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.

107 questions
1
vote
0 answers

Why is multiplication commutative - intuitive explanation

While I know that both addition and multiplication are commutative operations, I can easily visualize that, e.g. 3 + 4 = 4 + 3 = 7 by thinking of seven objects in a row and separating them into two heaps of three and four objects, respectively. Now…
user54031
1
vote
1 answer

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. $23 \times 7$, $39 \times 3$ and so on. Ask based on…
1
vote
4 answers

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, when I need to talk with my British friends…
1
vote
1 answer

prove that $5<\sqrt{5}+\sqrt[3]{5}+\sqrt[4]{5}$

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 $$f(x)=x-\sqrt{x}+\sqrt[3]{x}+\sqrt[4]{x}<0$$ does…
Albus Dumbledore
  • 11,548
  • 2
  • 10
  • 40
1
vote
1 answer

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 following: $2.7^4 = 53.1441 > 53$. $2.7^8 > 53^2 = 2809$. $e^{10}…
tchappy ha
  • 6,211
  • 3
  • 11
  • 23
1
vote
3 answers

Mental Math - Estimating Logarithms

How can we estimate logarithms with different bases? Take $\log_2 10$ ($1\over\log_{10}2$$\approx3.32192809$) for example. If we convert $10$ to binary, we get $1010_2$. So $\log_21010_2$ can clearly be estimated at between $3$ and $4$ because…
Justin
  • 2,447
  • 4
  • 18
  • 38
1
vote
1 answer

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 Calculate the number of digits in a product of large…
1
vote
1 answer

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 a calculator, and preferably without relying on…
mr-matt
  • 201
  • 2
  • 6
1
vote
2 answers

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 advance.
user649955
1
vote
0 answers

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 these on the spot? For 1), my consideration was to…
user107224
  • 2,128
  • 12
  • 22
1
vote
3 answers

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: $3^{3.6}=e^{3.6ln(3)}=e^{3.6*1.098} \approx e^{3.6*1.1}=e^{3.96} \approx e^4=54.5$
astudentofmaths
  • 666
  • 5
  • 19
1
vote
2 answers

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 $\frac{3}{200000}$, but how to approximate it as $\approx…
Donsert
  • 451
  • 3
  • 11
1
vote
0 answers

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 have some pattern I can explain, which I can also…
Tarbox
  • 11
  • 1
1
vote
2 answers

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 Water = 36:5 Relative downstream time along with…
1
vote
3 answers

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 $687$?