Questions on basic arithmetic, e.g. addition, subtraction, multiplication, division, powers, radicals, etc.

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3answers
32 views

Finding the remainder while dividing negative numbers? [on hold]

What is the remainder when dividing $-29$ by $8$?
4
votes
4answers
80 views

$(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3=24xyz$?

The question given is Show that $(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3=24xyz$. What I tried is suppose $a=(y+z-x),\ b=(z+x-y)$ and $c=(x+y-z)$ and then noted that $a+b+c=x+y+z$. So the ...
1
vote
2answers
77 views

How to show this fraction is not an integer

Suppose $k\geq 2$ is an integer. I want to show $$\frac{1+k+k(k-2)}{1+\frac{k-1}{k}+\frac{(-1-\sqrt{k-1} )^2}{k(k-2)}}$$ is not an integer. It is equal to $$\frac{(k-2) k (k^2-k+1)}{2 (k^2-2 ...
1
vote
6answers
129 views

If $a+b+c+d=1$ then why is the maximum value of $(a+1)(b+1)(c+1)(d+1)$ is ${\left(\frac{5}{4}\right)}^4$?

What I know is that for equations of type $x+y=8$, $xy$ attains its maximum value when $x=y$ and this can be proved by either solving the quadratic equation with completing the squares or finding the ...
4
votes
1answer
118 views

How do I find two integers - $x$ and $y$ - whose values satisfy the expression $x^2 + y^2 = z$, where $z$ is a perfect square?

I watched a YouTube video of an episode of Who Wants To Be A Millionaire?, in which a contestant was presented with a list of perfect squares. He was asked to choose the number that was also the sum ...
3
votes
2answers
75 views

If $\frac{(b−c)}{a} + \frac{(a+c)}{b} + \frac{(a−b)}{c}=1$ and $a-b+c \neq 0 $, then prove that $\frac 1a = \frac 1b + \frac 1c$

The question given is If $\dfrac{(b−c)}{a} + \dfrac{(a+c)}{b} + \dfrac{(a−b)}{c}=1$ and $a-b+c \neq 0 $ then prove that $\dfrac 1a = \dfrac 1b + \dfrac 1c$ I tried to take $abc$ on the right ...
-3
votes
1answer
41 views

Area of shadow and an object [on hold]

A $12 m \times 4 m$ rectangular roof is resting on four $4 m$ tall thin poles. Sunlight falls on the roof at an angle $45^\circ$ from the east, creating a shadow on the ground. What will be the area ...
1
vote
1answer
40 views

(Visual) Intuition: Division and complex fractions

When treating division as "groups of the numerator" (sorry, I don't know the technical term -- see image), why does a complex fraction in the denominator get added together to produce a 1 (number of ...
1
vote
2answers
29 views

Significant figures reduction of solution

I have a problem which has to be answered using two significant figures from the solution value. My solution value is x = 303.385789245434541 What should my answer be? Thanks
0
votes
1answer
16 views

Summing Bases and Comparing

Let $b$ be an integer greater than 2, and let $N_b = 1_b + 2_b + \cdots + 100_b$ (the sum contains all valid base $b$ numbers up to $100_b$). Compute the number of values of $b$ for which the sum of ...
2
votes
0answers
21 views

Determine if the members of a set can be made to equal a given number

Is there an easy way to determine if some combination of addition, subtraction, multiplication, and division will enable the numbers in a set to equal a given number? For example, if I have the ...
0
votes
1answer
64 views

Is multiplication commutative?

Say you have 3 apples and 2 oranges, and you want to multiply these two groups of fruits together to obtain a desired result, for instance: A. You want 3 apples for each orange, so you have 6 apples ...
-1
votes
0answers
32 views

Starting to proof… Fundamental Theorem of Arithmetic [duplicate]

I have the following: $$ m^2 = 3 n^2 \quad\text{where } m, n \in\mathbb{Z} \text{ and } n \neq 0 $$ I know how the Fundamental Theorem of Arithmetic works, every number is a unique product of ...
1
vote
1answer
42 views

Euler and probability - a $\zeta$-distributed random variable

Let's consider a random variable $X$ on $\mathbb{N}^*$ such as $\mathbb{P}[X=n]=n^{-s}\zeta(s)$. Thanks to that random variable we can prove that $\zeta(s)= ...
3
votes
1answer
73 views

Adding $inches^2 + inches$?

