Successive percentages: why do two 20% discounts not add up to 40%?
Learn why two successive 20% discounts equal 36%, with a changing calculation base, formula, and worked examples.
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Math Step by Step
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Quadratic formula with zero or negative discriminant: solve and check each case
Learn to identify a, b, and c, calculate the discriminant, and solve three quadratic equations, including repeated roots and cases with no real solution.
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Affine function from two points: find the equation and check the graph
Learn to calculate a and b from two points, verify the equation on a graph, and recognize when a vertical line is not a function of x.
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Does 0.999... Equal 1? Three Proofs and the Mistake of Treating It as an Approximation
Understand why 0.999... is exactly 1 through three proofs: algebra, 1/3, and a series/limit argument — and why there is no “last 9.”
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Numbers, addition, subtraction, multiplication, division, powers and other fundamentals explained from the ground up.
Fractions & Percentages4 articlesFractions, decimals, ratios, proportions, the rule of three and percentages explained step by step.
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Why does dividing by a fraction mean multiplying by its reciprocal? Three ways to understand it
See why fraction division becomes multiplication by the reciprocal using groups, scaling, and algebra — all with the same example.
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Reverse percentages: how to find the original value after a discount or increase
Learn how to recover the original value from a known final value by using the correct multiplier for discounts and increases, with worked examples and checks.
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Compound proportion with inverse quantities: decide by logic, not memorized arrows
Learn to identify direct and inverse relationships logically, solve two compound proportion problems, and check results with units and order of magnitude.
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Conditional probability tree: when to multiply, add, and renormalize without memorizing formulas
Learn to read a conditional probability tree: multiply paths, add alternatives, and renormalize after receiving new information.
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Simple or weighted average? How to spot hidden weights in tables and Enem questions
Learn when to use a simple or weighted average, especially when frequencies, group sizes, and percentages act as weights.
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Boxplots without memorizing: how to read the median, quartiles, interquartile range, and outliers in problems
Learn to interpret boxplots step by step, compare location and spread across groups, and recognize possible outliers without confusing a statistical flag with an error.
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Percentage points vs. percentages: how to avoid rate-change mistakes in Enem questions
Learn when to subtract rates in percentage points and when to calculate percent change, with examples and a practical method for Enem questions.
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PISA 2025: what Level 2 mathematics requires — with 3 step-by-step solved problems
Understand what the OECD associates with Level 2 mathematics in PISA 2025 and practice with three original teaching problems, fully solved and explained.
Read articleSuccessive percentages: why do two 20% discounts not add up to 40%?
Learn why two successive 20% discounts equal 36%, with a changing calculation base, formula, and worked examples.
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- 01PISA 2025: what Level 2 mathematics requires — with 3 step-by-step solved problemsProblems & Reasoning
- 02Simple or weighted average? How to spot hidden weights in tables and Enem questionsStatistics & Probability
- 03Percentage points vs. percentages: how to avoid rate-change mistakes in Enem questionsFractions & Percentages
- 04Boxplots without memorizing: how to read the median, quartiles, interquartile range, and outliers in problemsStatistics & Probability
- 05Does 0.999... Equal 1? Three Proofs and the Mistake of Treating It as an ApproximationFundamentals & Operations
Fundamentals & Operations
Numbers, addition, subtraction, multiplication, division, powers and other fundamentals explained from the ground up.
Does 0.999... Equal 1? Three Proofs and the Mistake of Treating It as an Approximation
Understand why 0.999... is exactly 1 through three proofs: algebra, 1/3, and a series/limit argument — and why there is no “last 9.”
Read articleNo articles published yet.
Fractions & Percentages
Fractions, decimals, ratios, proportions, the rule of three and percentages explained step by step.
Successive percentages: why do two 20% discounts not add up to 40%?
Learn why two successive 20% discounts equal 36%, with a changing calculation base, formula, and worked examples.
Read articleWhy does dividing by a fraction mean multiplying by its reciprocal? Three ways to understand it
See why fraction division becomes multiplication by the reciprocal using groups, scaling, and algebra — all with the same example.
Read articleReverse percentages: how to find the original value after a discount or increase
Learn how to recover the original value from a known final value by using the correct multiplier for discounts and increases, with worked examples and checks.
Read articlePercentage points vs. percentages: how to avoid rate-change mistakes in Enem questions
Learn when to subtract rates in percentage points and when to calculate percent change, with examples and a practical method for Enem questions.
Read articleAlgebra & Equations
Algebraic expressions, equations, systems, special products and other algebra concepts.
Quadratic formula with zero or negative discriminant: solve and check each case
Learn to identify a, b, and c, calculate the discriminant, and solve three quadratic equations, including repeated roots and cases with no real solution.
Read articleNo articles published yet.
Functions & Graphs
Functions, the Cartesian plane, graphs and interpretation of relationships between quantities.
Affine function from two points: find the equation and check the graph
Learn to calculate a and b from two points, verify the equation on a graph, and recognize when a vertical line is not a function of x.
Read articleNo articles published yet.
Math to understand, not just memorize
Mathematics does not have to be a sequence of formulas to memorize.
Math Step by Step was created to explain numbers, operations, algebra, geometry, functions, statistics, and other topics clearly and progressively, showing every stage of the reasoning.
Here, a solution does not end with an answer. We want to show where it came from, why the procedure works, which mistakes are common, and how to recognize similar situations in other exercises.
The content uses worked examples, visual explanations, everyday problems, and commented exercises to help students build a stronger foundation and progress at their own pace.
The idea is simple: fewer hidden steps and more mathematics that actually makes sense.