# 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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### 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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### 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?
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### 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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### 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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### 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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### 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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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?...