Math, explained clearly.
Read first. Each article walks through a topic with worked examples and common mistakes — then links you to practice and a calculator.
- 01Algebra3 min read
Exponential Growth & Decay
Exponential growth and decay describe situations where quantities multiply by a constant factor over equal time periods. The general form y = a · bˣ captures this pattern, where a represents the initial amount, b is the growth factor, and x is the number of time periods. When b > 1, the quantity grows exponentially; when 0 < b < 1, it decays exponentially.
- 02Algebra3 min read
Exponents & Powers
An exponent represents repeated multiplication, where a base number is multiplied by itself a specified number of times. The expression 2³ means 2 × 2 × 2, which equals 8. Exponents follow specific rules that make calculations with large numbers more manageable, such as 2⁴ × 2³ = 2⁷ = 128.
- 03Algebra3 min read
Inequalities
An inequality compares two expressions using symbols like <, >, ≤, or ≥ instead of an equals sign. Solving inequalities follows the same steps as solving equations, with one crucial exception: multiplying or dividing both sides by a negative number flips the inequality sign. For example, -2x > 6 becomes x < -3 after dividing by -2.
- 04Algebra3 min read
Linear Equations
A linear equation contains a variable raised to the first power and forms a straight line when graphed. The goal is to isolate the variable by performing the same operation on both sides of the equation. Linear equations appear in forms like x + 5 = 12 or 3x - 7 = 14, where the variable has no exponents or radicals.
- 05Algebra3 min read
Logarithms
A logarithm is the inverse operation of exponentiation, answering the question of what power a base must be raised to in order to produce a given result. The notation log_b(x) = n means that b^n = x, where b is the base, x is the argument, and n is the result. For example, log_2(8) = 3 because 2^3 = 8.
- 06Algebra3 min read
Polynomials
A polynomial is an algebraic expression consisting of variables, coefficients, and non-negative integer exponents combined using addition and subtraction. The expression 3x² + 2x - 7 represents a polynomial with degree 2, where the highest power of the variable determines the degree. Polynomials appear throughout algebra and serve as building blocks for more advanced mathematical concepts covered in CCSS.HSA.APR standards.
- 07Algebra3 min read
Quadratic Equations
A quadratic equation is a polynomial equation of degree 2, written in standard form as ax² + bx + c = 0, where a ≠ 0. These equations have at most 2 solutions, which represent the x-intercepts of a parabola when graphed. The solutions can be found through factoring, completing the square, or the quadratic formula.
- 08Algebra3 min read
Scientific Notation
Scientific notation expresses numbers as a coefficient between 1 and 10 multiplied by a power of 10, written in the form c × 10^n. The number 450,000 becomes 4.5 × 10^5, while 0.0032 becomes 3.2 × 10^-3. This system standardizes number representation across all magnitudes, from atomic scales to astronomical distances.
- 09Algebra3 min read
Systems of Equations
A system of equations consists of two or more equations that share the same variables and must be satisfied simultaneously. The solution represents the point where all equations intersect, typically expressed as an ordered pair (x, y) for two-variable systems. Systems appear throughout algebra, with CCSS 8.EE introducing basic solving methods and CCSS HSA.REI extending to more complex applications.
- 010Algebra3 min read
Two-Step Equations
A two-step equation contains one variable term and one constant term, requiring exactly two inverse operations to solve. These equations follow the pattern ax + b = c or ax - b = c, where the coefficient a and constant b can be any real numbers. The solving process systematically undoes operations in reverse order to isolate the variable.
- 011Arithmetic4 min read
Addition Properties
Addition properties are fundamental mathematical rules that govern how numbers combine in addition operations. The three main properties are commutative (order doesn't matter), associative (grouping doesn't matter), and identity (adding zero changes nothing). These properties form the foundation for arithmetic fluency and algebraic thinking in elementary mathematics, appearing in CCSS.1.OA and CCSS.2.OA standards.
- 012Arithmetic3 min read
Addition
Addition is the fundamental arithmetic operation that combines two or more numbers to produce their total sum. The process follows consistent rules regardless of whether adding single digits like 3 + 4 = 7 or larger numbers like 127 + 358 = 485. Addition appears in CCSS standards from kindergarten through grade 2, building from simple counting strategies to multi-digit algorithms with regrouping.
- 013Arithmetic3 min read
Decimal Arithmetic
Decimal arithmetic involves performing addition, subtraction, multiplication, and division operations with decimal numbers. The fundamental principle requires aligning decimal points for addition and subtraction, while multiplication and division follow specific rules for decimal placement. These operations form the foundation for working with money, measurements, and precise calculations in mathematics.
- 014Arithmetic3 min read
Decimal Word Problems
Decimal word problems combine decimal arithmetic with real-world contexts such as shopping, cooking, and measurement. These problems require identifying which mathematical operation to use based on the situation described, then performing calculations with numbers that include decimal points. Common scenarios involve calculating change from purchases, finding totals for multiple items, or determining unit prices.
- 015Arithmetic3 min read
Factors, GCF & LCM
Factors are whole numbers that divide evenly into another number without leaving a remainder. The Greatest Common Factor (GCF) represents the largest number that divides into two or more numbers, while the Least Common Multiple (LCM) is the smallest number that both original numbers divide into evenly. These concepts appear in CCSS Grade 4 standards for finding factor pairs and identifying prime and composite numbers.
- 016Arithmetic3 min read
Intro to Multiplication
Multiplication represents repeated addition of equal groups, where 4 × 3 means adding 3 four times to get 12. This operation appears in CCSS 3.OA standards as students transition from counting individual objects to working with equal groups. Arrays, equal groups, and skip counting provide visual foundations for understanding multiplication before memorizing facts.
- 017Arithmetic3 min read
Long Division
Long division is a systematic method for dividing large numbers by breaking the process into smaller, manageable steps. The algorithm involves repeatedly dividing, multiplying, subtracting, and bringing down digits until the entire dividend is processed. This method works with any divisor and produces exact quotients with remainders when necessary.
- 018Arithmetic3 min read
Modular Arithmetic
Modular arithmetic deals with remainders after division, focusing on what's left over when one integer is divided by another. The notation a mod n represents the remainder when a is divided by n, always yielding a value between 0 and n-1. Two numbers are congruent modulo n if they leave the same remainder when divided by n, written as a ≡ b (mod n).
- 019Arithmetic3 min read
Multiplication & Division in Daily Life
Multiplication and division represent two fundamental operations that solve opposite problems in everyday situations. Multiplication determines the total when combining equal groups, such as finding the cost of 8 notebooks at $3 each. Division splits quantities into equal parts or determines how many groups can be formed, like sharing 24 cookies among 6 people.
- 020Arithmetic3 min read
Multiplication Properties
Multiplication properties are mathematical rules that describe how numbers behave when multiplied together. These properties include the commutative property (order doesn't matter), associative property (grouping doesn't matter), identity property (multiplying by 1), and distributive property (multiplying over addition). The zero property states that any number multiplied by 0 equals 0.