# Math things I should have realized earlier **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [November 21, 2014, 4:42pm UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264 "2014-11-21T16:42:14Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![48Willys](https://avatars.discourse-cdn.com/v4/letter/4/db5fbb/32.png) [@48Willys](https://boards.straightdope.com/u/48Willys)\ **Post date:** [November 22, 2014, 12:08am UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/21 "2014-11-22T00:08:11Z")
> [@Leaffan](#): > > A long time ago I realized that multiplying by five is the same as taking half the amount and moving the decimal over, you know, like multiplying by .5. > > So 5 times, 360 becomes 1,800 and there’s almost no though to it. I estimate other calculations similarly. **3 times 175 is like a third and then move the decimal to get 600**. It’s useful for estimating. Bolding mine. I must be missing something: 3 X 175 = 600 ? (3 X 100) + (3 X 70) +(3 X 5)= 300 + 210 + 15 = 525 which does not equil 600. Or maybe, 175 / 3 = 58 1/3 = 58.33333333 moving the decimal gets, 583.3333333 Closer to 525, but no cigar. So even for an estiment this does not work. Wait, wait, I get it! You rounded up to 180 then; 180 / 3 = 60.0 move the decimal &, 60.0 X 10 = 600! This shows the error that can be achived by rounding early in the computation. If we are counting dollar bills, that is a $75.00 mistake. If, in your world, 600 is close enough to 525, then your system works! Its not even close in my world. ---
**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 22, 2014, 1:42am UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/22 "2014-11-22T01:42:57Z")
> [@48Willys](#): > > Bolding mine. > > I must be missing something: > > 3 X 175 = 600 ? > (3 X 100) + (3 X 70) +(3 X 5)= 300 + 210 + 15 = 525 which does not equil 600. > > Or maybe, 175 / 3 = 58 1/3 = 58.33333333 moving the decimal gets, 583.3333333 Closer to 525, but no cigar. > > So even for an estiment this does not work. > > Wait, wait, I get it! You rounded up to 180 then; > > 180 / 3 = 60.0 > > move the decimal &, 60.0 X 10 = 600! > > This shows the error that can be achived by rounding early in the computation. If we are counting dollar bills, that is a $75.00 mistake. > > If, in your world, 600 is close enough to 525, then your system works! Its not even close in my world. That’s why it’s called an estimate. I’m not talking about exact figures, just a finger in the wind quick estimate. I can do the real math in my head, of course, but sometimes, I dunno, like in a lumber yard looking for the cost of 14 sheets of finished plywood at $30 a pop, it’s nice to know “Hmm, that’s about $500.” I know 3 does not equal 3.33, so I would naturally round down a bit and come up with $450. I’m surprised how many people cant think like this. That’s all. ---
**Author:** ![Whatever4](https://avatars.discourse-cdn.com/v4/letter/w/f04885/32.png) [@Whatever4](https://boards.straightdope.com/u/Whatever4)\ **Post date:** [November 22, 2014, 6:48am UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/23 "2014-11-22T06:48:30Z")
Well, I can’t think like that. Grade school long division was the last math I understood. The only way I passed high school math was because the nun only taught the boys; she passed the girls so she wouldn’t look bad. My college math classes were taught by heavily accented foreign professors, who also passed everyone because no one could understand them. My semester long accounting project passed because the professor felt sorry for me. I don’t think he had ever used that much red ink on a student ledger before. Just looking at numbers makes me anxious. I truly do not understand how you do it. ---
**Author:** ![Smeghead](https://avatars.discourse-cdn.com/v4/letter/s/f1d935/32.png) [@Smeghead](https://boards.straightdope.com/u/Smeghead)\ **Post date:** [November 22, 2014, 11:14am UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/24 "2014-11-22T11:14:34Z")
I tried to explain to my teenager that math is really just a language. It’s a set of rules for manipulating things, and once you get the rules down, you can mix and change them all around to find cool ways of doing stuff like this. It never sunk in, I’m afraid. In other news, we had a new grad student work in our lab for a while who was baffled at the thought of multiplying or dividing by ten in her head. I was showing her how to do some dilution, and I said something like “we need one tenth of 8.34, so we use .834…” She stopped me there and started writing down numbers on her paper. I must have looked a bit surprised, because she said, “Oh, I’ll just trust you for now and work it out completely later.” She didn’t last long in the program. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [November 22, 2014, 2:04pm UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/25 "2014-11-22T14:04:39Z")
