Do you do simple math "out loud" in your head?
I was notoriously bad at arithmetic, and was only saved at university by the advent of pocket calculators. The small multiplication tables is something that is just fixed in my head, so I do not recite it when using it, but I often confuse parts of it with other parts, so I have to consider if it 6*4 that is 24 or if it is 7*4.
Additions are practically all done "loud" in my head. I do not see any dots hovering in front of me, but when I add 5 to 7, I start counting from 7 until I reach 12 (or whatever the result is). At the age of 49 I still cannot add two single-digit numbers without counting.
Strangely enough, my calculating skills have actually become better. Years of practice have resulted in giving me a feeling if I have received the correct amount of money back when I pay with a bill, and I also have a good idea about the amount that I should pay.
Additions are practically all done "loud" in my head. I do not see any dots hovering in front of me, but when I add 5 to 7, I start counting from 7 until I reach 12 (or whatever the result is). At the age of 49 I still cannot add two single-digit numbers without counting.
Strangely enough, my calculating skills have actually become better. Years of practice have resulted in giving me a feeling if I have received the correct amount of money back when I pay with a bill, and I also have a good idea about the amount that I should pay.
HarryKeogh
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No, don't have to. (and that's where my math expertise ends...the multiplication tables)
Though a friend of mine who is truly brilliant has to recite the alphabet out loud when he looks something up in a dictionary or has to put something in alphabetical order.
Though a friend of mine who is truly brilliant has to recite the alphabet out loud when he looks something up in a dictionary or has to put something in alphabetical order.
Brian said:
I was taught the old school way: rote memorization of multiplication tables. For me, 6*6 is 36. Period. On the other hand, when the multiplication gets beyond the memorized tables, I was taught to do it the long way. I found a great, old book in a used bookstore when I was a teenager. I think it was called Speed Math or something like that. From that book, I learned so many cool shortcuts, I couldn't believe it. I drive some friends bonkers sometimes with my car's outside thermometer, which I have set to centigrade. Because of tricks in this book, I can rapidly convert the readings to fahrenheit in my head. In the winter, it makes for interesting moments when an unsuspecting passenger sees "-22" on the display and remarks how it doesn't feel anywhere near that cold.
Rolfe
Adult human female
I do vocalise the sum in my head. My mother drilled me in mental arithmetic when I was at primary school, and I got really good.
I'd do 7x5 as 5x7, because the five times table is easier to remember than the seven times table. And just know that it was 35. But I can also "see" that seven fives are 35.
Rolfe.
I'd do 7x5 as 5x7, because the five times table is easier to remember than the seven times table. And just know that it was 35. But I can also "see" that seven fives are 35.
Rolfe.
Rolfe
Adult human female
Re: Re: Do you do simple math "out loud" in your head?
Rolfe.
Neat trick. That's one I always have trouble with. Care to share?BillHoyt said:
Rolfe.
Very Interesting Topic.
I do multiplication like Brian, with addition.
Simple addition is a little differnt, And it's visualised in my head in a non verbal way so bear with me. (I also had to do a whole bunch of simple math to analyse how I was doing it!).
It's like I have a rule* in my head from 1-10 that I measure the length of the number with, the numbers appear as bars of varying length.
If the addition of the units does is not greater than 10 ie 1+3+4, thats easy, 1 bar + 3 bar measures 4 + 4 bar reaches to 8.
On the other hand if the number is longer than my rule I have to do some subtraction. Eg 8+7,
8+7 is oops, scoop the remaing space after the 8 bar from the 7, (2 units visually diassaper), measure whats left, it's 5. So I have 1 full 10 rule and a 5, 15.
*Bear in mind this is all visual and I hadn't really named these things before, it's not exactly a rule but a kind of 10unit space which the numbers fit into. It's also very fast, so much so that I had to keep adding different numbers to see what my brain was doing.
Doing Higher numbers get's more complicated but analysing how I was doing it made me realise Perhaps I wasn't doing it in the most efficent manner. I seemd to go from left to right and had to re-factor the remainders in after, instead fo right to left, how you'd do it on paper. So perhaps if I practice I can "re-program" my brain to do it in a "1 pass algorythm" hehe.
O.
PS, There are a lot of parralels in the way computers do multiplication, I''ll leave that for now though as I'm at work!
I do multiplication like Brian, with addition.
Simple addition is a little differnt, And it's visualised in my head in a non verbal way so bear with me. (I also had to do a whole bunch of simple math to analyse how I was doing it!).
