# Arithmetic / Math shortcuts **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [November 16, 2007, 11:10pm UTC](https://boards.straightdope.com/t/arithmetic-math-shortcuts/426774 "2007-11-16T23:10:00Z")\ **Posts on this page:** 8\ **Page:** 2
**Author:** ![Kevbo](https://avatars.discourse-cdn.com/v4/letter/k/e47774/32.png) [@Kevbo](https://boards.straightdope.com/u/Kevbo)\ **Post date:** [November 19, 2007, 3:36am UTC](https://boards.straightdope.com/t/arithmetic-math-shortcuts/426774/21 "2007-11-19T03:36:30Z")
Liberal, thanks for establishing that the longest distance between any two points is a shortcut! ---
**Author:** ![Napier](https://avatars.discourse-cdn.com/v4/letter/n/ce73a5/32.png) [@Napier](https://boards.straightdope.com/u/Napier)\ **Post date:** [November 19, 2007, 3:43am UTC](https://boards.straightdope.com/t/arithmetic-math-shortcuts/426774/22 "2007-11-19T03:43:37Z")
And that if somebody is between you and your goal, they must be a leader. ---
**Author:** ![ASAKMOTSD](https://avatars.discourse-cdn.com/v4/letter/a/919ad9/32.png) [@ASAKMOTSD](https://boards.straightdope.com/u/ASAKMOTSD)\ **Post date:** [November 19, 2007, 1:07pm UTC](https://boards.straightdope.com/t/arithmetic-math-shortcuts/426774/23 "2007-11-19T13:07:40Z")
[QUOTE=Liberal] **Here’s a handy way to add 1 + 1:** First, define the natural numbers as the set N, such that N is the smallest set satisfying the following axioms… [/QUOTE] CHICAGO MATH !!! :smack: ---
**Author:** ![Spectre\_of\_Pithecanthropus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/spectre_of_pithecanthropus/32/12343_2.png) [@Spectre\_of\_Pithecanthropus](https://boards.straightdope.com/u/Spectre_of_Pithecanthropus)\ **Post date:** [November 19, 2007, 5:43pm UTC](https://boards.straightdope.com/t/arithmetic-math-shortcuts/426774/24 "2007-11-19T17:43:50Z")
For restaurant tips (20% is standard for good service in these parts) I just take the first digit on the total and multiply by 2, and then adjust upward or downward intuitively. So say the total is 41.50, then 4x2 is 8 so I might end up giving 9 to make sure it’s at least 20. OTOH if the total is $48.50 I’ll just give $10 because it is almost $50, after all. ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [November 19, 2007, 6:09pm UTC](https://boards.straightdope.com/t/arithmetic-math-shortcuts/426774/25 "2007-11-19T18:09:07Z")
[QUOTE=Spectre of Pithecanthropus] For restaurant tips (20% is standard for good service in these parts) I just take the first digit on the total and multiply by 2, and then adjust upward or downward intuitively. So say the total is 41.50, then 4x2 is 8 so I might end up giving 9 to make sure it’s at least 20. OTOH if the total is $48.50 I’ll just give $10 because it is almost $50, after all. [/QUOTE] So you figure money the way Congress does. 😛 ---
**Author:** ![Rico](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rico/32/3582_2.png) [@Rico](https://boards.straightdope.com/u/Rico)\ **Post date:** [November 19, 2007, 6:14pm UTC](https://boards.straightdope.com/t/arithmetic-math-shortcuts/426774/26 "2007-11-19T18:14:42Z")
Does anyone else have _New Math_ by Tom Lehrer running through their heads about now? > [@](#): > > You can’t take three from two, > Two is less than three, > So you look at the four in the tens place. > Now that’s really four tens > So you make it three tens, > Regroup, and you change a ten to ten ones, > And you add 'em to the two and get twelve, > And you take away three, that’s nine. > Is that clear? And my favorite: > [@](#): > > Now, that actually is not the answer that I had in mind, because the book that I got this problem out of wants you to do it in base eight. But don’t panic! Base eight is just like base ten really - if you’re missing two fingers! Pure genius. ---
**Author:** ![Yeticus\_Rex](https://avatars.discourse-cdn.com/v4/letter/y/a698b9/32.png) [@Yeticus\_Rex](https://boards.straightdope.com/u/Yeticus_Rex)\ **Post date:** [November 19, 2007, 9:00pm UTC](https://boards.straightdope.com/t/arithmetic-math-shortcuts/426774/27 "2007-11-19T21:00:49Z")
When reconciling bank account statements, if you find an error that is divisible by 9, then it is most likely that you have transposed numbers in one or more of your amounts…and the quotient is the number that is also the difference between the two transposed numbers. Ex. Right amount: 284.96 Wrong amount: 248.96 The error is 36.00, which is divisible by 9 exactly 4 times. The 4 represents the difference of the two switched numbers, 8 & 4. The 36.00 tells you that it was the tens and ones places that were switched. Now you can quickly scan each amount on the bank statement for a difference of 4 between the tens and ones places. If you find one, compare to your written amount to find the error. RA = 34.72 WA = 37.42 The error is 2.70, divided by 9 = .30. The 3 in .30 is the difference between the two switched numbers, 4 & 7, and the 2.7 means tells you the units and tenths place were switched. Now, let’s add the two to have an example of two errors on the same bank statement… RA = 319.68 WA = 286.38 The error is 33.30, which is divisible by 9, which is 3.70, but it has two significant digits, which means you have more than one error with a combination of switched integers in different placeholders or an error that spans two placeholders (see other example below). A bit trickier to track down, but at least you know what to look for. Find them, correct them and then reconcile again to see if those corrections reconciled the whole statement or if they simplified the remaining errors to search for. This also works for any pair of switched places… RA = 69533 WA = 63593 The error is 5940, divisible by 9 for the quotient of 660. The difference is 6 and the placeholder difference is 2. (The two sixes). It gets a little sketchy for me beyond this. This reduces the time greatly to find errors, not only in the financial world, but scientific as well dealing with large amounts of data points or data entry accuracy. [Ah, here’s a better textbook description.](http://books.google.com/books?id=0YkBAAAAYAAJ&pg=PA140&lpg=PA140&dq=accounting+transposed+number+division+by+9+rule&source=web&ots=vhBydPzgGW&sig=3bvXORj9btc59hlfyHPChIFZqBQ) ---
**Author:** ![Leaffan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leaffan/32/299_2.png) [@Leaffan](https://boards.straightdope.com/u/Leaffan)\ **Post date:** [November 19, 2007, 10:05pm UTC](https://boards.straightdope.com/t/arithmetic-math-shortcuts/426774/28 "2007-11-19T22:05:59Z")
[QUOTE=Spectre of Pithecanthropus] For restaurant tips (20% is standard for good service in these parts) I just take the first digit on the total and multiply by 2, and then adjust upward or downward intuitively. So say the total is 41.50, then 4x2 is 8 so I might end up giving 9 to make sure it’s at least 20. OTOH if the total is $48.50 I’ll just give $10 because it is almost $50, after all. [/QUOTE] Huh? Why not just take ten percent and double it? $41.50 10% is about $4.20 times 2 = $8.40. Round up or down based on service. I usually aim for 15% for average service. I get that by finding 10% and then adding half of that again. So. $41.50 $4.20 $6.30 $7 tip [Previous page](https://boards.straightdope.com/t/arithmetic-math-shortcuts/426774.md?page=1)