> [@Leaffan](#): > > That’s why it’s called an estimate. I’m not talking about exact figures, just a finger in the wind quick estimate. I can do the real math in my head, of course, but sometimes, I dunno, like in a lumber yard looking for the cost of 14 sheets of finished plywood at $30 a pop, it’s nice to know “Hmm, that’s about $500.” I know 3 does not equal 3.33, so I would naturally round down a bit and come up with $450. > > I’m surprised how many people cant think like this. That’s all. My method for something like that is 10x30 (300) + 4x30 (120) = 420, which is actually a bit faster for me than dividing by 3. (With the other one, I’d do 200x3 - 25x3, also a quickie.) But, yeah, point taken that the ability to estimate with more difficult problems is a good skill to have, no matter how you do it (like with three or four digit numbers, I’d start lopping off some ending digits.) ---
**Author:** ![WhyNot](https://avatars.discourse-cdn.com/v4/letter/w/c77e96/32.png) [@WhyNot](https://boards.straightdope.com/u/WhyNot)\ **Post date:** [November 22, 2014, 2:37pm UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/26 "2014-11-22T14:37:53Z")
> [@standingwave](#): > > This is probably trivial but dividing by 5 is kinda like multiplying by 2. > > Quick. What is $415 split five ways? > > Take 415 and double it to 830. > > [THIS STEP THAT YOU DIDN’T MARK IS TO DIVIDE BY 10] > > The answer is $83. It’s \*exactly \*like multiplying by 2 and dividing by 10! Because 10 divided by 2 is 5. What you did was perfect, and much easier for most people to do in their heads. You did, ultimately, divide by 5, by using two operations that equal 5! It’s awesome that you figured this out intuitively. This is exactly the sort of strategy that modern math education in the US is trying to give our students. Exactly the kind of thing that’s making parents’ heads explode on Facebook ranting about “Common Core Math”. But it makes things so much easier in the long run! Another example: my daughter recently asked me “what’s 12 times 7?” I’ll be honest, even I don’t have that one memorized. So I asked her to come up with a strategy. “Well, I know 12 is 6 X 2… so if I do 6X7, that’s 42, and double it is 84?” PERFECT! She was able (with fourth grade “Common Core math,” 9 years old) to intuit that 2(6X7)=12X7. She’s “factoring” the 12, she just doesn’t have that word for it yet! I wouldn’t have been able to do that until 7th or 8th grade pre-algebra back in my day. As for the OP: I get stuck a bit on the upper end of the 9 multiplication table. Up to 9X5, I’ve got it just by rote. After that, for years I’d struggle. 9 X 6 is, um…53? 56? Crap. Then I learned that the 9’s have a neat pattern. Up to 9X10, the answer’s digits add to 9. So if I can remember the first number, and I can, whatever else adds to that to make 9 gives me the right answer. 9X2=18; 1+8=9 9X3=27; 2+7=9 9x4=36; 3+6=9 9x5=45; 4+5=9 9x6=54; 5+4=9 9X7=63; 6+3=9 9X8=72; 7+2=9 9X9=81; 8+1=9 Neat, huh? 😃 ---
**Author:** ![Digital\_is\_the\_new\_Analog](https://avatars.discourse-cdn.com/v4/letter/d/a88e4f/32.png) [@Digital\_is\_the\_new\_Analog](https://boards.straightdope.com/u/Digital_is_the_new_Analog)\ **Post date:** [November 22, 2014, 2:48pm UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/27 "2014-11-22T14:48:13Z")
As an American who used to visit Canada for work (and talk to Canadians on the phone daily), I found it useful to be able to estimate temperature conversions between F and C quickly. Classic formula: 9/5 \* C + 32 = F If all I want to know is if it’s cold or hot…would I need a bathing suit, a light jacket, or ski clothes…then 9/5 is a bit less than 2 and 32 is a bit more than 30. So 2 \* c + 30 is close to F You can’t use this for science or cooking, but it works well for casual conversation. ---
**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 22, 2014, 3:33pm UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/28 "2014-11-22T15:33:10Z")
> [@Digital\_is\_the\_new\_Analog](#): > > As an American who used to visit Canada for work (and talk to Canadians on the phone daily), I found it useful to be able to estimate temperature conversions between F and C quickly. Classic formula: > 9/5 \* C + 32 = F > > If all I want to know is if it’s cold or hot…would I need a bathing suit, a light jacket, or ski clothes…then 9/5 is a bit less than 2 and 32 is a bit more than 30. So > 2 \* c + 30 is close to F > > You can’t use this for science or cooking, but it works well for casual conversation. Yep. When Celsius was new to Canada that’s what we all did: double it and add 30. For most weather temperatures it’s close enough. Similarly for kilometres to miles just multiply by .6: close enough for driving speeds. 100 kph = 60 mph 60 kph = 36 mph etc. ---
