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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Why doesn't $26\times 24 = 25\times 25?$ (I remove and $+1$ from both numbers)

I'm solving a math puzzle: "how quickly can you multiply $26$ by $24?$" I don't know the answer so I use tutorials. One tutorial say to do it quickly you can round numbers up and down to closest power of $5$ or $10$. In my example $26\times 24$ I…
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Faster mental calculations

Currently I am preparing for trading exams which tests faster arithmetic skills. For ex- 80 questions (like calculating 0.abc* 0.cd) to be done in 8 minutes. I am trying to memorize the squares and tables and using simple tricks to solve these but…
uzumaki
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What is the fastest method to find which of $\frac {3\sqrt {3}-4}{7-2\sqrt {3}} $ and $\frac {3\sqrt {3}-8}{1-2\sqrt {3}} $ is bigger manually?

What is the fastest method to find which number is bigger manually? $\frac {3\sqrt {3}-4}{7-2\sqrt {3}} $ or $\frac {3\sqrt {3}-8}{1-2\sqrt {3}} $
user220382
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Mental multiplication of two digit numbers

There is a common way of mentally doing squares of two-digit numbers all the way up to 19*. This is how it works (example is for calculating $13^2 = 13*13 = xyz$): The ones digit is the ones digit of the two numbers (3 for both) multiplied -> $13^2…
TanMath
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Calculating logs in your head

I quite often need to estimate $\log_2(x)$ for positive integer values of $x$. I find it frustrating that I have to rely on a calculator/computer to do this. By way of contrast, I can happily compute as many decimal places as I like of…
user66307
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Are there human integrators?

Are there human "integrators", "differentiators", or "analysts"? I've heard of and seen people capable of performing seemingly complex arithmetic calculations mentally. Often this involves memorizing an algorithm which simplifies the process…
jdods
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mental math: approximating fractional exponents

Does anyone have any good tricks for estimating expressions with fractional exponents (besides guess and check)? For example, I want to easily calculate $9.1^{1/3}$. Currently, the best I've got is trial and error, but besides that $2^3 = 8$ and…
DilithiumMatrix
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The optimal way of improving fluency in elementary maths techniques, whilst holding a 9-5 job?

As an example of someone who has discovered maths at a later point in my life than average, and who has (perhaps unusually?) proven the point that it is perfectly possible to study undergraduate mathematics with almost no prerequisites, I am now…
Seraphina
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Faster mental arithmetic with powers of 10

Please excuse me if this question is too vanilla. What's a faster way to do mental arithmetic involving powers of ten? I've always had to do this and I do it using scientific notation which I'm equivocal about, but am finding myself roaringly slow.…
NNOX Apps
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Multiplication of decimal numbers

I was wondering if anyone knows any good resources to use or tricks to be able to solve these kinds of mental-arithmetic questions(See image below)? Would be really grateful for any help ! Edit: I would have around 10 to 15 seconds for each…
M.Ross
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I want to learn math from basics the Indian way and am looking for a book to guide me and some workbooks to practice. Any recommendations?

I was taught math in a very stoic method during my childhood and as a result became math-phobia. Now as an adult, I wish to relearn math as a long term hobby and a cure for my phobia. I found that in India, they value the process of solving…
user502833
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Is there an easy way to multiply two 2-digit numbers that have flipped digits?

I am currently a sophomore in high school competing in UIL academics in Texas. I am competing in the number sense test. Among the questions is the need to quickly multiply 2 two digits numbers, but as with all the questions present in the test,…
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Calculating power without using a calculator, for example $1.05^{10}$

How to find (or estimate) $1.0003^{365}$ without using a calculator? Do we have any fast algorithm for cases where base is slightly more than one? Say up to $1.1$ with tick $0.05$.
pmor
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Fast arithmetic, without a calculator?

This has been on my mind for quite a while now... Is it really crucial to be able to crunch numbers on the fly? I have considerate difficulty making out the quotient of $1 / 0.732 $ for example. I can approximate it well, but still (~1.3...). When I…
Curiosity
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How to solve a fraction with a numerator in exponential form and a denominator in numerical form without a calculator?

The question: "Imagine unwinding (straightening out) all of the DNA from a single typical cell and laying it "end-to-end"; then the sum total length will be approximately $2$ meters. Assume the human body has $10^{14}$ cells containing DNA. How many…