It's like I have a rule* in my head from 1-10 that I measure the length of the number with, the numbers appear as bars of varying length.
If the addition of the units does is not greater than 10 ie 1+3+4, thats easy, 1 bar + 3 bar measures 4 + 4 bar reaches to 8.
On the other hand if the number is longer than my rule I have to do some subtraction. Eg 8+7,
8+7 is oops, scoop the remaing space after the 8 bar from the 7, (2 units visually diassaper), measure whats left, it's 5. So I have 1 full 10 rule and a 5, 15.
*Bear in mind this is all visual and I hadn't really named these things before, it's not exactly a rule but a kind of 10unit space which the numbers fit into. It's also very fast, so much so that I had to keep adding different numbers to see what my brain was doing.
Doing Higher numbers get's more complicated but analysing how I was doing it made me realise Perhaps I wasn't doing it in the most efficent manner. I seemd to go from left to right and had to re-factor the remainders in after, instead fo right to left, how you'd do it on paper. So perhaps if I practice I can "re-program" my brain to do it in a "1 pass algorythm" hehe.
O.
PS, There are a lot of parralels in the way computers do multiplication, I''ll leave that for now though as I'm at work!
OH Brain flash!!!!
Brian mentiond the dot's he learned at school. As A child I played with LEGO constantly, I think the Bars I visulise might actualy be an abstract of the side of a LEGO brick. I will have been trying to get the lenght of my walls right and ration my bricks about the same time as I was lerning how to do addition.
O.
Brian mentiond the dot's he learned at school. As A child I played with LEGO constantly, I think the Bars I visulise might actualy be an abstract of the side of a LEGO brick. I will have been trying to get the lenght of my walls right and ration my bricks about the same time as I was lerning how to do addition.
O.
supercorgi
Dog Everlasting
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I don't do it with additions but I sure have to think it out loud for multiplications (and I'm hopeless at division). Some multiplication tables I learned better than others. When I was little I learned a finger trick to do basic multiplication by 9s and I find that I still have to use it to figure out something like 9x8.
Re: Re: Do you do simple math "out loud" in your head?
I've worked in the sciences my whole life and I still don't think in centigrade. The best I can do is interpolate between a few known points, knowing that a celsius degree is about 2 fahrenheit degrees. So for instance I know 37 is body temperature, so an outside temperature of 40 is darned hot. I know water boils at 100 and freezes at 0, so I know -22 C is subzero F, but not too far subzero. I also know there's a crossover point at -40: -40 C = - 40 F.
The only places where I come close to "thinking in C" are at extreme low temperatures, where I was never exposed to the fahrenheit equivalents. So I know that absolute 0 is -273 C, that helium boils at 4 K (-269 C) and that nitrogen boils at 77 K (-196 C), and I have no idea what the equivalent fahrenheit values are off the top of my head.
Incidentally on the original topic: I go by memory of multiplication and addition tables. I have noticed that often when memorizing numbers such as phone numbers, it's easier for me to remember it if I vocalize it (so I guess I remember the sounds of the numbers) but my multiplication tables are purely numerical. In either form, I remember numbers much easier than words.
BillHoyt said:
I've worked in the sciences my whole life and I still don't think in centigrade. The best I can do is interpolate between a few known points, knowing that a celsius degree is about 2 fahrenheit degrees. So for instance I know 37 is body temperature, so an outside temperature of 40 is darned hot. I know water boils at 100 and freezes at 0, so I know -22 C is subzero F, but not too far subzero. I also know there's a crossover point at -40: -40 C = - 40 F.
The only places where I come close to "thinking in C" are at extreme low temperatures, where I was never exposed to the fahrenheit equivalents. So I know that absolute 0 is -273 C, that helium boils at 4 K (-269 C) and that nitrogen boils at 77 K (-196 C), and I have no idea what the equivalent fahrenheit values are off the top of my head.
Incidentally on the original topic: I go by memory of multiplication and addition tables. I have noticed that often when memorizing numbers such as phone numbers, it's easier for me to remember it if I vocalize it (so I guess I remember the sounds of the numbers) but my multiplication tables are purely numerical. In either form, I remember numbers much easier than words.
Re: Re: Re: Do you do simple math "out loud" in your head?
I wonder what temperatures you and BillHoyt are used to. Where I live - in Denmark, which among Europeans is generally considered a "cold" country - we regard -22 C as damned cold! In normal winters we only reach -10 C.rppa said:
Re: Re: Re: Re: Do you do simple math "out loud" in your head?
