Pre-Algebra and Elementary Algebra (ACT)

Number Operations

Order of Operations (PEMDAS)

Example: $3 + 4 \times 2^2$

1. Exponents: $2^2 = 4$
2. Multiply: $4 \times 4 = 16$
3. Add: $3 + 16 = 19$

Fractions and Decimals

• Adding fractions: Find common denominator
• Converting: $0.25 = \frac{1}{4}$
• Percent to decimal: $15\% = 0.15$

Simple Equations

One-step: $x + 7 = 12 \quad \Rightarrow \quad x = 5$

Two-step: $3x - 5 = 10 \quad \Rightarrow \quad 3x = 15 \quad \Rightarrow \quad x = 5$

Word Problems

Strategy:

1. Identify the unknown (let $x$ = ...)
2. Write an equation
3. Solve
4. Check if answer makes sense

Example: "Five more than twice a number is 17" $2x + 5 = 17 \quad \Rightarrow \quad x = 6$

ACT Tips

• Calculator allowed! Use it for complex arithmetic
• Work backwards: Plug answer choices into equations
• Estimate: Eliminate unreasonable answers