Questions tagged [mental-arithmetic]
Mental arithmetic comprises arithmetical calculations using only the human brain, with no help from calculators, computers, or pen and paper.
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Does practicing mental math increase mathematical intuition? [closed]
Has any experienced mathematician on this site found that practicing mental math was associated with the development of mathematical intuition and conceptual understanding? I was considering ...
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Can you propose any hack for remembering multiplication tables from $13-19$?
I memorized multiplication tables from $2-12$ when I was in elementary school.
Regarding tables $13-19$:
I remember some intermittent elements
I find others by multiplication by recombination. E.g., ...
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Trick for calculating the 5th order derivative of $(2x^3+1)e^{x^2}$ evaluated at $0$
Are there any tricks for calculating the 5th order derivative of $(2x^3+1)e^{x^2}$ evaluated at $0$?
I guess it involves binomial expansion but it still seems too complicated.
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Mental math to quickly solve a product of mixed numbers with variables
I've come across the following question: "Let $6\frac{1}{m}\times n\frac{2}{11}=21$, where m, n are natural numbers. Find m+n."
Outside of actually solving the question, I've tried to guess ...
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How to quickly eyeball maximum sum subarray?
Given an integer array, I want to find the continuous subarray (containing at least one number) which has the largest sum. There are some algorithmic solutions to this here: https://en.wikipedia.org/...
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An app for learning the 1-100 times tables
Do anyone knows an app for android that help you learn $1$ to $100$ times table? I tried a few but none was quite what I need. I want it to:
Ask answers for two digit by one digit multiplication. $23 ...
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In time t, a dog does 3 jumps whereas a fox does 5. If distance covered in a jump by a dog is thrice that of the fox, find ratio of speed of dog : fox
This looks (and I think it is) a pretty simple problem.
My reasoning is as follows :
...
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Sum of values from 1 to 100 excluding values with digits of 7 and/or 8
I want to quickly sum values from 1 to 100, but exclude values with digits of 7 and/or 8 (e.g., 7,8,17,18,70,78,....) from the sum.
This is a mental math problem that I want to do in a really quick ...
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Is there a reasonably accurate and easy way to approximate lbs-stones or kg-stones (and vice versa)?
For example, when I need to talk with my American friends about body weight:
$\mathrm{KG}\times2+10\%$
($100\times2=200$, $200+10\%=220$... Pretty accurate and easy to do mentally, both ways)
However, ...
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prove that $5<\sqrt{5}+\sqrt[3]{5}+\sqrt[4]{5}$ [duplicate]
prove that $$5<\sqrt{5}+\sqrt[3]{5}+\sqrt[4]{5}$$
.A little use of calculator shows that $\sqrt{5}+\sqrt[3]{5}+\sqrt[4]{5}=5.44$.Thus the inequality is indeed true.
Generalising this result with $...
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Prove that $e^\pi > 21$. Without a proof, you can use the two facts: $e > 2.71$ and $\pi > 3.14$.
I heard that the following problem is for high school students.
Prove that $e^\pi > 21$.
Without a proof, you can use the two facts: $e > 2.71$ and $\pi > 3.14$.
My solution is the ...
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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. ...
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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 ...
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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 ...
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I want to learn math do I need to memorise the times tables?
As a front end developer, I do not need Math, however, I want to seriously learn it so that, maybe, one day, I might be able to get so good at it as to get into AI.
I started with Algebra 1 and ...
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Whats best method to calculate multiplication mentally?
I would like to know which method is better for mentally multiplication calculation between
a) Cross-Multiplication
and b) Left-to-Right Multiplication
Thank you!
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How many digits are there in $99^{99}$? [duplicate]
Question: How many digits are there in $99^{99}$?
My attempt:
Observe that
$$99^{99} = (100\times 0.99)^{99} = 100^{99}\times 0.99^{99}.$$
Note that $100^{99} = 10^{198}$ has $199$ digits and
$$0....
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Calculate $2^{5104} \bmod 10$ using mental arithmetic
I am practising interview for Jane Street's trader internship and I found the following question.
Question: Calculate $2^{5104} \bmod 10$ using mental arithmetic.
I know that $2^5 \bmod 10 \...
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Determine the number of digits of the product a.b
If $ a = 3,643,712,546,890,623,517 $ and $ b = 179,563,128 $, determine the number of digits of the product $ a.b $. I went searching the site and found this post where advise to use logarithm ...
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Are there techniques for quickly seeing patterns in numbers?
Recently I was watching 8 out of 10 cats does countdown (S18E01 - 26 July 2019), for which the math question there was the following numbers:
if you haven't seen countdown, you are provided 6 numbers,...
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are combinatorics-leaning mathematicians very good at mental math? [closed]
a common cliché in movies is that mathematicians who specialize in combinatorics are very adept at mental math (arithmetic), is that a real thing? if yes why?
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Can a mental calculator plot any function in seconds? [closed]
As we learnt at school, to draw the graph of a function in details it may be necessary to perform some steps of calculation such as finding domain and codomain, limits, asymptotes and sign of ...
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How do you calculate bitwise XOR in your head?
Subtraction has an easy method: you can literally count down until you get it.
So does addition, multiplication, division, etc.
