Math Blog
Math ideas, tricks and charts worth bookmarking
65 articles with worked examples generated by the real calculators, written and reviewed by Mateuss M.
How-to guides · 3 min readPercentage Increase and Decrease: Formulas and Examples
How to calculate percentage increase and decrease, find the new value, and why a 25% rise followed by a 25% fall does not return you to the start.
Charts & references · 3 min readFraction to Decimal Chart: 25 Common Fractions
A printable fraction to decimal and percent chart for halves to twentieths, with the rule for spotting repeating decimals and how to convert any fraction.
How-to guides · 3 min readHow to Convert a Fraction to a Percent (With Examples)
Convert any fraction to a percent in two steps: divide, then multiply by 100. Worked examples for 3/8, 7/20 and 5/6, plus mixed numbers.
How-to guides · 3 min readOrder of Operations: Why PEMDAS Trips People Up
PEMDAS, BODMAS and the viral “8 ÷ 2(2+2)” puzzle explained: what the rules actually say, where they are ambiguous, and how to write unambiguous math.
Concepts · 3 min readThe Birthday Paradox: Why 23 People Is Enough
In a group of 23 people the chance two share a birthday is just over 50%. The full calculation and a table up to 70 people.
Money & everyday · 3 min readCompound Interest Formula Explained With Worked Examples
A = P(1 + r/n)^(nt) explained step by step, comparing simple, annual, monthly and continuous compounding with a computed table.
Concepts · 3 min readThe Monty Hall Problem Explained (Why Switching Wins 2/3)
The Monty Hall puzzle solved with a full enumeration table: why switching doors wins two times out of three and staying only one in three.
Charts & references · 3 min readPrime Numbers Up to 200: Full List and How to Find Them
All 46 prime numbers up to 200, how the Sieve of Eratosthenes finds them, and quick tests to check any number for primality.
How-to guides · 3 min readHow to Convert a Decimal to a Fraction (Including Repeating)
Turn terminating and repeating decimals into simplified fractions with step-by-step examples: 0.375, 0.6 and 0.333…
How-to guides · 3 min readReverse Percentage: How to Find the Original Price
Work backwards from a sale price or a price with tax to the original value. Divide by the multiplier — not subtract the percentage.
Money & everyday · 3 min readHow to Calculate a Discount and Sale Price (Stacked Too)
Calculate the discount amount, the sale price, stacked discounts and tax with clear formulas and worked examples.
Study tips · 3 min readWeighted Average Explained: Grades, Finals and Targets
How weighted averages work, how to calculate your current grade from weighted scores, and how to find the score you need on the final.
How-to guides · 3 min readHow to Convert Celsius to Fahrenheit (and Back) Fast
The exact Celsius ↔ Fahrenheit formulas, a mental shortcut for estimates, and worked examples for weather, cooking and body temperature.
How-to guides · 3 min readBinary to Decimal Conversion: A Clear Step-by-Step Method
Convert binary to decimal with place values and decimal to binary by repeated division, with worked examples and a practice table.
How-to guides · 3 min readRatio and Proportion Explained: Simplify, Scale, Share
Simplify ratios, solve proportions by cross-multiplying, scale recipes and share amounts in a given ratio, with worked examples.
How-to guides · 3 min readHow to Find the Area and Circumference of a Circle
Area = πr² and circumference = 2πr. Worked examples from radius, diameter, circumference or area, plus the most common mistakes.
Money & everyday · 3 min readWhat Is BMI and How Is It Calculated? (Limits Included)
How BMI is calculated in metric and imperial units, the standard adult ranges, and an honest look at what BMI cannot tell you.
Money & everyday · 3 min readHow to Calculate Age in Years, Months and Days
Calculate exact age between two dates, handle leap-year birthdays and month-end dates, and count total days with a worked example.
How-to guides · 3 min readSpeed, Distance and Time Formula: Examples and Average Speed
The speed-distance-time triangle, unit conversions, and why average speed for a round trip is not the average of two speeds.
How-to guides · 3 min readHow to Round Numbers: Decimal Places and Significant Figures
The rules for rounding to decimal places, significant figures and the nearest ten, hundred or other multiple, with edge cases like 1.005.
How-to guides · 3 min readHow to Multiply and Divide Fractions and Mixed Numbers
Multiply across, divide by flipping, convert mixed numbers first and simplify at the end — with four worked examples.
Study tips · 3 min readHow to Solve Math Word Problems: A Four-Step Method
A repeatable four-step method for math word problems — read, define, calculate, check — with percentage and speed examples.
