Questions tagged [arithmetic]
Questions on basic arithmetic involving numerical quantities only. Questions involving variable values (other than the result of the operation) should be placed under the (algebra-precalculus) tag. Questions about number theory (sometimes called "arithmetic") should not use this tag and should instead use (number-theory) or (elementary-number-theory).
6,383 questions
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How do we pick how many decimals to use when solving problems? [closed]
I was working on an exercise from a chemistry textbook which was about an application of the osmotic pressure formula.
When I checked the solution the answer give was 62ドル.05$ while I was getting as a ...
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In binary subtraction, is it possible to apply the mathematical notion of borrowing expecting a result equivalent to a two's complement calculation?
TL;DR. Question in a very short fashion could be:
In subtraction of two binary numbers, minuend smaller than subtrahend
and using just (school) borrowing method (not two's complement, etc), how do ...
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I found a way to multiply numbers, is this a new method or someone else had already found this?
I recently noticed a fast way to multiply two numbers near 50ドル$.
Let the numbers be $a$ and $b$ both close to 50ドル$.
Define
$$x = 50−a,\ y =50−b$$
(so $x,y$ are the "deficiencies" from 50ドル$ )
My ...
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Can lasso selection in Plotly interactive plots describe rational point density?
I am exploring the number of rational points on $\mathbb{P}^2(\mathbb{})$ with bounded height, for example, height less than or equal to 32. More specifically, I am calculating
$$N_{\mathbb{P^2}}(B) = ...
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What is the minimum number of 114154ドル$'s required to construct an expression—using only parentheses and the four basic operators—that equals 1919810? [closed]
Let $x=114514,ドル What is the minimum number of $x$'s required to construct an expression—using only parentheses and the four basic operators—that equals 1919810?
So far, we have a 28ドル$-number solution ...
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5
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394
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Concrete Definition for a Ratio
I had a question about ratios. I couldn't seem to find a rigorous definition on them. I understand the concept of fractions being numbers of the form a/b where a is divided by b (or a multiplied by 1/...
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What is the algorithm for a square root in balanced ternary?
I'm confused by wikipedia's explanation of balanced ternary's algorithm for the square root. They only show a formula I don't know how to generalize to more digits than 2, and the example given doesn'...
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What happens to $\sf PA$ if we remove the schema of Induction and replace it with a rule version?
Peano Arithmetic ($\sf PA$) differs from Robinson Arithmetic ($\sf Q$) only in that the former includes the axiom schema of Induction:
$\forall x((\phi(0) \land \forall y (A(y) \to A(s(y)))) \to A(x))$...
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About sequences and common difference?
I've been working on sequences lately, and I know that to find the $n$-th value of the sequence "$a$" you multiply $n-1$ times $d$ and that will give you the answer. From what I understand ...
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4
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Is $x^{1/2}$ really the same as $\sqrt{x}$?
This is a confusion I have been struggling with ever since I got to know about how $\sqrt{x^2}$ is the same as $|x|$.
So, what is $x^{1/2}$ then? Say, for example, I want to know the values of $\sqrt{...
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2
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Does a double negative signify subtraction or negation?
Just to clarify, I already know that (-1)(-x)=0-(-x). In other words, interpreting -(-x) as either negating (flipping the sign) of a negative or subtracting a negative seems valid either way. However, ...
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Different approaches to $p$-typical Witt vectors
When looking at different approaches of defining addition and multiplication in the ring of Witt vectors $W(A)$ of a ring $A,ドル I came up with the following question.
So what I first learned was that ...
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1
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Why do we draw one fewer line than the number of bars in area or bar models?
I’m learning multiplication and fractions using visual methods like bar models or area models.
Something confuses me:
If I want to divide a rectangle into 4 equal vertical bars, I draw 3 vertical ...
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1
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81
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Fast reduction modulo some power
To reduce a number $x$ by $m^k,ドル one could first compute the power $m^k,ドル then the modulo operation by this power.
Is there a better way, taking advantage of the fact that the modulo argument is a ...
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Why does this division trick work?
My teacher told me a trick of divisibility and when I asked him "why does it work?" He didn't have any answer. The trick is for divisibility by numbers that are 1 less than a multiple of 10. ...