Pre-Algebra and Number Sense Essentials

Pre-Algebra Foundations

The early ACT Math questions reward solid arithmetic. On the Enhanced ACT every question has four choices (A-D), so eliminating one or two answers quickly is powerful. Master these core skills first.

Fractions and Decimals

To add fractions, find a common denominator: 1/3 + 1/4 = 4/12 + 3/12 = 7/12. To divide, multiply by the reciprocal: (2/3) / (4/5) = (2/3)(5/4) = 10/12 = 5/6.

Percents

Percent means "per hundred." Three patterns cover most questions:

• •Part = percent x whole: 20% of 80 = 0.20 x 80 = 16.
• •Percent = part / whole: 12 out of 48 = 0.25 = 25%.
• •Percent change = (new - old) / old. A rise from 40 to 50 is 10/40 = 25%.

Ratios and Proportions

A ratio compares quantities; set proportions equal and cross-multiply. If 3 pens cost $4.50, then 7 pens cost (4.50/3) x 7 =$10.50.

Exponents

• •Multiply: x^3 x x^2 = x^5 (add exponents).
• •Divide: x^5 / x^2 = x^3 (subtract).
• •Power of a power: (x^2)^3 = x^6 (multiply).
• •Zero power: x^0 = 1 for any nonzero x.

Order of Operations

Use PEMDAS: parentheses, exponents, multiplication/division (left to right), addition/subtraction (left to right). Compute 2 + 3 x 4^2 = 2 + 3 x 16 = 2 + 48 = 50.

Key Takeaways

• •Common denominators rule fraction addition; reciprocals rule division.
• •Translate percent words into part, whole, and percent.
• •Cross-multiply proportions.
• •Add, subtract, or multiply exponents by the rule, and always follow PEMDAS.