**Author:** ![WhyNot](https://avatars.discourse-cdn.com/v4/letter/w/c77e96/32.png) [@WhyNot](https://boards.straightdope.com/u/WhyNot)\ **Post date:** [November 22, 2014, 3:43pm UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/29 "2014-11-22T15:43:28Z")
When I need a pretty-close-but-not perfect conversion of kilograms to pounds, I double the number and add the first two digits to the tens and ones. That’s hard to put in words. 60 kilo. Double it, 120. Add 12 to get 132 pounds. Actual conversion: 132.27 70 kilo. Double it, 140. Add 14 to get 154 pounds. Actual conversion: 154.32 85 kilo. Double it, 170. Add 17 to get 187 pounds. Actual conversion: 187.39 I haven’t figured out an easy way to go from pounds to nearly accurate kilos in my head yet, though. Anyone have one? ---
**Author:** ![DCnDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dcndc/32/2842_2.png) [@DCnDC](https://boards.straightdope.com/u/DCnDC)\ **Post date:** [November 22, 2014, 3:49pm UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/30 "2014-11-22T15:49:58Z")
Doing arithmetic left to right rather than right to left, as I was taught (back in the early 80s). **48Willys** already did this upthread: > [@48willys](#): > > 3 X 175 = 600 ? > (3 X 100) + (3 X 70) +(3 X 5)= 300 + 210 + 15 = 525 Particularly useful when you don’t need an exact number, or for quickly eliminating wrong answers on a multiple choice test. Apparently left to right is taught now as part of the Common Core, but back in my time right-to-left was “the proper way.” ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [November 22, 2014, 4:52pm UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/31 "2014-11-22T16:52:15Z")
> [@DCnDC](#): > > Doing arithmetic left to right rather than right to left, as I was taught (back in the early 80s). **48Willys** already did this upthread: > > Particularly useful when you don’t need an exact number, or for quickly eliminating wrong answers on a multiple choice test. Apparently left to right is taught now as part of the Common Core, but back in my time right-to-left was “the proper way.” The [del]New Math[/del] Common Core stuff calls that the “partial products” method. I think it’s a far better way to teach it. Students still learn the traditional algorithm later, since it’s faster to do on paper for larger numbers. But the partial products method makes it a lot clearer conceptually. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [November 22, 2014, 6:56pm UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/32 "2014-11-22T18:56:19Z")
> [@WhyNot](#): > > When I need a pretty-close-but-not perfect conversion of kilograms to pounds, I double the number and add the first two digits to the tens and ones. That’s hard to put in words. > > 60 kilo. Double it, 120. Add 12 to get 132 pounds. Actual conversion: 132.27 > > 70 kilo. Double it, 140. Add 14 to get 154 pounds. Actual conversion: 154.32 > > 85 kilo. Double it, 170. Add 17 to get 187 pounds. Actual conversion: 187.39 > > I haven’t figured out an easy way to go from pounds to nearly accurate kilos in my head yet, though. Anyone have one? Halve it and then subtract 10 percent. So 220 pounds: Half is 110. Subtract 11: 99. Actual conversion: 99.79 kilos. If you want to get even closer, then add 1% back in: (100.1 vs 99.79.) ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [November 22, 2014, 7:06pm UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/33 "2014-11-22T19:06:58Z")
> [@pulykamell](#): > > Halve it and then subtract 10 percent. > > So 220 pounds: Half is 110. Subtract 11: 99. Actual conversion: 99.79 kilos. If you want to get even closer, then add 1% back in: (100.1 vs 99.79.) Whoops, I meant 1% of the final step back in, so it should be: 220/2 = 110. Subtract 10% (11) = 99. Add 1% back in = 99.99 vs the true value of 99.79. But the two-step process should be enough for most estimations. Just know that with two steps, you’re going to be slightly under. (The two steps essentially gives you a conversion factor of 1 lb = 0.45 kg instead of 0.453592 kilograms, the true value.) ---
**Author:** ![DCnDC](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dcndc/32/2842_2.png) [@DCnDC](https://boards.straightdope.com/u/DCnDC)\ **Post date:** [November 22, 2014, 7:26pm UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/34 "2014-11-22T19:26:35Z")
> [@WhyNot](#): > > Then I learned that the 9’s have a neat pattern. Up to 9X10, the answer’s digits add to 9. So if I can remember the first number, and I can, whatever else adds to that to make 9 gives me the right answer. > > 9X2=18; 1+8=9 > 9X3=27; 2+7=9 > 9x4=36; 3+6=9 > 9x5=45; 4+5=9 > 9x6=54; 5+4=9 > 9X7=63; 6+3=9 > 9X8=72; 7+2=9 > 9X9=81; 8+1=9 Interesting. My method for “the 9s” is: 9 \* X = (10 \* X) - X so: 9 \* 2 = (10 \* 2) - 2 = 20 - 2 = 18 9 \* 3 = (10 \* 3) - 3 = 30 - 3 = 27 and so on. ---
