Blog — Math

Guides, worked examples and explainers.

Math

What Calculator Should I Use for Engineering?

Engineering students need exact-form math, complex numbers, vectors, matrix algebra, and statistics. Here are the right calculators for college engineering and the FE/PE exams.

May 15, 2026
Math

What Calculator Should I Use for Trigonometry?

Any scientific calculator can do trig — but some make life much easier than others. Here are the right picks for high-school, college, and engineering trig.

May 15, 2026
Math

Pythagorean Triples: Patterns, Generators, and Why They Matter

A Pythagorean triple is three integers (a, b, c) with a² + b² = c². There are infinitely many — and they follow surprisingly clean patterns.

May 15, 2026
Math

The Section Formula: Dividing a Segment in Any Ratio

The section formula generalizes the midpoint formula. Here is how to find the point that divides a segment in any ratio — internally or externally.

May 15, 2026
Math

The Distance Formula vs the Pythagorean Theorem: They Are the Same Thing

The distance formula looks complicated but it is just the Pythagorean theorem dressed in coordinate notation. Here is the connection.

May 15, 2026
Math

Negative and Fractional Exponents Explained: From 2⁻³ to 8^(2/3)

Negative and fractional exponents look strange but follow simple rules. Here is what each one means, with worked examples and common confusions cleared up.

May 15, 2026
Math

Ratios, Proportions, and Rates: What Is the Difference?

Ratios, rates, and proportions all compare two quantities — but each has a specific meaning. Here is how to tell them apart and use each correctly.

May 15, 2026
Math

The 68-95-99.7 Rule: How Standard Deviation Maps to Probability

For normal data, 68% of values fall within 1 SD of the mean, 95% within 2 SDs, and 99.7% within 3 SDs. Here is why, and how to use it.

May 15, 2026
Math

Pythagorean Theorem Proofs: Three Ways to See Why a² + b² = c²

The Pythagorean theorem has hundreds of proofs. Here are three of the cleanest: by area, by similar triangles, and by algebra.

May 15, 2026
Math

Golden Ratio in Design: What It Is and When to Use It

The golden ratio (1:1.618) has appeared in art, architecture, and design for thousands of years. Here is what it really is, when it helps, and when it is just myth.

May 15, 2026
Math

What Calculator Should I Use for the SAT?

The College Board allows specific graphing and scientific calculators on the SAT. Here is the approved list, with our top picks for each price range.

May 15, 2026
Math

Standard Deviation Explained: What the Number Actually Means

Standard deviation measures spread. But what does a "standard deviation of 5" actually tell you? Here is the intuitive explanation, with examples.

May 15, 2026
Math

Simplified Radicals: How to Reduce Square Roots to Lowest Form

A "simplified radical" pulls perfect-square factors out from under the root sign. Here is the technique, with worked examples and common traps.

May 14, 2026
Math

Midpoint Formula in Geometry: What It Is, Why It Works, and Where You Use It

The midpoint of a segment is the average of its endpoints. Here is why that formula works and where it shows up in geometry, physics, and design.

May 14, 2026
Math

Real-World Uses of Logarithms: From pH to Music to Earthquakes

Logarithms feel abstract in algebra class but they describe real systems. Here is where you encounter them — sound, chemistry, geology, music, and finance.

May 14, 2026
Math

Slope-Intercept, Point-Slope, and Standard Form: Choosing the Right Equation

A line has three common equation forms. Each is best for a different question. Here is when to use which, and how to convert between them.

May 14, 2026
Math

How to Add Fractions with Different Denominators (The Easy Way)

Adding fractions with different bottoms is the step where most students stumble. Here is the reliable method, a shortcut, and common pitfalls to avoid.

May 14, 2026
Math

GCF vs LCM: What Is the Difference and When to Use Each

Greatest common factor and least common multiple solve opposite problems. Here is how to tell them apart and recognize which one the problem is asking for.

May 13, 2026
Math

What Calculator Should I Use for A Level Maths?

UK A Level Maths and Further Maths require an approved calculator with statistical and matrix functions. Here are the picks that match the JCQ exam regulations.

May 13, 2026
Math

What Calculator Should I Use for Calculus?

Calculus requires features beyond basic scientific calculators — derivatives, integrals, sequences, and graphing. Here are the right picks for AP Calc, college calculus, and beyond.

May 12, 2026
Math

The Quadratic Formula: Where It Comes From and Why It Always Works

Every quadratic equation can be solved by a single formula. Here is how the formula is derived from completing the square.

May 12, 2026
Math

The Fast Way to Calculate Percentages in Your Head

Tipping, discounts, and quick estimates do not need a calculator. Five tricks that let you do percentage math in seconds.

May 11, 2026
Math

Common Log vs Natural Log: When to Use log vs ln

log and ln look interchangeable but they use different bases. Here is when each is used, why both exist, and how to switch between them.

May 10, 2026
Math

What Does Slope Actually Mean? Real-World Interpretations

Slope is "rise over run" in algebra class. In real life, it means rate of change — and it shows up in every chart, graph, and physical measurement.

May 10, 2026
Math

How to Calculate Percentage Step by Step

Three simple percentage formulas cover almost every real-world question. Here is each one with worked examples.

May 9, 2026
Math

How to Use a TI-84 Calculator for SAT and AP Math

The TI-84 is the most-used calculator on the SAT and AP exams. Here are the menus, shortcuts, and programs that actually save time on test day.

May 8, 2026
Math

Exponent Rules Cheat Sheet: Every Rule You Need for Algebra

Exponent rules trip up students because they look similar but apply differently. Here is every rule, in one place, with examples.

May 7, 2026
Math

Converting Fractions to Decimals and Back: A Practical Guide

Moving between fractions and decimals is a core math skill. Here is how to convert in both directions, handle repeating decimals, and know which form to use.

May 6, 2026
Math

Standard Deviation Explained in Plain English

Standard deviation measures how spread out your data is. Here is what it really means, how to calculate it, and how to interpret the number you get.

May 5, 2026
Math

Extending the Distance Formula to 3D and Higher Dimensions

The 2D distance formula generalizes cleanly to 3D and beyond. Here is what it looks like in higher dimensions and where you encounter it.

May 4, 2026
Math

How to Find Square Roots by Hand (When Your Calculator Is Not Available)

Calculators are not always available. Here are three reliable methods to find square roots without one — including the algorithm taught before pocket calculators.

May 3, 2026
Math

Prime Factorization Made Easy: A Step-by-Step Guide

Every whole number has a unique prime "fingerprint." Here is how to find it with a factor tree, why it matters, and how it powers GCF, LCM, and fractions.

May 2, 2026
Math

Mean vs Median vs Mode: Which Average Should You Use?

Three numbers all called "the average" — but each tells a different story. Here is when to use mean, median, and mode, with real examples.

May 1, 2026
Math

Completing the Square: The Technique Behind Half of Algebra

Completing the square shows up in the quadratic formula, conic sections, integrals, and optimization. Here is how it works — and why.

Apr 30, 2026
Math

Percent Change vs Percentage Points: The Confusion That Misreads Every News Story

A rate going from 5% to 6% is a 1 percentage point increase and a 20% increase. Both are true. Confusing them changes the story entirely.

Apr 29, 2026
Math

TI-84 vs TI-Nspire vs Casio fx-9750: Which Calculator Should You Buy?

The TI-84 dominates U.S. high schools, but the TI-Nspire is more powerful and the Casio fx-9750 is half the price. Here is which one fits your needs.

Apr 28, 2026