Questions tagged [mental-arithmetic]
Mental arithmetic comprises arithmetical calculations using only the human brain, with no help from calculators, computers, or pen and paper.
104
questions
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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, ...
1
vote
1answer
113 views
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 $...
1
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1answer
72 views
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 ...
3
votes
4answers
125 views
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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0answers
8 views
Average and growth rate of multiple observations
A really simple question about averages, and the pitfalls of calculating them wrongly.
We have observations between 2 periods: a and b periods. In Each period there are two miles of per gallon for ...
2
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5answers
69 views
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 ...
0
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0answers
67 views
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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1answer
41 views
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!
6
votes
1answer
180 views
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....
3
votes
9answers
291 views
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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1answer
75 views
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 ...
0
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0answers
256 views
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,...
0
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1answer
64 views
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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1answer
65 views
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 ...
2
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2answers
295 views
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 ...
1
vote
1answer
86 views
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 ...
0
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3answers
48 views
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 ...
1
vote
2answers
93 views
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 ...
1
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0answers
69 views
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 ...
4
votes
4answers
427 views
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 ...
0
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1answer
543 views
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 ...
0
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2answers
146 views
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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2answers
110 views
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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2answers
201 views
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 ...
29
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3answers
3k views
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 ...
0
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2answers
328 views
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 ...
2
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3answers
236 views
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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3answers
152 views
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*...
0
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4answers
237 views
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. ...
2
votes
1answer
81 views
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 ...
3
votes
2answers
981 views
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 ...
7
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1answer
292 views
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 ...
0
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1answer
236 views
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 ...
4
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6answers
542 views
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 ...
6
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3answers
3k views
(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 ...
2
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2answers
65 views
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$$ ...
1
vote
2answers
51 views
Approximate this fraction (simple arithmetic)
If I have
$1.5\cdot10^{-5}=\frac{1.5}{10^5}$
, how can I rewrite (approximate) this fraction as
$$
\approx \frac{1}{66.7\cdot 10^3}\quad ?
$$
My calculator gives the exact answer $\frac{3}{200000}$, ...
5
votes
3answers
170 views
Is there a quick way of finding the coefficients in an expression like $(ax^3+bx^2+cx+d)^3$?
We can raise a sum to the power of $n$ quickly and easily using Pascal's triangle, due to the binomial theorem:
$$(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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1answer
2k views
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 ...
3
votes
5answers
888 views
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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2answers
85 views
How to multiply any number with decimal number [closed]
I can't remember multiplication tables, is there any math trick for multiplication?
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2answers
1k views
Multiplying very small numbers without the use of a calculator
As part of my college course I have to sit some math exams and I cannot use a calculator. The problem is I suck at maths with a calculator not to mind how bad I am at it without using a calculator!
...
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9answers
6k views
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 ...
2
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2answers
1k views
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 ...
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0answers
34 views
Pandigital strings that end in $0$ and available to mental arithmetic?
I'm looking for a sequence that includes every number from $1$-$9$ and then ends with $0$. It should look random on first glance (or as random as possible given the mental arithmetic constraint) but ...
0
votes
3answers
417 views
Mentally calculate the first 9 terms of this Fibonacci sequence.
There was a question in a mental math test and it expected me to calculate the first 9 terms of the following Fibonacci sequence (Note that this is how the problem was exactly given.):
The sum of ...
0
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4answers
80 views
Problems on Trains
A train Leaves station $x$ at $5 AM$ and reaches station $y$ at $9AM$. Another train leaves station $y$ at $7AM$ and reaches station $x$ at $10.30 AM$ . At what time do the two trains cross each other?...
1
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2answers
89 views
Mental Arithmetic Problems
The speed of a Motor - Boat is that of the current of water as 36:5.The boat goes along with the current in 5 hours 10 Minutes,It will Come Back in which time?
I have Tried:
Speed of Motor : Speed of ...
1
vote
3answers
283 views
Divison In Mental ArithMatic
The nearest number to $99548$ which is divisible by $687$ is?
How can I find the answer quickly, is there any short cut to check if a number is divisible by $687$?
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1answer
148 views
Boats and Streams [closed]
A boat can travel with a speed of $13$ km/hr in still water. If the speed of the stream is $4$ km/hr, find the time taken by the boat to go $68$ km downstream.
Can you Explain the Difference between ...
