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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1answer
23 views

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), ...
-1
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2answers
146 views

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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2answers
34 views

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 ...
2
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3answers
53 views

Solving this inequality

Question: Solve: $$\frac{5x-6}{x+6}<1$$ My attempt: $$\frac{5x-6-x-6}{x+6}<0$$ $$\Rightarrow \frac{4x-12}{x+6}<0$$ $$\Rightarrow \frac{x-3}{x+6}<0$$ $$\Rightarrow (x-3)(x+6) < 0$$...
2
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4answers
308 views

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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2answers
60 views

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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3answers
58 views

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 $x \in (3, 2)$...
2
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6answers
207 views

Why does $\frac{4}{2} = \frac{2}{1}$?

I take for granted that $\frac{4}{2} = \frac{2}{1}$. Today, I thought about why it must be the case. My best answers amounted to $\frac{4}{2}=2$ and $\frac{2}{1}=2$; therefore $\frac{4}{2}=\frac{2}{...
2
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1answer
77 views

Prove this simple arithmetic relation

Prove that if $$a \mid b$$ and $$a \mid c$$ then $$a \mid bx+cy$$ for any integers $x$ and $y$. Here's my proof: $$b = ak$$ $$c = am$$ $$bx+cy = akx+amy = a(kx+my)$$ Notice that $kx+my$ is an ...
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3answers
736 views

Which is greater: $1000^{1000}$ or $1001^{999}$

Question: Find the greater number: $1000^{1000}$ or $1001^{999}$ My Attempt: I know that: $(a+b)^n \geq a^n + a^{n-1}bn$. Thus, $(1+999)^{1000} \geq 999001$ And $(1+1000)^{999} \geq 999001$...
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3answers
123 views

Generate numbers that add up to X

I have isolated the algorithm of a keygenme, but I am running into difficulty with creating the keygen. The key has a length of seven digits, and the sum of each of the digits in the key must be ...
3
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1answer
61 views

Prove the sequences $\lfloor \alpha n\rfloor $ and $\lfloor \beta n\rfloor $ are disjoint

Here is another problem from a problem set that I can't solve. Let $\alpha$ and $\beta$ be irrational positive numbers such that $\frac{1}{\alpha}+\frac{1}{\beta}=1$ Prove that the sets $\{ \...
2
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5answers
161 views

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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1answer
189 views

Solution of $\large\binom{x}{n}+\binom{y}{n}=\binom{z}{n}$ with $n\geq 3$

I found this question in an old problem set. There's no hint or solution mentioned. For $n \geq 3$, prove or disprove the existence of $(x,y,z) \in \mathbb N^3, \large\binom{x}{n}+\binom{y}{n}=\...
2
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2answers
168 views

The number $25!$ has exactly 7 trailing zeros, true or false?

I don't know how to determine it... any hints?
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2answers
43 views

Solving two systems with two unknown?

Let's say if we are giving the following two equations: $$ 1= X/(X^2 +Y^2) $$ $$ 2= Y/(X^2 +Y^2) $$ How are we going to solve for X and Y [ by HAND ] ? Why would Summing the squares of the two ...
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1answer
51 views

If $p=1\cdot 3 \cdot 5 \cdot 7 \cdot 9 \cdot … \cdot 2011$, then the units digit of $p$ is five

I know there is a $5$ on the sequence, but i don't know how and why his presence leads to the final units digit of the product.
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1answer
41 views

My small theory…

It is given that 'a,b,c' are whole nos. Now 'a' is an odd no. while 'b' is an even no. Prove that:- a/b + c = x where 'x' is a fraction, equal to 'n/d' where n is an odd no. and d is an even no. and ...
2
votes
0answers
191 views

Relationship between two elements of two matrices with two numbers are not elements of the two matrices

I have two matrices, $$A= \left[ \begin{matrix} 5 & 10 & 15 & \cdots \\ 17 & 28 & 39 & \cdots \\ 35 & 52 & 69 & \cdots \\ \vdots & \vdots & \vdots & \...
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1answer
73 views

The function $f(t)=2+\sin(t)+\sin(t\sqrt2)$

The function $f$ defined on $\mathbb{R}$ by $$f(t)=2+\sin(t)+\sin(t\sqrt2)$$ can never reach $0$. Can we find some sequence $(t_n)_{n\geq0}$ such that $$\lim_{n \to \infty}f(t_n)=0 \ \ \ ?$$ Or in ...
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2answers
58 views

Does $\frac{8k-1}{4}$ belongs to $\mathbb{Z}$?

