Anonymous at Fri, 31 May 2024 08:56:16 UTC No. 16202215

>>16202184
at least a rough estimate 4300 should be easy to see

Anonymous at Fri, 31 May 2024 09:01:06 UTC No. 16202221

>>16202184
All you really need to do is memorize square numbers and you will be able to easily solve those types of problems fast.

87*49 = 68^2 - 19^2 = 4624 - 361 = 4263

Anonymous at Fri, 31 May 2024 09:03:57 UTC No. 16202224

>>16202215
how?

>>16202221
where did those squares come from?

Anonymous at Fri, 31 May 2024 09:10:03 UTC No. 16202226

>>16202224
[eqn]a \cdot b = \left(\frac{a+b}{2} \right)^2 - \left(\frac{a-b}{2} \right)^2[/eqn]
The product of two numbers is always equal to the square of their arithmetic mean minus the square of the distance to the mean.

Anonymous at Fri, 31 May 2024 09:19:21 UTC No. 16202232

>>16202226
that's way harder

Anonymous at Fri, 31 May 2024 09:26:17 UTC No. 16202238

87*49 = 87*50-87 = 8700/2 - 87 = 4350-87 = 4263
For an estimation, just skip the last subtraction and say 4300.

Anonymous at Fri, 31 May 2024 09:28:09 UTC No. 16202241

>>16202184
87*49
80*50 = 8*5*100 = 4000
7*50 = 350
4350-87 = 4263

Anonymous at Fri, 31 May 2024 10:52:26 UTC No. 16202321

>>16202184
why is nobody answering OPs question? OP didnt ask how to solve it but how important mental math is.

Anonymous at Fri, 31 May 2024 13:59:57 UTC No. 16202505

>>16202224
>how?
80*50 + 7*50 = 4000 + 350 = 4350
but 49<50, so cull it down a bit, 4300

Anonymous at Fri, 31 May 2024 14:01:37 UTC No. 16202511

>>16202321
Is this your first day on /sci/?

Anonymous at Fri, 31 May 2024 14:05:49 UTC No. 16202514

>>16202184
It's not important at all for mathematics.

Anonymous at Fri, 31 May 2024 14:08:51 UTC No. 16202518

>>16202184
this is what I did mentally
87 x 49? ok lets' do 87 x 50 - 87. so 87 by 10 is 870. so 870 by 5 is 8700 / 2, which is 4350. so 4350 - 87 is 4300 - 37 which is 4263.

Anonymous at Fri, 31 May 2024 15:34:41 UTC No. 16202622

>>16202184
quoting my professors, to do math you need to be able to count to 3 and know three alphabets. As for mental calculations, in the lab I'm faster with scratch paper and pen than with calculators, and being able to estimate the solution will prevent you from going with your erroneous calculations, but's thats essentially just knowing multiplication table

Anonymous at Fri, 31 May 2024 15:57:52 UTC No. 16202656

>>16202184
you should definitely be able to do 90*50 by rounding to nearest 10s and know its under 4500 and above 4000

Anonymous at Fri, 31 May 2024 16:02:45 UTC No. 16202660

>>16202184
i dont even know 16+435 off the top of my head, 6x5.3 takes a calculator. I did not start paying attention in school in till HS

Anonymous at Fri, 31 May 2024 17:52:52 UTC No. 16202772

>>16202184
>should i be able to do 87*49 in my head?
Yup! Because it's 87*50-87.

Anonymous at Fri, 31 May 2024 18:11:12 UTC No. 16202801

All these retards using numerals instead of picturing the math geometrically have all failed to do math mentally, imagine not picturing a fucking square when thinking of Pythagoras but instead only think of it algebraically

Anonymous at Fri, 31 May 2024 18:29:15 UTC No. 16202809

>>16202184
87*50-87
yes, you should be able to do that

Anonymous at Fri, 31 May 2024 19:21:44 UTC No. 16202871

87*49 = 87*100/2-87 = 8700 / 2 -87 = 4350 - 87 = 4300 - 37 = 4263

Anonymous at Sat, 1 Jun 2024 02:27:33 UTC No. 16203441

>>16202518
>>16202871
>4350-87 = 4300-37 = 4263
Unless you're working with pocket change daily, it's faster and less strenuous to use radix complements, since it avoids the mental burden of carrying.
4350 - 87 = 4250 + 13 = 4263

Anonymous at Sat, 1 Jun 2024 02:53:12 UTC No. 16203475

>>16202184
no, but at a point its easier to know it than not. carpenters need to do mental math while roofers never even touch the subject. store clerks can learn mental math but nowadays their cash register will always give a correct and automated answer. if you want to count your own change, learn mental math for the novelty.

Anonymous at Sat, 1 Jun 2024 06:46:29 UTC No. 16203728

>>16202184
You should have a cognitive framework to process such an equation. The framework and ability to form abstractions and methodologies to process complex datasets is much more valuable than the actual computation.

>87*49 -> 87, 49, FUNCTION: *
> DIGIT MUTABILITY:
> (87): 3 STEPS TO 1 UNIQUE DIGIT (100)
> (49): 2 STEPS TO 1 UNIQUE DIGIT (100)
> 2 < 3 -> MODIFY (49)
> CLOSEST SIMPLE:
> ((87 * 100) / 2) - (87 * 1)
> 87 % 2 = 1 -> SIMPLIFY
> 87 = 88 - 1
> SUBSTITUTE IN MODULO RELEVANT SECTIONS
> ((88 * 100) / 2) - (1 * 100 / 2) - (87 * 1)
> REDUCE UNIQUE DIGIT COUNT TO MINIMUM
> (44 * 100) - (1 * 50) - (87)
> SIMPLIFY ARITHMETIC
> (4400) - (50 * 2) - (37)
> (4400) - (100) - (37) = 4263

(this is a lot faster mentally than writing it out stepwise)

Anonymous at Sat, 1 Jun 2024 06:48:53 UTC No. 16203730

>>16203441
This. Minimize the computational complexity of the function through modulo math and unique digit reduction.

Anonymous at Sat, 1 Jun 2024 07:29:46 UTC No. 16203766

>>16202184
I was atrocious at this level of maths, which meant by like the start of high school I was put in the lowest maths class and completely hated it. By university I did a comp sci degree with 50% maths courses and did very well at it. The whole difference was by the time of advanced maths they just expect you to be using a calculator. I still do basic shit in my head.

Anonymous at Sat, 1 Jun 2024 09:29:17 UTC No. 16203886

>>16202184
Not that important but doesn't hurt.
There is plenty of mathematicians unable to do it.