
A proportion states that two ratios are equal: .
Part 5: Order of Operations
โก Exponents & Roots
Part 5 of 7 โ Rules of Exponents, Square Roots & Order of Operations
Exponents appear frequently on the ACT. Know these rules cold:
| Rule | Formula | Example |
|---|---|---|
| Product |
Part 6: Problem-Solving Workshop
๐ Basic Statistics
Part 6 of 7 โ Mean, Median, Mode, Range & Reading Charts
The ACT loves simple data-analysis questions. Know these four measures:
| Measure | Definition | Example for |
|---|---|---|
| Mean | Sum รท count |
Part 7: Review & Applications
๐ Review & Mixed Practice
Part 7 of 7 โ Formula Cheat Sheet & Mixed ACT Pre-Algebra Problems
Pre-Algebra Formula Cheat Sheet
| Topic | Key Formulas |
|---|---|
| Factors / Multiples |