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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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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1answer
49 views

How do people do calculation in mind for large numbers? [closed]

I can easily tell the answer of the following questions in few seconds: 2500+2500 2500x2 5000/5 These are easy, because of small numbers. But how do people do calculation of large numbers in mind ...
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2answers
76 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 ...
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0answers
24 views

Approximating values while calculating percentage changes

At times, in certain types of data interpretation questions that usually get asked in aptitude examinations, some techniques are employed to cut time on calculation and get a near perfect answer. One ...
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0answers
50 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 ...
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4answers
214 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 ...
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1answer
171 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 ...
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2answers
80 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
55 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
91 views

This quantity (see question) will end with how many zeros?

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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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 ...
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2answers
84 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 ...
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3answers
185 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
131 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*...
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4answers
183 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. ...
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1answer
70 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 ...
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1answer
252 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 ...
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1answer
202 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 ...
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1answer
167 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
500 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 ...
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3answers
1k 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
59 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: $$8/2=4$$ ...
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2answers
48 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 $\frac{3}{200000}$, ...
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3answers
149 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
984 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
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5answers
420 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
74 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
687 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! ...
41
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10answers
5k 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 ...
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2answers
696 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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5answers
828 views

Let $\frac{A}{B}=\frac{B}{C}=\frac{C}{D}=\frac{3}{4}$. If $B$ gets Rs $308$ less than $D$, find the individual amount with $A$, $B$, $C$, and $D$.

Some amount is divided among $A$, $B$, $C$, and $D$ such that $\frac{A}{B}=\frac{B}{C}=\frac{C}{D}=\frac{3}{4}$. If $B$ gets Rs $308$ less than $D$, find the individual amount with $A$, $B$, $C$, and $...
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0answers
23 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 ...
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3answers
228 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 ...
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4answers
62 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?...
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2answers
75 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 ...
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2answers
183 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
120 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 ...
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2answers
193 views

Simplifying this fraction in a different base

Note: I would appreciate a solution that DOES NOT convert back to base 10. How would one simplify $\frac{43}{70}_8$? I assume, like in decimal, I must recognize a common factor and divide by that ...
3
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1answer
207 views

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 ...
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3answers
519 views

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?
2
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1answer
115 views

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 ...
4
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5answers
508 views

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}} $
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1answer
57 views

Is there a simple way of computing when $a^n=b^m$

I don't want exact equality just close enough to be useful in approximation. i.e. $2^{10 }= 10^3$ is very useful and used daily for an approximation. Is there a do this efficiently? Is there a way ...
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2answers
1k views

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(...
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1answer
137 views

How can I mentally calculate $\cos(x), x∈(0.7, 1.2)$

I'm trying to learn how to calculate trig functions in my head. I'm planning on learning $\cos(x), x∈[0,π/2]$ and then using symmetry to calculate the others. I think the quadratic Maclaurin series ...
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3answers
3k views

Calculating trigonometric function values mentally

This may sound dumb, but does such a way exist to mentally (and quickly) determine the values of trigonometric functions such as $\sin(47^\circ)$ and so forth--quickly being a mere matter of seconds? ...
4
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1answer
637 views

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 ...
2
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3answers
2k views

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 ...
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1answer
65 views

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
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0answers
82 views

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, ...