Applied Math
What a 3-to-2 Ratio Tells You About the Whole
For an event that needs 750 cards in a blue-to-green ratio of 3 to 2, order 450 blue cards and 300 green cards. The ratio gives the relative…
Alex Ion
Articles
Applied Math
Why Rectangles with the Same Area Can Have Different Perimeters
Two garden beds can hold the same amount of soil at the same depth and require different lengths of fence. A bed 3 feet wide and 8 feet…
Applied Math
Two Products Can Average Four Stars and Tell Different Stories
Two products can display the same four-star average and the same review count while their customers report very different experiences. Imagine each product has eight reviews. Everyone who…
Applied Math
What Happens When Three Teams Tie for the Last Spot?
Three teams are tied at 91 points, and there is one seat left in the final. The leaderboard can tell you which teams are tied. Filling the seat…
Applied Math
Why 00123 and 123 Are Not Always the Same ID
The product codes “00123” and “123” can identify two different items even though both become the number 123. A column full of digits is not necessarily a column…
Applied Math
A Missing Day Is Not the Same as a Zero-Sales Day
A day with no sales and a day with no sales report tell you different things. One records an outcome. The other leaves an unanswered question. That difference…
Applied Math
Why 1.20 and 1.2 Can Tell Different Measurement Stories
Numerically, 1.20 and 1.2 are equal. The extra zero does not make a length larger or change the rules of arithmetic. In a measurement record, however, that zero…
Applied Math
Why Your Calculator Shows More Digits Than Your Measurement Deserves
A calculator can produce more decimal places than your measurements can support. Multiply 18.7 by 4.3 and you get 80.41. The arithmetic is right. Whether all those places…
Probability and Statistics
Why Matching Birthdays Become Likely Sooner Than You Expect
In a group of 23 people, the probability that at least two share a birthday is about 50.73% under the usual simplified model. That is much larger than…
Probability and Statistics
Choosing a Team and Choosing a Podium Are Different Problems
Six people are available for a three-person team. There are 20 possible teams. If the same six people compete for three distinct podium places, there are 120 possible…
Essential Math
Two Numbers Have the Same Sum. Why Can Their Products Be So Different?
The pairs 1 and 11, 3 and 9, and 6 and 6 all add to 12. Their products are 11, 27, and 36. A fixed sum does not…
Essential Math
What a Quadratic Graph Can Tell You Before You Solve It
The graphs of \(y=x^{2}-6x+5\), \(y=x^{2}-6x+9\), and \(y=x^{2}-6x+13\) have the same shape. Moving the constant term shifts the parabola vertically. Those shifts change whether the curve crosses, touches, or…