Charts & references · 3 min readPercent to Fraction Chart: 5% to 200% in Lowest Terms
Convert common percentages to fractions and decimals instantly with this chart, plus the three-step method for any percent.
Charts & references · 3 min readSquare Numbers and Square Roots Chart (1 to 30)
Perfect squares from 1² to 30², square roots of common non-squares to four decimals, and quick tricks for squaring and spotting squares.
Charts & references · 3 min readCube Numbers and Cube Roots Chart (1 to 20)
Perfect cubes from 1³ to 20³ with cube roots, plus how cubes relate to volume and a quick way to recognise them.
Charts & references · 3 min readRoman Numerals Chart 1 to 100 With Conversion Rules
Every Roman numeral from 1 to 100 in a printable chart, with the seven symbols, the subtractive rule and how to read or write any numeral.
Charts & references · 3 min readMultiplication Table Chart 1 to 12 and Tricks to Learn It
The complete 12 × 12 multiplication table, patterns for the 2s, 5s, 9s and 11s, and a practice routine that works.
Charts & references · 3 min readPowers of 2 Table: 2⁰ to 2²⁰ and Why Computers Love Them
Powers of two from 2⁰ to 2²⁰ plus 2³², with binary, byte and memory examples, and how doubling grows faster than most people expect.
Charts & references · 3 min readFactorials Chart: 0! to 20! and What They Count
A chart of factorials from 0! to 20! with exact values, the meaning of n!, and how factorials drive permutations and combinations.
Charts & references · 3 min readMetric to Imperial Conversion Cheat Sheet (Exact Factors)
Exact conversion factors between metric and US/imperial units for length, mass and volume, with worked conversions you can reuse.
Charts & references · 3 min readCelsius to Fahrenheit Chart (−40 to 100 °C) With Kelvin
A quick Celsius, Fahrenheit and Kelvin conversion chart from −40 °C to 100 °C, the formulas, and the single temperature where both scales agree.
Charts & references · 3 min readGPA Letter Grade Chart: The 4.0 Scale Explained
The standard 4.0 GPA scale from A+ to F, how credits weight each grade, a worked example, and why your school’s scale may differ.
Charts & references · 3 min readGeometry Formulas Cheat Sheet: Area, Perimeter, Volume
A one-page geometry formula sheet for area, perimeter, circumference, surface area and volume of common shapes, with worked examples.
Charts & references · 3 min readTrigonometry Cheat Sheet: SOH CAH TOA, Identities, Values
SOH CAH TOA, the sine/cosine/tangent values for 0°–90°, the key identities and the laws of sines and cosines, with decimals from the calculator.
Charts & references · 3 min readAlgebra Formulas Cheat Sheet: Identities, Exponents, Quadratics
The algebra formulas you need most: special products, exponent and log rules, the quadratic formula, slope and distance, with a worked check.
Concepts · 3 min readPythagorean Theorem: A Visual Proof and Pythagorean Triples
Why a² + b² = c² is true, shown with a simple area rearrangement, plus a table of Pythagorean triples generated by Euclid’s formula.
Concepts · 3 min readFibonacci Sequence and the Golden Ratio, Computed
The first 20 Fibonacci numbers, how their ratios converge to the golden ratio φ ≈ 1.618034, and Binet’s formula — with every value computed.
Concepts · 3 min readPascal's Triangle and the Binomial Theorem Explained
Build Pascal's triangle, see how each entry is a combination nCr, and expand (a + b)ⁿ using its rows.
Concepts · 3 min readLogarithms Explained Simply: What They Are and Why They Matter
Logarithms as “the power you need”, with tables for base 10 and base 2, the product rule, and real uses like pH and the Richter scale.
Concepts · 3 min readThe Unit Circle and Trigonometry Basics (Degrees and Radians)
Understand sine and cosine as coordinates on the unit circle, convert degrees to radians, and read key angle values from a computed table.
Concepts · 3 min readThe Remainder Theorem and Factor Theorem Explained
When you divide P(x) by (x − a) the remainder is P(a). Worked examples, how the factor theorem finds roots, and a full factorisation check.
Concepts · 3 min readCalculus Basics: Derivatives and Integrals With Numbers
A gentle introduction to derivatives as slopes and integrals as areas, with numerical tables showing slopes and sums converging to exact answers.
Concepts · 3 min readStandard Deviation Explained With a Worked Example
What standard deviation measures, how to calculate it step by step, the sample vs population difference and the 68-95-99.7 rule.
Concepts · 3 min readStatistics vs Probability: What Is the Difference?
