Why doesn't a 20% increase reverse a 20% decrease?
A 25% increase is required to reverse a 20% decrease. A formula, edge case and coupon example show when the order of discounts matters.
Read article →Guides and worked examples
Ten practical guides to percentages, averages, units and recipe quantities. Follow the examples, then calculate with your own figures.
10 articles
Sequential discounts: what is the combined effect of a coupon and a sale?
Sequential discounts, fixed coupons and shipping step by step. We also work backwards from a total payment budget to determine the minimum coupon required.
Read article →Percentage points and percentage change: how to describe the difference accurately?
Percentage points, relative change and the choice of base using our own examples. We also derive how the overall rate can decrease while every subgroup improves.
Read article →Proportional scaling: different multipliers for length, area and volume
Length, area and volume change by different multipliers. Using a box example, we also calculate how much scaling fits within three specified size limits.
Read article →Mean, median and standard deviation: the same dataset answers three different questions
Using small, verifiable datasets, we demonstrate the impact of outliers, the difference between population and sample standard deviation, and the limitations of estimates derived from class intervals.
Read article →Weighted grade average and target average: which grades achieve the set result?
Double-weighted assignments, credits, new grades and varying weights: worked examples show how the average changes and when a target becomes mathematically unattainable.
Read article →Average speed for a round trip: when to calculate using distance, and when using time?
The average of 60 and 40 km/h over a route of equal length is 48 km/h. We show the derivation, the effect of stops, differing segments, and the distance calculated back from time.
Read article →Converting km/h and m/s: speed from a short measurement segment
Deriving the m/s to km/h conversion, the uncertainty of short measurements, and correctly combining two road sections with different speeds.
Read article →Fractions and ratios in practice: scaling recipes, calculating mixtures and remainders
What does a three-quarter portion, the 2:3 ratio and a third of the remaining quantity mean? We help with precise fractions, common units and several fully worked-out quantity examples.
Read article →Resizing cake tins: ingredient ratios, batter depth and baking time
Comparing round tins, baking trays and multiple smaller tins with numbers. We show you how to scale the recipe and why baking needs separate checking.
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