**Author:** ![Annie-Xmas](https://avatars.discourse-cdn.com/v4/letter/a/ecc23a/32.png) [@Annie-Xmas](https://boards.straightdope.com/u/Annie-Xmas)\ **Post date:** [November 22, 2014, 8:04pm UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/35 "2014-11-22T20:04:27Z")
To convert Celsius to Fahrenheit for weather purposes, double it and add 30. Don’t try this with cooking or scientific experiments. I work as a cashier in a store where every price ends in .99. If I’m posting volumes (i.e., two at), I make sure the final price ends in a number that, when the number of items is added to it, makes 0. Two items? 8. Three? 7. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [November 23, 2014, 8:59pm UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/36 "2014-11-23T20:59:23Z")
> [@Digital\_is\_the\_new\_Analog](#): > > If all I want to know is if it’s cold or hot…would I need a bathing suit, a light jacket, or ski clothes…then 9/5 is a bit less than 2 and 32 is a bit more than 30. So > 2 \* c + 30 is close to F _30, 20, 10, 0: Hot, nice, cold, ice!_ ---
**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 23, 2014, 10:35pm UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/37 "2014-11-23T22:35:41Z")
> [@Spectre\_of\_Pithecanthropus](#): > > In a similar vein, I didn’t understand until long after high school that this is related to the fact that if the sum of the digits is divisible by 9, then the entire number will be as well. > > Or that if you consider that for any number, say 50761, the numeral is shorthand for a polynomial, with x=10; in this case, > > ``` > 5x[sup]5[/sup] + 7x[sup]3[/sup] + 6x[sup]2[/sup]+1 > > ``` > > Similarly, that you can generalize this principle to any value of x, such that if you show that the sum of the coefficients is divisible by (x - 1), then the entire expression will be. > > I might have been able to learn this in HS if only I could have handled the basic algebraic abstractions needed. FTR: I just discovered that superscripting doesn’t work in Tapatalk, or maybe it’s just my device. ---
**Author:** ![Digital\_is\_the\_new\_Analog](https://avatars.discourse-cdn.com/v4/letter/d/a88e4f/32.png) [@Digital\_is\_the\_new\_Analog](https://boards.straightdope.com/u/Digital_is_the_new_Analog)\ **Post date:** [November 24, 2014, 4:23am UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/38 "2014-11-24T04:23:44Z")
> [@Senegoid](#): > > _30, 20, 10, 0: > Hot, nice, cold, ice!_ I like it. I no longer work for a Canadian company, and still live in the US…so I may not need it any time soon. But I like it. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [November 24, 2014, 5:41am UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/39 "2014-11-24T05:41:24Z")
> [@WhyNot](#): > > Then I learned that the 9’s have a neat pattern. Up to 9X10, the answer’s digits add to 9. So if I can remember the first number, and I can, whatever else adds to that to make 9 gives me the right answer. > > 9X2=18; 1+8=9 > 9X3=27; 2+7=9 > 9x4=36; 3+6=9 > 9x5=45; 4+5=9 > 9x6=54; 5+4=9 > 9X7=63; 6+3=9 > 9X8=72; 7+2=9 > 9X9=81; 8+1=9 > > Neat, huh? 😃 Brings back memories: [Nine, nine nine.](https://www.youtube.com/watch?v=Q53GmMCqmAM) [You want another one?](https://www.youtube.com/watch?v=-WOgLltWhgg) ---
**Author:** ![48Willys](https://avatars.discourse-cdn.com/v4/letter/4/db5fbb/32.png) [@48Willys](https://boards.straightdope.com/u/48Willys)\ **Post date:** [November 24, 2014, 5:56am UTC](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264/40 "2014-11-24T05:56:23Z")
> [@WhyNot](#): > > When I need a pretty-close-but-not perfect conversion of kilograms to pounds, I double the number and add the first two digits to the tens and ones. That’s hard to put in words. > > 60 kilo. Double it, 120. Add 12 to get 132 pounds. Actual conversion: 132.27 > > 70 kilo. Double it, 140. Add 14 to get 154 pounds. Actual conversion: 154.32 > > 85 kilo. Double it, 170. Add 17 to get 187 pounds. Actual conversion: 187.39 > > I haven’t figured out an easy way to go from pounds to nearly accurate kilos in my head yet, though. Anyone have one? Try this, Divide by eleven then multiply by 5 . (X lbs/ 11) x 5 = Y kilo So (187.32 lbs / 11) x 5 = 17.029090909 x 5 = 85.1454545 kilo or 85 kilo and (132.27 lbs / 11) x 5 = 12.02454545 x 5 = 60.1227272727 kilo or 60 kilo Or in one step; X lbs x (5 / 11) = Y kilo X lbs x .454545 = Y kilo so 154 lbs x .454545 = 70.14539 or 70 kilo. Or use one of the earlier formulas to get very close. [Previous page](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264.md?page=1) [Next page](https://boards.straightdope.com/t/math-things-i-should-have-realized-earlier/705264.md?page=3)