Probability predicts data from a known model; statistics infers the model from data. A coin-flip example computed both ways.
Concepts · 3 min readLottery Odds Explained: Combinations Behind Pick-6 Games
How combinations give the odds of a pick-6 lottery: 1 in 13,983,816 for 6 of 49, with partial matches and a reality check on expected outcomes.
Concepts · 3 min readWhat Is Euler's Number e? Compound Growth and Series
e ≈ 2.718281828 explained through compound interest, the limit (1 + 1/n)ⁿ and the factorial series, with computed tables.
Concepts · 3 min readMatrices for Beginners: Multiplication, Determinant, Inverse
What a matrix is, how to multiply 2×2 matrices, how to compute a determinant and an inverse, with a fully computed example.
Concepts · 3 min readThe Prisoner's Dilemma: Game Theory Basics With a Payoff Table
A clear introduction to game theory using the prisoner's dilemma: payoff table, best responses, Nash equilibrium and why cooperation is hard.
Money & everyday · 3 min readSimple vs Compound Interest: The Difference in Numbers
Simple interest grows in a straight line, compound interest in a curve. See both for 2,000 at 4% over 1 to 30 years in one table.
Money & everyday · 3 min readThe Rule of 72: How Fast Does Money Double?
Divide 72 by the annual growth rate to estimate doubling time. See how accurate the rule is against exact calculations from 2% to 15%.
Money & everyday · 3 min readLoan EMI Formula Explained: How Monthly Payments Are Calculated
The equal monthly payment formula M = P·r(1+r)^n / ((1+r)^n − 1), with two worked loan examples and total interest, for learning purposes.
Money & everyday · 3 min readMarkup vs Margin: The Difference, Formulas and Examples
Markup is profit as a percent of cost; margin is profit as a percent of price. Formulas, conversions and a worked example with a comparison table.
Money & everyday · 3 min readUnit Price Comparison: How to Tell Which Pack Is Cheaper
Compare prices by cost per 100 g (or per unit) to find the better deal, with a worked example and a table showing when bigger is not cheaper.
Money & everyday · 3 min readSalary to Hourly Wage: How to Convert (With the 2,080-Hour Rule)
Convert an annual salary to an hourly rate using hours per year (40 × 52 = 2,080), see a conversion table and adjust for different schedules.
Money & everyday · 3 min readInflation and Purchasing Power: What 3% a Year Really Does
How inflation compounds, what 2%, 3% and 5% do to prices and purchasing power over 10 to 30 years, with a computed table and formulas.
Study tips · 3 min read10 Common Algebra Mistakes (With Numbers That Prove They’re Wrong)
The ten algebra errors students make most often, each disproved with a quick numerical check — (a+b)² ≠ a²+b², √(a+b) ≠ √a+√b, and more.
Study tips · 3 min readEstimation Techniques: Get Close Fast and Catch Mistakes
Round to leading digits, use benchmark fractions and compensate to estimate sums, products and percentages — with exact answers to show how close you get.
Study tips · 3 min readHow to Check Your Math Answers: Five Reliable Methods
Five ways to verify a math answer: inverse operations, substitution, estimation, a second method and unit checks — with worked examples.
Study tips · 3 min readHow to Study Math Effectively: Habits That Work
Practical habits for learning maths: practise retrieval, space your sessions, keep an error log, study worked examples, and check with step-by-step tools.
Study tips · 3 min readMath Formulas to Know for the SAT, ACT and Similar Exams
A revision list of the algebra, geometry, trigonometry and statistics formulas students commonly need for school-leaving and admissions tests, with practice links.
Study tips · 3 min readFive Mental Math Shortcuts That Save Real Time
Practical mental math tricks — 10% building blocks, halving, squaring numbers ending in 5 and divisibility checks — each verified with worked numbers.
Concepts · 3 min readMean vs Median: When Averages Lie
How a single extreme value changes the mean but barely moves the median, with a worked data set and a simple rule for choosing which average to report.
Concepts · 3 min readWhy 0.1 + 0.2 Is Not Exactly 0.3 in Computers
Floating-point arithmetic explained simply: why computers store 0.1 inexactly, what the famous 0.30000000000000004 means, and how a calculator hides it.
Concepts · 3 min readPrime Numbers and Internet Security, Explained Simply
Why multiplying primes is easy but factoring is hard, and how that asymmetry protects online messages — with a tiny worked example.
Concepts · 3 min readThe Quadratic Formula: Where It Comes From
A short derivation of the quadratic formula by completing the square, the meaning of the discriminant, and a worked example you can check with the solver.