Domain 1 • Foundations
Pre-Algebra on ALEKS
Pre-Algebra forms the bedrock of the ALEKS adaptive assessment. If you make careless errors here, the adaptive algorithm will never elevate your test to higher-scoring Algebra or Pre-Calculus questions!
Core Tested Concepts
Order of Operations (PEMDAS)Parentheses, Exponents, Multiplication & Division (left to right), Addition & Subtraction (left to right).
Signed Number ArithmeticAdding, subtracting, multiplying, and dividing positive and negative numbers. Negative times negative equals positive.
Fractions & DecimalsFinding LCD, reducing to simplest form, converting improper fractions to mixed numbers, decimal operations.
Ratios, Rates & ProportionsCross-multiplication to solve proportions (a/b = c/d), unit rate calculations, sales tax and percentage discounts.
High-Yield Cheat Sheet
Essential Pre-Algebra Rules
Double Negatives
a - (-b) = a + b
Fraction Division
(a/b) ÷ (c/d) = (a/b) · (d/c)
Percent of a Number
Part = (Percent/100) · Whole
Practice Drills
5 Authentic Pre-Algebra Practice Questions
1Practice Problem
Evaluate the expression: -15 - (-8) + (-12)
Hint: Subtracting a negative is equivalent to adding a positive: -15 - (-8) = -15 + 8.
Formula: a - (-b) = a + b
2Practice Problem
Multiply the fractions and write your answer in simplest form: (7/12) × (8/21)
Hint: Cross-cancel common factors: 7 and 21 divide by 7; 8 and 12 divide by 4.
Formula: (a/b) × (c/d) = (a·c)/(b·d)
3Practice Problem
Solve the proportion for x: 5 / 8 = x / 40
Hint: Cross-multiply: 5 × 40 = 8 × x.
Formula: a/b = c/d => ad = bc
4Practice Problem
A pair of shoes originally cost $60. If the price increases by 15%, what is the new price?
Hint: Calculate 15% of 60, then add it to 60 (or multiply 60 by 1.15).
Formula: New = Original × (1 + rate)
5Practice Problem
Evaluate the order of operations: (6 + 2)² - 3 × 5
Hint: Parentheses first: (6 + 2) = 8, then exponent: 8² = 64.
Formula: PEMDAS