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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How do people perform mental arithmetic for complicated expressions?

This is the famous picture "Mental Arithmetic. In the Public School of S. Rachinsky." by the Russian artist Nikolay Bogdanov-Belsky. The problem on the blackboard is: $$ \dfrac{10^{2} + 11^{2} + 12^{2} + 13^{2} + 14^{2}}{365} $$ The answer is easy…
Vlad
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How can I easily double any size number in my head?

I'm a software engineer, and I often double numbers especially when doing binary to decimal conversions. When numbers get large, I have trouble doubling a number in my head without using paper. For example, I can double 128 in my head easily because…
void.pointer
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a big number that is obviously prime?

I once heard it asserted that $91$ is the smallest composite number that is not obviously composite. The reasoning was that any composite number divisible by $2$, $3$, or $5$ is obviously composite, and the only composite numbers less than $91$…
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How to find a volume of this figure (which is $3080 \text{ cm}^3$) in a few seconds?

I was watching this Japanese game show and came across this question: The contestants were told that each small cube is 2cm on its side and were asked to find the volume of the above figure. The answer was 3080 $cm^3$. While I was counting the…
Maru
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Mental estimate for tangent of an angle (from $0$ to $90$ degrees)

Does anyone know of a way to estimate the tangent of an angle in their head? Accuracy is not critically important, but within $5%$ percent would probably be good, 10% may be acceptable. I can estimate sines and cosines quite well, but I consider…
brianmearns
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What is the fastest way to multiply two digit numbers?

I been playing different math games on my Android lately (for example: Math Cruncher). I've noticed that I'm unable to quickly (under 7-8 seconds) multiply two digit numbers (i.e $ 18 * 17$). So my question is, what is the fastest way to multiply…
MichaelS
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Did Feynman mentally compute $\sqrt[3]{1729.03}$ by linear approximation?

In the biopic "infinity" about Richard Feynman. (12:54) He computes $\sqrt[3]{1729.03}$ by mental calculation. I guess that he uses linear approximation. That is, he observe that $1728=12^3$. Let $f(x)=\sqrt[3]{x}$. Then…
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Mental Primality Testing

At a trivia night, the following question was posed: "What is the smallest 5 digit prime?" Teams (of 4) were given about a minute to write down their answer to the question. Obviously, the answer is googleable, so I'm not asking what the answer to…
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Daily exercises to speed up my mental calculations?

When I was a kid in school my father prevented me from using a calculator when solving my math homeworks. However at that time I was not convinced as of why not to use such a useful tool! So I kept on using it for multiplications and division, in…
Jack Twain
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Books, sites, guides about mental arithmetic by hand and tricks?

Please recommends books I can get, from amazon? I need to get really good at mental math and math by hand, because I'm taking an exam soon without a calculator.
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Why is Division harder than Multiplication?

Both conceptually and computationally it feels easier to see that: $ 6 \cdot 3.7 = 22.2$ than it is to see that $ 22.2 \div 6 = 3.7 $. Thoughts about the roots of this asymmetry? An analogous question might be asked of anti-differentiation and…
David D.
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Better Divisibility by 8

Everywhere I look, when you want to see if something is divisible by $8$ then you see if the last $3$ digits are divisible by eight. But how do you know if the last $3$ digits are divisible by $8$? For example, I can't tell you immediately that…
Joao
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Mental Math Techniques

What are some interesting mental math techniques that you know? Here's one that I got from my Grandmother who got it from a book: To square a two-digit number (from $26$ to $49$), take the number minus $25$ and put that in the first two digits, and…
user142299
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Mental Math: Finding Square Roots to 1 Decimal Point

I have 2 questions here. What is the most effective and easy way of calculating square roots in your head to an accuracy of 1 decimal point? This would need to work with at least two digit, non-perfect squares and would have to be doable…
m.smakg
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Mentally generating a (pseudo)random {0,1}-sequence with uniform distribution

I want to learn of good ways by which to generate $\{0,1 \}$-sequences in my head which are (pseudo)random with uniform distribution, so that I may simulate flipping a fair two-sided, standard coin. I want to do this because sometimes, I need to…
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