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
35 views

What is the remainder of an n-th root called?

I feel like there should be a better word than remainder, but I don't know it. What do you call the thing that's left over when performing an $n$-th root? For example, $\sqrt[3]{29}$ is $3$ with 2 ...
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1answer
33 views

Proof of Specific Distribute Property for Vectors

Wasn't really able to find something here or on Google which answers my question. I am asked to prove the distributive property of vectors such that $$(r + s) * \vec{a} = r * \vec{a} + s * \vec{a}$$ ...
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1answer
187 views

Is there an example of nonassociative arithmetic addition?

Are there any clear, accepted examples of operations that are appropriately defined as "addition" but are not associative? Although I can find references to abstract discussions of arithmetic systems ...
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1answer
65 views

A strain of bacteria doubles every 14 h. If there are 100 bacteria cells to start with in a colony, how many will there be in 7 days?

A strain of bacteria doubles every $14$ h. If there are $100$ bacteria cells to start with in a colony, how many will there be in $7$ days? This is a sequence question. My answer: We start with ...
6
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1answer
89 views

Why is multiplication treated differently to addition?

I am a grade 11 student in South Africa. Just so you know, this is my first time posting here. My understanding is that multiplication is simply a shorter way of writing addition problems. E.g. ...
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2answers
1k views

How do we find out angle from x & y coordinates?

I found the following sentence. To find the angle you use the arctangent function like this, angle $=\tan^{-1}\left(\frac{y}{x}\right)$. But I am curious, is this the only way to know the angle? ...
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2answers
272 views

How to find out the greater number from $15^{1/20}$ and $20^{1/15}$?

I have two numbers $15^{\frac{1}{20}}$ & $20^{\frac{1}{15}}$. How to find out the greater number out of above two? I am in 12th grade. Thanks for help!
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2answers
207 views

Paradox - minus one equals one using square roots [duplicate]

I was looking on Howard Eves's book "An Introduction to the History of Mathematics" and I stumbled upon a demonstration on how $-1 = 1$. The demonstration follows: $$ \sqrt{-1} = \sqrt{-1} $$ $$ ...
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3answers
20 views

Regarding the simplest multiplying methods

I got something method like the simplest multiplying methods when I googling. If you had a number, like 123.456 and you wanted to multiply by 100 you'd just ... Move the decimal point to the ...
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0answers
44 views

Modulus to a range -x to x

I'm trying to solve positions of the planets as described in this paper. Step 3 of the computation starts with "Modulus the mean anomaly so that $-180^o \lt M \lt +180^o$." I understand what that ...
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5answers
170 views

How does one explain addition?

What is $1 + 2$? The question may seem dumb but how can one prove the answer? I heard there is a proof but don't know where to find it so please help. Thanks in advance.
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1answer
194 views

Multiplication and binary xor

I have to prove one thing that combines logical xor and arithmetical sum of binary representation of some numbers. Could you direct me what can I read on this topic? Specifically, I need to prove ...
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2answers
57 views

Why negative times negative is positive? [duplicate]

I know that many people would say I don't even know this. But I know it very well that negative × neagtive = positive. But I don't know Why? So kindly give a logical answers.
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0answers
41 views

Question about the sums of the entries in an infinite array

Imagine you have an infinite array of numbers. You can divide this array in columns with labels of opposite signs that go to infinity and negative infinity starting from the center of the array. Each ...
2
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1answer
71 views

How can one make sense out of a negative number?

We know that if you have 3 apples and somebody gives you 4 apples, you then have 7 apples but then if we deal with negative numbers and we have -3 apples and somebody gives us -4 apples, things can ...
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2answers
27 views

Problem in substitution

I have a very stupid question, it seems that I've forgotten most of my math and can't figure this out. Considering the following, ...
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1answer
280 views

Representing predicate logic as arithmetic

Summary Since the below is quite long, I thought I'd add this summary. Given the following: A statement in proposition logic can be converted to an arithmetic expression over the integers modulo ...
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2answers
75 views

Why do Smith numbers have to be composite numbers?

As you may know, a Smith number is a number that if all the digits are added together that answer is equal to the sum of its prime factors' digits. Why are 2 and 3 not Smith numbers?
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5answers
244 views

What is the remainder when $213987654213473846989272654857367287454572836418486364$ is divided by $48$? [closed]

Can it be done by hand i.e. to find the remainder when $213987654213473846989272654857367287454572836418486364$ is divided by $48$?
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1answer
4k views

brain teaser that has me totally confused [closed]

A man stole \$50 from a shop owner. He came back and used the same \$50 to purchase a bread that cost \$40 and received \$10 change. How much money in all did the shop owner lose?
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1answer
28 views

Tools for dealing with a divisibility problem with powers of 2 and 3?

