Math guides
6 guides — practical answers with the math shown, each paired with a free calculator.
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