Math guides
10 guides — practical answers with the math shown, each paired with a free calculator.
Math
The GPA Scale Is Not a National Standard
Every GPA page prints a 4.0 table as though it were fixed. Rice changed what an A+ is worth in 2018, and Memphis pays 3.84 for an A− — the scale is policy, set school by school.
September 4, 2026 · 7 min read
Math
Why the Quadratic Formula Loses Accuracy on One of Its Two Roots
Completing the square takes four lines and produces the formula. It also shows which of the two roots is safe to trust, and the calculator on this site was corrected to use the other route.
August 19, 2026 · 10 min read
Math
Geometry Backwards: Finding the Radius from the Area
Every geometry formula is printed in the direction you need least. Running it backwards is not the same operation reversed; it is a root, and roots can refuse.
August 17, 2026 · 10 min read
Math
When Cross Multiplication Gives You the Wrong Answer
Cross multiplication answers every question you put to it, including the ones it should refuse. The test is one line: if the input were zero, would the output be zero?
August 17, 2026 · 10 min read
Math
How to Add Fractions With Different Denominators — and Why the Rule Works
1/2 + 1/3 done the wrong way gives 2/5 — smaller than the 1/2 you started with. A sum must beat both addends, and that check is free.
August 16, 2026 · 10 min read
Math
Percent Grade to Degrees: Why a 100% Grade Is 45 Degrees, Not Vertical
A 100% grade is 45 degrees. Percent grade has no ceiling; degrees stop below 90, and that mismatch is where every conversion error starts.
August 16, 2026 · 9 min read
Math
Scale Factor: Why Doubling the Size Gives Four Times the Area
Twice as big means four times the paint and eight times the water. Lengths take k, areas take k², volumes take k³, and every scaling error is the wrong exponent.
August 16, 2026 · 9 min read
Math
Percentage Difference vs Percentage Change: Which One Do You Want?
40 and 60 are 40% apart, 50% more, and 33.3% less. All three are correct. The denominator is the decision.
August 15, 2026 · 9 min read
Math
How to Find the Volume of Hollow, Partial, and Composite Solids
A decomposition-first guide to pipes, frustums, domes, and partly filled tanks, with formulas and checks for avoiding geometric and unit errors.
August 12, 2026 · 12 min read
Math
How to Compare Two Data Sets: Center, Spread, and Relative Difference
A practical workflow for deciding whether two sets are comparable, describing their typical values and variation, and reporting differences without overstating them.
August 11, 2026 · 10 min read