A couple years ago at a party at Pam’s place (not her current place), someone was trying to figure out how to split 53, four ways. (I think four girls had thrown a party … you fill in the blanks.) Pretty quickly I determined it to be 13 and a quarter, because 53 is really close to 52, which is the number of cards in a deck, and there are 13 cards of each suit, and then you take that extra dollar and split it four ways.
What’s the point? It’s useful math. Here’s another example.
Ever have trouble converting percentages to fractions, or vice versa? I remember being a kid, thinking that 10% was the same as 1/10, so 14% must be 1/14. Sitting down with a pencil and paper took care of that. So how do you calculate this stuff quickly? Long division in your head is a pain in the ass, especially if you’re like, eight.
Remember multiplication tables? 3×1=3. 3×2=6. 3×3=9. 3×4=12. Etc. Well I developed a sort of fuzzy Product-100 Table. With this table, we’re talking about conversational, estimated, seat-of-your pants calculation. It’s useful if you’re talking about sports or foods or a lot of different “close enough” topics.
Just like in a multiplication table, we’ve got three columns. The first column is the percentage number. It’s the number out of a hundred. The second column is the closest whole number to the quotient you get when you divide 100 by the number in the first column. The third column is the product of the numbers in the first to columns, in case you want to know just how close you are. Let’s take a look. If you’re starting with 4 percent, and you want to know what that translates to as a fraction, the second column shows you that it’s 1/25, and the third column tells you that it’s exact. If you’re starting with 7 percent, the second column shows you that it’s 1/14, and the third column tells you that it’s close, but not exact.
| Percent | ~Quotient | (Percent * ~Quotient) |
| 1 | 100 | 100 |
| 2 | 50 | 100 |
| 3 | 33 | 99 |
| 4 | 25 | 100 |
| 5 | 20 | 100 |
| 6 | 17 | 102 |
| 7 | 14 | 98 |
| 8 | 13 | 104 |
| 9 | 11 | 99 |
| 10 | 10 | 100 |
| 11 | 9 | 99 |
| 12 | 8 | 96 |
| 13 | 8 | 104 |
| 14 | 7 | 98 |
| 15 | 7 | 105 |
| 16 | 6 | 96 |
| 17 | 6 | 102 |
| 18 | 6 | 108 |
| 19 | 5 | 95 |
| 20 | 5 | 100 |
| 21 | 5 | 105 |
| 22 | 5 | 110 |
| 23 | 4 | 92 |
| 24 | 4 | 96 |
| 25 | 4 | 100 |
I only spell out the chart to 25, because that’s where its usefulness starts to break down. If you examine the lower portion you’ll see why — The whole number which, when multiplied by 18, gets you closest to 100 is 5, as it is for 19, 20, 21, and 22 (5 results). You get 4 all the way from 23 to 28 (6 results), 3 all the way from 29 to 40 (12 results), and so on. I’ll post a comment with a more complete chart.
So, I think they should teach both the card stuff and the Product-100 Table. Maybe some schools already do.
Here’s the table to 250:
(PS – Microsoft Excel made the calculations and code for this table a breeze.)