# Tagged Questions

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.

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### How to add up multiple intervals and check if they complete a known interval?

If my initial/known interval is [0,20) or length 19 And the 3 intervals are: [0,5), ...
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### Why Can't We Divide by Zero? [duplicate]

It always seemed to me any number X divided by zero would simply be X, since we're dividing by nothing, so then the original number wouldn't be altered. Why isn't this true? Can this ever be true?
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### Divisibility Problem: How can I solve this?

Suppose that $a,b,q,r$ are any integers such that $b > 0$ and $a = bq + r$, with $0\le r<b$, and suppose $b|a$. Must it be the case that $r = 0$? Justify your answer. Can anyone please let me ...
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### Solving this inequality

Question: Solve: $$\frac{5x-6}{x+6}<1$$ My attempt: $$\frac{5x-6-x-6}{x+6}<0$$ $$\Rightarrow \frac{4x-12}{x+6}<0$$ $$\Rightarrow \frac{x-3}{x+6}<0$$ $$\Rightarrow (x-3)(x+6) < 0$$...
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### How do you work out $\sqrt[4]{16^3}$ without a calculator.

$$\sqrt[4]{16^3}$$ I just don't know what to do when I get to $4096$. The original equation was $16^{3/4}$.
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### Isn't this wrong?

This worksheet This question: $$w^2 - w \leq 0$$ This answer: $$(-\infty, -1] \cup [0, 1]$$ Isn't this wrong ? At $w = -2$, it becomes: $(-2)^2 - (-2)$, which is $4 + 2$, which is $\geq 0$. But ...
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### How to solve this inequality question without manual checking?

Question: Find the maximum integral value which satisfies: $$\frac{x-2}{x^2-9}<0$$ I know that this means either of the following: #1. $x-2<0$ and $x^2-9>0$. Implies that $x \in (3, 2)$...
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### How much zeros has the number $1000!$ at the end?

I know that it depends of the factors of five and two. But the number is too long to figure how much factos of five and two there are. Any hints?
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### Operations in the exterior algebra. Multiplication in the direct sum of rings.

Let the exterior algebra $\Lambda(V)$ of a vector space $V$ over a field $K$ be the direct sum of the exterior powers $\Lambda^k(V),\quad k\in\overline{0,n}$. Then an element $x\in\Lambda(V)$ has the ...
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### Identity and zero in a Ring

Given a ring R with with addition and multiplication on $\mathbb Z$ defined by $a\oplus b = a+b-4$ and $a\otimes b = ab-4a-4b+20$, what is the zero and what is the identity? My thoughts: are they ...
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### Identifying special arithmetic

$R$ is a ring of even integers with special rules for multiplication and addition. Suppose that $f : Z \to R$ is an isomorphism that is defined by $f(x) = 2x+4$. What are the special rules for ...
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Ok, there's no problem in defining a binomial coefficient the way it this: $$\binom {a} {b} = \frac{a!}{b!(a-b)!}$$ I can also prove to myself that if I have $n$ elements, like: $\{a_1, a_2, \ldots, ... 1answer 86 views ### Convert Degrees of Latitude to Feet I need to check this formula I have to compute the distance of a point with latitude$lat$from the equator: $$\mathrm{feet} = \mathrm{lat} * 10000 \times 3280 / 90$$ Example: A point at$40....
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How do I go about finding the hexadecimal sum of 9A88 and 4AF6? I know how to find the decimal sum, but have little understanding of how to find the sum of a hexadecimals?
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### what are the units for a rate of return?

My understanding of "rate" is more physics oriented. For example, distance/time is understandable for me and something I can explain. However, a rate of return: "The return, or rate of return, can ...
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### $n$ = sum of numbers in progression $2^n$

I have looked everywhere and cannot find an answer. If the answer already exists, please refer me to it. I have a number $n$ and need to know the formula to find the numbers in the series $2^n$ that ...
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### Performing mental arithmetic without a base

I'm sure many of you will be aware of the amazing ability for some people to 'see' mathematical calculations as shapes, and to perform mental arithmetic with very little conscious effort, simply by ...
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### Divisibility of the sum of a number and its 'mirror'

I came across the following puzzling problem in an elementary algebra textbook: Problem. Prove that the sum of a two-figure number and the number written with the same digits in the reverse order ...
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### Trivial sequence: $32,21,14,\dots$

My little brother (third grade) asked me for help with this math problem on his homework, which was: Find the next number in the sequence $32,21,14,\dots$ I was not able to see a trivial ...
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### Arithmetic and Algebra exercises on latex source code.

I´m currently writing a little book for two student that I teach. The book covers school arithmetics and algebra, and it include theory and examples. Since I don´t have time to prepare a good sets of ...
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### I need help with percent change and percent difference

I would love if someone were to clear up my confusion. Who is right and what are these things telling me? I'm trying to show the percent change in some software performance times here at work, and I'...