The past few weeks, here up on the mountain, I awake to -11 C on a regular basis. A few mornings started out at -22 C just recently. That's only -8 F. I've seen -25 F (-31 C) some winters, and that wasn't up here on the mountain, but in a valley normally 8 - 10 degrees (F) warmer.
steenkh said:
The past few weeks, here up on the mountain, I awake to -11 C on a regular basis. A few mornings started out at -22 C just recently. That's only -8 F. I've seen -25 F (-31 C) some winters, and that wasn't up here on the mountain, but in a valley normally 8 - 10 degrees (F) warmer.
Brown
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I still do some simple math out loud. I find that I can often catch and correct errors that way, and can get a better feeling of whether a result makes sense.
When I was a teenager, I worked at McDonald's, in an age when the cash registers did not add up the tab for you. You had to add up the bill and add tax, and you had limited writing space on your order form. I developed my own system by which I could add up the bill very quickly in my head (more quickly than anyone else), but I would utter some of the computations out loud. The oral computations sounded like nonsense to others.
Some of the customers were very impressed by this. Others were angry. "Add it up the RIGHT way!" demanded one customer, after I computed a very large order in my head, mumbling some computations as I did so. I complied with the customer's request: I wrote the price next to each item on the pad, wrote the figures in columns, and added them up, making sure to carry my 1's, 2's and 3's. It took me maybe three minutes to do this. In the end, the result was exactly the same as what I had previously computed in a matter of seconds. I tried not to be smug.
When I was a teenager, I worked at McDonald's, in an age when the cash registers did not add up the tab for you. You had to add up the bill and add tax, and you had limited writing space on your order form. I developed my own system by which I could add up the bill very quickly in my head (more quickly than anyone else), but I would utter some of the computations out loud. The oral computations sounded like nonsense to others.
Some of the customers were very impressed by this. Others were angry. "Add it up the RIGHT way!" demanded one customer, after I computed a very large order in my head, mumbling some computations as I did so. I complied with the customer's request: I wrote the price next to each item on the pad, wrote the figures in columns, and added them up, making sure to carry my 1's, 2's and 3's. It took me maybe three minutes to do this. In the end, the result was exactly the same as what I had previously computed in a matter of seconds. I tried not to be smug.
Re: Re: Re: Do you do simple math "out loud" in your head?
Sure thing. I break the formula down this way:
F = 9/5C + 32
9/5 is 1/5 shy of 2, so the first move is to simply double C. To which 32 can be added quickly. The final trick is to recognize that 1/5 is 2/10. 10ths can be handled quickly, because that's just a decimal shift, right? So, put it all together:
double C, add 32, subtract 2/10s:
100C -> 200F-> 232F-> 212F
I know the explanation is a bit long, but it beats the heck out of the long way:
9 times 100, then divide by 5, then add 32.
The "double and add" step becomes very quick with some practice, so I usually do that pretty much at once.
-10C -> 12F -> 14F
(When working with negative readings, you have to remember that the subtract 2/10s step is done later for convenience, but is actually a correction for the first doubling step.)
The basic ideas here are three
o doubling is simple
o thinking in 10ths is simple
o doubling and then subtracting 2/10s is the same as multiplying by 9/5s
Does that make sense or does it sound overly complicated?
Rolfe,Rolfe said:
Sure thing. I break the formula down this way:
F = 9/5C + 32
9/5 is 1/5 shy of 2, so the first move is to simply double C. To which 32 can be added quickly. The final trick is to recognize that 1/5 is 2/10. 10ths can be handled quickly, because that's just a decimal shift, right? So, put it all together:
double C, add 32, subtract 2/10s:
100C -> 200F-> 232F-> 212F
I know the explanation is a bit long, but it beats the heck out of the long way:
9 times 100, then divide by 5, then add 32.
The "double and add" step becomes very quick with some practice, so I usually do that pretty much at once.
-10C -> 12F -> 14F
(When working with negative readings, you have to remember that the subtract 2/10s step is done later for convenience, but is actually a correction for the first doubling step.)
The basic ideas here are three
o doubling is simple
o thinking in 10ths is simple
o doubling and then subtracting 2/10s is the same as multiplying by 9/5s
Does that make sense or does it sound overly complicated?