I'm trying to solve an equation with congruences: $$ \sum_{i=1}^{N}2^{\sum_{j=1}^{i} n_j}3^{N-i} \equiv 0 \; (\text{mod} \; 2^{\sum_{j=1}^{N}}-3^N) $$ The unpacked version (assuming ...
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4answers
52 views

How to determine the number removed from the list [duplicate]

One number is removed from a set of integers from 1 to n,the average of the remaining numbers is $\large{\frac{163}{4}}$. Which number was removed? I tried to find the mean of ...
2
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1answer
58 views

Last Value of an Arithmetic Sequence of a Particular Sum

I was able to derive the formula for summing consecutive integers: sum $= \dfrac{n(n + 1)}{2} \Longrightarrow n = 4$, sum $= 10$ Nothing difficult there, but then I would like a formula for giving ...
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0answers
33 views

Uniqueness of finite continued fractions expansions

Under wich condition on $a_0, \dots , a_n$ the continued fraction expansion of a positive rational number $$r= a_0- \frac{1}{ \ddots -\frac{1}{a_n}}$$ is unique?
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0answers
112 views

How to find the nth term of the merged Mutiplication Table of two numbers?

Given two numbers $x$ and $y$ both $\le 2000$ and $x\le y$. Multiplication table is build of $x$ and $y$ and merged and terms arranged in ascending order, removing the duplicates and finally, need to ...
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1answer
41 views

$|x+2|\ge 0.001$ at wolfram alpha [closed]

Shouldn't it be $x\ge -1.999$ and $x\le -2.001$? Why wolfram alpha says $x>-1.999$? http://www.wolframalpha.com/input/?i=|x%2B2|%3E%3D0.001 Sorry by the stupid question
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0answers
44 views

upper and lower bounds related to $\sqrt[3]{a^3 + b}$ with $b \ll a$

We can use Taylor series to approximate $a + \frac{b}{3a}\approx \sqrt[3]{a^3 + b}$ with $b \ll a$. However, what are precise upper and lower bounds for this quantity? $$ a + \frac{b}{3a^2} < ...
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2answers
105 views

Is there a mathematical term for three orders of magnitude?

I've been playing this github game for a while called Swarm Simulator. I like it a lot and there are a bunch of other simulators going around either in-browser like Swarm or iOS apps, etc. These ...
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2answers
60 views

Interesting Array of Integers with Strange Pattern

I was experimenting and I found this pattern: Start with an (infinite) array with top row with all ones, and leftmost two columns also all ones. $$ \begin{matrix} 1 & 1 & 1 ...
0
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1answer
43 views

Interpreting predicate formulas in the structure of arithmetic

Given two formulas a) $(\forall x)(\phi(x)\rightarrow\varphi)\;\;\;\;\;\;$ b)$(\forall x)\phi(x)\rightarrow\varphi\;\;\;\;\;$ Let $\;\mathbb{S}=(\mathbb{N},+,\times,\le,0,S)$ (where $S$ stands for ...
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1answer
138 views

A runs 7/4 times as fast as B. If A gives B a start of 84m, how far must the winning post be…?

The problem statement in the book is: $A$ runs $7/4$ times as fast as $B$. If $A$ gives $B$ a start of $84$m, how far must the winning post be so that $A$ and $B$ might reach it at the same time? ...
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0answers
378 views

The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. How much a day does the clock gain?

The question in the textbook is: The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. How much a day does the clock gain? My method: The correct ...
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8answers
2k views

Compare two powers of numbers without common divisor

Which of the numbers $2^{60}$ and $3^{43}$ is greater? There is no common divisor and it must be done without a calculator.
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1answer
43 views

$ P\mid n \implies \exists (a,b)\in\mathbb{Z}^2 \quad an+b(p-1)=1$

show that $$ p\mid n \implies \exists (a,b)\in\mathbb{Z}^2 \quad an+b(p-1)=1$$ with p is the least prime dividing my attempts Indeed, Let $d=n\wedge (p-1)=gcd(n,p-1)$ and we try to show ...
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1answer
25 views

change from recurrence relation to iterative approach

An investment of 1,000,000 receives a 10% bonus every year. A total of $48,000 is withdrawn from the investment each year. Assume that you have got the 10% bonus before you withdraw each year. I just ...
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3answers
3k views

