Guide
Match the guide to the exact question, not the general topic
Several everyday math questions share surface wording but need different formulas: percentage change, percentage of a total, and percentage difference are three distinct calculations that people ask for interchangeably, and they return different numbers for the same two figures. The first step in any of these guides is confirming which of the three your actual problem is asking for, before entering anything.
Each guide is built the same way: the formula stated plainly, one or more worked examples with realistic numbers, and a reference table for common cases. Read the worked example first to confirm you understand which quantity plays which role, then apply the same structure to your own numbers.
Articles
Where to start in math
If you only read one article here, start with Long Division with Zeros: A Step-by-Step Guide for Students & Teachers, Long Division in Real Life: Bills, Recipes, Budgets, Sports & More, and Long Division with 2-Digit, 3-Digit & Decimal Divisors: Advanced Techniques. These cover the most common questions in this category and link to the calculator that matches.
41 articles are published in this category so far. Each one follows the same structure: the formula or method, a worked example, a comparison table where relevant, and a direct link to the live calculator.
Context
Where math guides get misapplied
Order and sign matter more than they look. Percentage change is directional: (new minus old) divided by old. Swapping old and new does not just flip the sign, it changes the denominator and the magnitude. A rise from 40 to 50 is a 25% increase; a fall from 50 to 40 is a 20% decrease, and that asymmetry catches people who assume the two should mirror each other.
Sample versus population statistics is the other recurring trap: sample standard deviation divides by n−1, population standard deviation divides by n, and using the wrong one skews results noticeably on small data sets. The guide states which one it is demonstrating. Check that it matches what your problem or course actually requires.
Scenarios
Sanity-check the answer before trusting it
Estimate before calculating. If you expect roughly 15% of 800 and a full calculation returns 1,200, something was entered as its reciprocal or a decimal was misplaced. This habit catches more mistakes than re-reading the inputs does, because it checks the answer against independent reasoning rather than the same misunderstanding that produced it.
For geometry and coordinate guides, sketch the problem: a slope that comes out negative when the line visibly rises on the page means the coordinate pairs were entered in the wrong order, and that is faster to catch by eye than by re-deriving the formula.
Comparison
The same value in three different forms
Fractions, decimals, and percentages are three representations of one value, and converting between them is often the actual task a guide is solving. 3/8, 0.375, and 37.5% are identical; which form to use depends on the audience and whether the value needs to stay exact. A recurring decimal is the case where the fraction is the honest representation and the decimal is an approximation.
Mean, median, and mode answer different questions about the same data set. When a distribution is skewed, the median usually describes the typical case better than the mean does, and the size of the gap between them is itself informative about how skewed the data is.
Limits
A guide checks the arithmetic, not the model
A math guide and its calculator can confirm that a formula was applied correctly; neither can confirm the formula suited the problem. Applying a linear model to something that compounds, or a normal-distribution method to data that plainly is not normal, produces an answer that is internally consistent and practically wrong.
Floating-point arithmetic also has real limits: results built from very large or very small magnitudes can carry small representation errors that compound across repeated operations. For coursework specifically, check which method your syllabus expects, since more than one of these problems has multiple valid approaches and marks often attach to the working shown, not just the final figure.