Jorghnassen
Illuminator
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- Nov 14, 2004
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- 3,942
I used to be able to do calculations in my head. Now I can barely add 2 and 2 together. That's what a math degree does for you.
/went into statistics after my undergrad... Oh and -22C is the average minimum temperature in my hometown in January.
/went into statistics after my undergrad... Oh and -22C is the average minimum temperature in my hometown in January.
Re: Re: Re: Re: Do you do simple math "out loud" in your head?
I grew up in Syracuse, NY, which is not by any stretch of the imagination the coldest place in North America, or even in the US. When hearing weather reports, I'd always feel sorry for folks up in the mountains a couple hours north, where it was REALLY cold.
Most days in winter it's in the 20s F (er... around -5 C). Lots of days in the teens (-10 C), and not unusual at all to see a fair number of days down as far as -10 F (-23 C). Temperatures below that are relatively uncommon, but certainly not unheard of, nor are they enough to cancel school or close the government. One time before we married, my then-fiance' visited in the middle of a cold spell of 10 successive days of temperatures around -25 F (-31 C). Her car battery froze solid during the visit.
When it gets that cold you just put on more layers. Basically when you're dressed right, you can't tell the difference between -5 C and -30 C, or at least I can't, except by how the snow feels underfoot (cold snow is crunchy). Also you can tell by how quickly icicles form in your moustache, or how quickly your glasses fog up when you come indoors.
It's hard on cars. In colder places than Syracuse, it's common for people to own special heaters for their car engines, and for parking lots to provide places to plug them in. Syracuse doesn't get enough cold weather to justify that, so starting a cold car is always an adventure.
steenkh said:
I grew up in Syracuse, NY, which is not by any stretch of the imagination the coldest place in North America, or even in the US. When hearing weather reports, I'd always feel sorry for folks up in the mountains a couple hours north, where it was REALLY cold.
Most days in winter it's in the 20s F (er... around -5 C). Lots of days in the teens (-10 C), and not unusual at all to see a fair number of days down as far as -10 F (-23 C). Temperatures below that are relatively uncommon, but certainly not unheard of, nor are they enough to cancel school or close the government. One time before we married, my then-fiance' visited in the middle of a cold spell of 10 successive days of temperatures around -25 F (-31 C). Her car battery froze solid during the visit.
When it gets that cold you just put on more layers. Basically when you're dressed right, you can't tell the difference between -5 C and -30 C, or at least I can't, except by how the snow feels underfoot (cold snow is crunchy). Also you can tell by how quickly icicles form in your moustache, or how quickly your glasses fog up when you come indoors.
It's hard on cars. In colder places than Syracuse, it's common for people to own special heaters for their car engines, and for parking lots to provide places to plug them in. Syracuse doesn't get enough cold weather to justify that, so starting a cold car is always an adventure.
Re: Re: Re: Re: Do you do simple math "out loud" in your head?
Marginally faster (to me) is the following:
(reminder) F = 9/5 C +32
So you take C, double (10/5), and substract 10% of the new value. Then add 32.
10% of twice the staring value is 2/10=1/5, so it works.
My method goes, using Bill's example:
100 => 200 => 20 substracted => 200 - 20 = 180 => 212
The advantage, as I see it, is that you don't even have to compute 2/10ths of the starting C value. You just drop 10% from the doubled value.
BillHoyt said:
Marginally faster (to me) is the following:
(reminder) F = 9/5 C +32
So you take C, double (10/5), and substract 10% of the new value. Then add 32.
10% of twice the staring value is 2/10=1/5, so it works.
My method goes, using Bill's example:
100 => 200 => 20 substracted => 200 - 20 = 180 => 212
The advantage, as I see it, is that you don't even have to compute 2/10ths of the starting C value. You just drop 10% from the doubled value.
SpaceFluffer
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I find the easiest way to convert is to remember that 10C = 50F (exactly). Once you have that, and you know that every 10 degrees C is 18 degrees F, you can easily jump around and ballpark your temperature.
eg.
20C = 50+18 = 68F
30C = 68+18 = 86F
40C = 86+18 = 104F
....
0C = 50-18 = 32F
-10C = 32-18 = 14F
-20C = 14-18 = -4F
...
there's less to remember and less arithmetic to do this way.
eg.
20C = 50+18 = 68F
30C = 68+18 = 86F
40C = 86+18 = 104F
....
0C = 50-18 = 32F
-10C = 32-18 = 14F
-20C = 14-18 = -4F
...
there's less to remember and less arithmetic to do this way.