Finding the square root of a big number, like 676? [closed]

I am having trouble understanding and finding the square roots of large numbers. How would I go about finding this number efficiently?
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2answers
32 views

Four lots of sums using only $4$

You need to make exactly four sums using only the number $4$ each time. For example, $4+4+4+4 = 16$ or $4×4-4÷4 = 3$. You can use $+ - × ÷$, square, or square root. Another example: $4^2 × 4 + 4 ÷ ...
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3answers
153 views

Why does $\frac{49}{64}\cos^2 \theta + \cos^2 \theta$ equal $\frac{113}{64}\cos^2 \theta $?

I have an example: $$ \frac{49}{64}\cos^2 \theta + \cos^2 \theta = 1 $$ Then what happens next: $$ \frac{113}{64}\cos^2 \theta = 1 $$ Where has the other cosine disappeared to? What operation ...
2
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2answers
71 views

decimal to fractions

When being asked how to solve the Arithmetic Means of 8, 7, 7, 5, 3, 2, and 2, I understand that adding these numbers then dividing by 7 (the amount of numbers) gives me the decimal 4.85714... But ...
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2answers
105 views

There is a number if you multiply it by 6 first, and then subtract 7 from the result, you get 65. what's the number? [closed]

I've been stuck on this question for a while can someone help me thanks :)
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1answer
302 views

IEEE-754 Format Conversion

Represent 11.0011 x 2^10 using the IEEE-754 standard for 32-bit floating point representation. 0-Sign Bit 10001010-Exponent 1001100000000000000000-Mantissa Is this answer is correct ? I am bit ...
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4answers
3k views

How to position negative sign of fraction

For example we have: $$ \frac{-1}{2} $$ Does this mean that only the numerator of the fraction is negative? Can we put it like this? $$ -\frac{1}{2} $$ Does this means that the whole fraction is ...
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2answers
155 views

How do we add numbers?

How do we compute sums in general? How can we tell the result of the operation $A+B$? Even when we talk about very basic numbers like $\Bbb{N}$ I find it hard to understand the algorithm we use to ...
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2answers
66 views

Alternating Sum of Cubes [closed]

How is it possible to evaluate: $$\sum_{k=1}^n{((-1)^{n-k}\cdot k^3)}=n^3 - (n-1)^3 + (n - 2)^3 - \cdots \pm 1^3$$ The fact that there is the $\pm$ at the end makes it difficult.
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3answers
65 views

find nth term of a few sequences

first $4,-1,-11,-26,-46$ I found a recurrence relation of $U_{n-1} - 5(n-1)$ but I don't know how to find an explicit nth term formula second $0,3,8,15,24$ It goes up by $+3,+5,+7,+9$ I'm not sure ...
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2answers
215 views

Find $x;y$ such that: $\frac{x^2+y^3}{xy-1} \in \mathbb{Z}$ [closed]

Let $x,y \in \mathbb{Z}$ such that: $$\frac{x^2+y^3}{xy-1} \in \mathbb{Z}$$ Find $x,y$ I don't have any ideas about this problem.
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1answer
48 views

Speeding up integer division if only certain bits in result are needed

Let's say I need to divide two integers $x$ and $y$, but I only care about the lowest 8 bits of the answer, i.e. I'm calculating: $$r = \frac{x}{y}\,\,\%\,\,256$$where % is the modulus operator. Is ...
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1answer
32 views

Subtraction of trigonometric functions

I was working on a problem booklet and came across the following equation. $$\sqrt2\sin(2x)-\cos(2x)=\sqrt3\sin(2x-a)$$ $a \in \mathbb{R}$ is a specific value that I'm supposed to find, but I don't ...
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1answer
24 views

Find the lower and upper bounds

I'm stuck with this question: $-2 < x < 6$ and $-4<y<-2$ What are the bounds of $x^2-y^2$? I thought that they are $(-2)^2-(-4)^2 = -12$ and $6^2-(-2)^2 = 32$, but apparently they are ...
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1answer
128 views

Why is $\sqrt{X}\times\sqrt{X}=X$?

Today I was solving the limit $(\ln(x))/(2*(x^{1/2})$ but then faced the step after applying the derivation that ended up with $(1/x)/(1/x^{1/2})$ and the result of that was $1/x^{1/2}$. When I asked ...