Pre-Algebra Basics

Number properties, fractions, percents, ratios, exponents and basic statistics.

🔢 Number Properties

Part 1 of 7 — Factors, Multiples, Primes & Divisibility Rules

The ACT Math section gives you 45 questions in 50 minutes, each with 4 answer choices. Its official reporting categories are Preparing for Higher Math and Integrating Essential Skills — there is no separate "Pre-Algebra" score — but number properties, fractions, percents, and ratios run through both. Mastering them gives you quick, reliable points.

First 10 primes: $2, 3, 5, 7, 11, 13, 17, 19, 23, 29$

Remember: $1$ is neither prime nor composite, and $2$ is the only even prime.

Is $n$ prime? Test only the primes up to $\sqrt{n}$. If none of them divides $n$, then $n$ is prime (any factor larger than $\sqrt{n}$ would have to pair with one smaller than $\sqrt{n}$).

• $91$: $\sqrt{91} \approx 9.5$, so test $2, 3, 5, 7$. Since $91 = 7 \times 13$, it is not prime.
• $97$: $\sqrt{97} \approx 9.8$, so test $2, 3, 5, 7$. None divides $97$, so it is prime.

🍕 Fractions & Decimals

Part 2 of 7 — 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:

Always simplify your final answer.

💯 Percents

Part 3 of 7 — Percent of a Number, Increase/Decrease, Tax/Tip/Discount

"Percent" means "per hundred." So $45\%$ means $\frac{45}{100} = 0.45$.

Core conversions:

Percent of a number:

$\text{Part} = \text{Percent} \times \text{Whole}$

Example 1: What is $30\%$ of $250$?

$0.30 \times 250 = 75$

⚖️ Ratios & Proportions

Part 4 of 7 — Setting Up, Cross-Multiplying, Scaling & Unit Rates

A ratio compares two quantities: $a : b$ or $\frac{a}{b}$.

A proportion states that two ratios are equal: $\frac{a}{b} = \frac{c}{d}$.

Cross-multiplication is the go-to strategy:

$\frac{a}{b} = \frac{c}{d} \implies ad = bc$

Example 1: If $\frac{3}{5} = \frac{x}{20}$, find $x$.

$3 \times 20 = 5 \times x \implies 60 = 5x \implies x = 12$

⚡ Exponents & Roots

Part 5 of 7 — Rules of Exponents, Square Roots & Order of Operations

Exponents appear frequently on the ACT. Know these rules cold:

📊 Basic Statistics

Part 6 of 7 — Mean, Median, Mode, Range & Reading Charts

The ACT loves simple data-analysis questions. Know these four measures:

For an even number of data points, the median is the average of the two middle values.

📝 Review & Mixed Practice

Part 7 of 7 — Formula Cheat Sheet & Mixed ACT Pre-Algebra Problems

Pre-Algebra Formula Cheat Sheet