Does $\frac{8k-1}{4}$ belongs to $\mathbb{Z}$ for some $k\in \mathbb{Z}$ ? or we can prove that this never belongs to $\mathbb{Z}$ ?
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1answer
228 views

Grade School Math: Bad math, or new meanings?

I came across this online quiz discussing the new Common Core education standards, and it all seemed pretty reasonable, until I came across this question: In the number below, how many times ...
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1answer
347 views

Comparing powers with different bases without logarithms

I want to compare : $17^{31}$ and $31^{17}$ , this is a solution but I want another one and without using logarithms, only using the fact that $17=16+1=(2^4)+1$ and $31=(2^5)-1$ how could it ...
0
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1answer
30 views

Can we define the equality as $a=b$ iff $\frac{a}{b}=1$?

Well, The title i guess is enough to get what i'm looking for: I'm wondering if we can define equality of let's say $a$ and $b$ that the devision of $a$ over $b$ or $b$ over $a$ is $1$ : $$a=b \...
4
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2answers
155 views

Why is the language of arithmetic usually $(+, \cdot, 0, s)$, not $(+, \cdot, 0, 1)$?

The formalized theory of arithmetic has usually $(+, \cdot, 0, s)$ as its language. However, from what we usually do in ring theory, it seems natural to use $(+, \cdot, 0, 1)$ as the language of ...
1
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1answer
18 views

Ratio problem of a beverage

I'm given the following data on a problem: A company wants to produce a beverage AZ which is a mixture of beverage A and Z. Cost/liter of A = 3.00$ Cost/liter of Z = 2.00$ I'm asked to determine ...
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2answers
34 views

Decimal to days hours

I have $10.73$ and $37.27$ days and I need to convert both to the days:hours format but I'm getting confused mid way. Taking $10.73$ as example I can do $10.73\times24$ to get $257.52$ hours but how ...
8
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1answer
69 views

Existence of root of a polynomial over $\mathbb F_p$.

I came accross the following question and I can't find an easy proof of this fact : Let $p\geq 17$ be a prime number such that $p\equiv 1 \pmod 4$. Show that for any $z\in \mathbb F_p\backslash\{0\}...
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1answer
89 views

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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3answers
49 views

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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2answers
26 views

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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3answers
1k views

Proof that the combination formula actually gives you the number of combinations

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, ...
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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....
2
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3answers
169 views

Hexadecimal Sum

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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4answers
75 views

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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2answers
47 views

$n$ = 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 ...
4
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1answer
305 views

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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2answers
162 views

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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3answers
174 views

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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0answers
74 views

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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2answers
72 views

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'...
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1answer
14 views

How can I find the price of house and the garden?

A house and a garden were bought for 1000$, the cost of the house was 5 times that of garden.Find the price given for each. (Actually I don't have any guidance book to solve this type of questions I ...
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3answers
3k views

number between 17 and 18, and has a rational square root

"number between 17 and 18, and has a rational square root" Is there even one? They all keep coming up irrational for me
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3answers
454 views

How do I solve this square root problem?

I need to solve the following problem: $$\frac{\sqrt{7+\sqrt{5}}}{\sqrt{7-\sqrt{5}}}=\,?$$
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2answers
353 views

Can an odd number $n$ divide $2^n-1$?

Clearly an even number $n$ cannot divide $2^{n}-1$, but about odd ones ? If $n$ is an odd prime this cannot happen neither since for an odd prime $p$ we have $2^p\equiv 2\pmod p$ and so $p$ cannot ...
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vote
1answer
58 views

decimal number to another base

There is a formula to convert a decimal number into another base. In below example, we use decimal 255 and we divide it by the base, which could be base 16 or base 2 or another. The first question ...
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2answers
40 views

A number which can be expressed as the sum of the squares of 6 odd integers

Which one of the numbers below can be expressed as the sum of the squares of 6 odd integers? $${1998,1996,2000,2002,2004}$$ I first started this by saying if $m$ is odd then $m = 2k+1$ so $$m^2 = 4k^...
0
votes
1answer
53 views

Rationalize a fraction using conjugates [duplicate]

I need help rationalizing the following expression using a conjugate: $$\dfrac{1}{\sqrt{3} + \sqrt{2}-\sqrt{5}}$$ I have had no luck rationalizing this expression with a conjugate of the denominator....
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2answers
51 views

Conjugates of radicals

I am not sure if one exists but is there a conjugate of the following: $$\sqrt{3}+\sqrt{2}-\sqrt{5}$$ I attempted it many times but can't get anything.
0
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1answer
266 views

What expression represents the total cost?

A customer calculated the cost of a new jacket , c, including a 7% sales tax, by multiplying 0.07 times the cost of the jacket and adding the product to the cost of the jacket. What is another way to ...