Questions tagged [mental-arithmetic]

Mental arithmetic comprises arithmetical calculations using only the human brain, with no help from calculators, computers, or pen and paper.

Mental arithmetic comprises arithmetical calculations using only the human brain, with no help from calculators, computers, or pen and paper.

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Mental arithmetic: Add numbers by combining numbers that add up to 10

I'm reading a book on mental arithmetic, and came across this paragraph: You were taught - or should have been taught - at school that speed in addition is acquired by combining pairs of successive numbers that add up to 10. I've never been taught…
user302157
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How do you calculate bitwise XOR in your head?

Subtraction has an easy method: you can literally count down until you get it. So does addition, multiplication, division, etc. However, does bitwise XOR have a method like this that you can do in your head (apart from converting into binary)? If…
virchau13
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Why is it so good to know that $(1+x)^n \approx 1+nx$ for $nx \ll 1$?

I’ve often heard that it’s good to memorize the fact that $(1+x)^n \approx 1+nx$ for $nx \ll 1$ (most recently here), especially for mental arithmetic or making quick approximations. But why? Could you post an example or two that illustrate its…
Ben Kovitz
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How can I best mentally calculate the total sum of a sequence of linear increases?

I often run into the following situation: In January, I'm producing $10$ items/month. By December, I want to be producing $65$ items/month. So assuming things improve linearly, my production is increasing by $5$ items/month. Question: How many…
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Numeric synaesthesia: uses of and advice for learning math.

It turns out that my adolescent son might have numeric synaesthesia-- numbers have specific colors and possibly other distinguishing characteristics for him. He has shown that he can commit long sequences of numbers to memory, apparently by breaking…
f1r3br4nd
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Mental division of two fractions?

I've got a non-calc paper coming up, and when going through a test, this fraction came up: $$ \frac{8}{-0.4} \equiv \frac{8}{\big(\frac{-2}{5}\big)} $$ Going through the answers he says: $$8/2=4$$ I then assume he did -(4*5) so:…
user429273
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Why does this method for finding the square root of a number work?

Recently I read this, which teaches a trick for finding the square root of a number very quickly and was quite astounded. How/why does this method work? For those of you with linkphobia, I copied and pasted part of the page below: Step-1: Look at…
suomynonA
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Shortcut for finding cube of the Numbers

Is there a shortcut for finding cube of a particular number like $68^3$ ? If anyone knows how to solve for two- and three digit numbers, can you please share the answer?
user356321
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Nice approximation to pattern

Does anyone know a good general approximation (within 5 percent) for the sum of the products of two numbers such that the sum of one number of one product and another of another product is equal two the other two numbers MENTALLY. Format:…
Ian L
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$f(n)=7^{6n} - 6^{6n}$, where $n$ is a positive integer.

$f(n)=7^{6n} - 6^{6n}$, where $n$ is a positive integer. find the divisors of $f(n)$ for odd and even values of $n$. Is there a general solution for the…
HOLYBIBLETHE
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Square three digit numbers, the efficient way

I would like to square a three digit number in my head. Now I know that the formula is $$ ( X + r ) ( X - r ) + r^2 = X^2 - rX + rX - r^2 + r^2 = X^2 $$ Where $\,r\,$ is a number such that $\,X + r\,$ is divisible by $10$ and/or $100$ Now the…
Quillion
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Finding the percent of a division fast and mentally

3/8= (0.125*3) = 0.375 = 37.5% is easy to calculate mentally but is there a better way to find the percent of the following divisions fast and mentally? 3.5/8 4.5/7
Math is fun
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Does anyone know of a Mental Math Game for blind students?

I'm looking for any computer game made for blind students where the math exercises are asked through a computer's speaker and answered through a microphone by the student. Unlike normal math games, answers shouldn't be typed using the keyboard's…
Ronnie
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Best algo for finding no. of steps required to convert a sequence to a palindromic sequence

[My first question of Math SE, so, HI!] I'm not sure of what the rules are around the place, but I have a straightforward question as follows... The sequences 23, 45, 23 and 23, 45, 56, 23, 23, 56, 45, 23 are examples of palindromes. The sequence…
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fast mental arithmetic: is it an algorithm or table-like structure?

edit Removing the fluff, the question is: When solving problem X by heart, how does the mind reaches the solution very fast? by 'running' an algorithm or 'accessing' a table The 'fluffy' version: Since I was a kid I was always amazed by mental…
Draconar
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