However, does bitwise XOR have a method like this that you can do in ...
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Mental techniques for large arithmetic and decimals
Consider the following problems:
$$\frac{14}{4.6\dot{6}}$$
$$20 \cdot 45$$
$$\frac{7}{6}$$
$$28 \cdot 0.28$$
$$\frac{42}{168}$$
I'm looking for some techniques to solve these problems fast without ...
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Efficient modular reduction of integers in radix representation
I'm trying to find an easy and fast way to get the result of
$$353094232\bmod721$$
I would solve this by dividing manually the terms until I get the remainder of dividing, but I was wondering if there ...
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Estimating square numbers
A large dice has a side length of 9.2 cm.
Estimate the surface area of the cube.
What I did:
6× $9^2$
= 6 × 81 = 6 × 80 = 480
But the answer says that $9.2^2$ is 85 as an estimate.
How do I get ...
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What would be the best way to memorize the 10 by 10 multiplication table?
Hear me out before you start downvoting please. I have a learning disability so no matter how hard I try I can’t memorize the table. Please give some tips/hints on how to memorize the table. Thanks in ...
user649955
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Mental approximations of 1) log, 2) non-integer power
I am currently preparing for a interview that is notorious for asking mental approximations. Two example questions came up: 1) $\ln 514$ and 2) $3^{3.6}$.
What are some of the best ways to calculate ...
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What method for mentally computing 2-digit multiplication problems, minimizes the amount of mental steps?
So I've been practicing alot of mental math recently and ofcourse as a part of that, multiplying a double-digit number by another double-digit number. I have been doing some research into what the ...
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Vinculum number of 989?
To find vinculum number I was subtracting finding the complement of 989 and cosidering the number to be 0989 I raised the 0 to 1 so my answer was 1011 , but why was the answer given 1111 ? Do I also ...
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Age questions: How to approach solving this?
Completely foxed by this question:
Moses is twice as old as Methusaleh was when Methusaleh was one-third as old as Moses will be when Moses is as old as Methuselah is now. The difference in their ...
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Generating "random" mental calculation exercises?
I recently tried to come up with "random" mental calculation exercises in an attempt to fight traffic jam boredom. Unfortunately, I quickly got bored by the lack of creativity of the problems I can ...
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How many zeros will $ 3^{3}4^{4}5^{5}6^{6} - 3^{6}4^{5}5^{4}6^{3}$ ends with?
I have this GRE practice question, asking me to find the quantity $$ 3^{3}4^{4}5^{5}6^{6} - 3^{6}4^{5}5^{4}6^{3}$$ will end in how many zeros?
The answer given is $4$, but I don't quite understand ...
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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 ...
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Multiplication tables: up to what number should I memorise? [closed]
I never memorised them and suffered immensely through school as a result. Eg. I calculated 7x8 as (7x10=70) minus 7 using my fingers (63) then minus again on my fingers (56).
In Australia children ...
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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 ...
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What is the method for mentally computing $3^{3.5}$ and similar calculations?
What is the method for mentally computing an approximation of $3^{3.5}$ and similar calculations?
(without using any calculator)
The best I did is:
$3^{3.6}=e^{3.6ln(3)}=e^{3.6*1.098} \approx e^{3.6*...
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Without using a calculator how to solve $x^x = 100$? [duplicate]
Without using a calculator how to solve $x^x = 100$ ?
A way of finding an approximation to 2 decimals would be good neough.
I know about the Lmabert W function but one cannot compute it mentally. ...
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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 ...
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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 ...
user502833
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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 ...
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Proof behind this mental math multiplication?
Recently came across this technique of multiplying two $2$-digit numbers involving the same digit at the tens place and the sum of digits at units place being $10$. E.g., $73 X 77$ has same digit at ...
user356774
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Why doesn't $26\times 24 = 25\times 25?$ (I remove and $+1$ from both numbers) [closed]
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 ...
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(Quickly) finding the smallest fraction
Please see these fractions:
(A) $\frac{33}{128}$ (B) $\frac{45}{138}$ (C) $\frac{53}{216}$ (D) $\frac{83}{324}$ (E) $\frac{15}{59}$.
I need to find out quickly (in about a minute) the smallest of ...
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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$$ ...
user429273
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Approximate this fraction (simple arithmetic)
If I have
$1.5\cdot10^{-5}=\frac{1.5}{10^5}$
, how can I rewrite (approximate) this fraction as
$$
\approx \frac{1}{66.7\cdot 10^3}\quad ?
$$
My calculator gives the exact answer $\frac{3}{200000}$, ...
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Is there a quick way of finding the coefficients in an expression like $(ax^3+bx^2+cx+d)^3$?
We can raise a sum to the power of $n$ quickly and easily using Pascal's triangle, due to the binomial theorem:
$$(a+b)^n = \sum_{i=0}^n {n \choose i} a^i b^i$$
For sums of more than one term, we ...
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Mixture and Alligation:::
A solution contains alcohol and water in the ratio 3:1, 16 litres of
the Mixture is drawn off and 12 litres of water is added.11 litres of
Mixture is replaced by 11 litres of water.The alcohol and ...
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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 ...
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How to multiply any number with decimal number [closed]
I can't remember multiplication tables, is there any math trick for multiplication?