At our school we have a "summer packet" we have to complete. In this packet was the following problem: At first the "sum" part puzzled me. I had no idea why they would quiz us on basic arithmetic ...
5
votes
1answer
55 views

What are examples of cases where floating-point $aaaa\ne(aa)(aa)$?

As explained in answers to this question on SO, due to non-associativity of floating-point arithmetic repeated multiplication like $aaaa$ can't be optimized to $(aa)(aa)$. Of course, aside from just ...
-2
votes
0answers
16 views

Addition and multiplication tables for the Ring [closed]

Construct both the addition and multiplication tables for the ring $$ F_3[x]/x^2+2 $$
2
votes
2answers
44 views

Do negative signs count as subtraction or multiplication?

Would $-x$ count as $0 - x$ or $(-1)\times x$?
5
votes
0answers
39 views

Primitive recursion and $\Delta^0_0$

Until recently I assumed that primitive recursive relations are exactly $\Delta^0_0$ (i.e. bounded) ones, but I learned they're different (the former is a proper superclass of the latter). I have ...
0
votes
1answer
20 views

Permutation of numbers that there are all modulo M .

Let's say I have $M-1$ integers, all of them different from each other, and all of them smaller than integer M: $$1,2,3...M-1$$ I multiply each of them by another integer S, and write the result ...
2
votes
1answer
35 views

Saving should start early

This is a very interesting word problem that I came across in an old textbook of mine. So I know its got something to do with compound interest, but other than that, the textbook gave no hints really ...
-4
votes
1answer
76 views

How do you make the number 43 using all of these numbers:7,7,6,5 [closed]

How do you make the number 43 using all of these numbers:7,7,6,5
-1
votes
0answers
38 views

Calculate the loss

If a man walks in to a shop and steals £50 then the next day goes back to the shop and spends £40 but gets £10 change.How much does the shop keeper loose?
2
votes
3answers
44 views

Why are there opposite rules for dividing positive numbers and negative numbers?

I'm in confusion from some time about division of negative numbers. When we divide a positive number with a positive number, for example $$5/3 = 1.66 $$ we see what is biggest multiple of 3 which is ...
0
votes
0answers
27 views

Addition set confusion [duplicate]

Prove that for any two sets we have the following: ∣A∪B∣=∣A∣+∣B∣−∣A∩B∣. Not sure what the + means here.
0
votes
1answer
47 views

Set Addition proof

Prove that for any two sets we have the following: A∪B=A+B−A∩B Not sure what the + means here. Do i just add the two sets together including the duplicated elements? Yes sorry it should be ...
0
votes
0answers
31 views

Is this an improper method of averaging grades? If so, what is a simple mathematical way of explaining it?

I have a professor who employs a unique method of averaging grades. On each assessment, the professor assigns a raw numerical score to each student based on performance. He then converts particular ...
1
vote
1answer
31 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 ...
1
vote
1answer
12 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 $$(r + s) * \vec{a} = r * \vec{a} + s * \vec{a}$$ ...
1
vote
1answer
37 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 ...
1
vote
1answer
39 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
votes
1answer
72 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. ...
3
votes
2answers
39 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? ...
6
votes
2answers
170 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!
0
votes
2answers
53 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: $$ \sqrt{-1} = \sqrt{-1} $$ $$ ...
0
votes
3answers
19 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 ...
0
votes
0answers
26 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 ...
2
votes
4answers
105 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.
1
vote
1answer
19 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 ...
-8
votes
4answers
106 views

Why is $3 \times 0 = 0$? [closed]

Can someone explain? $3$ is $3$. It has a value. $0$ is $0$. It is nothing. Then why is $3 \times 0 = 0$?
0
votes
2answers
36 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.
0
votes
0answers
18 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
votes
1answer
67 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 ...
1
vote
2answers
19 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, ...
12
votes
1answer
170 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 ...
1
vote
2answers
52 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?
4
votes
5answers
199 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 $48$?
-2
votes
1answer
2k 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?
-2
votes
1answer
43 views

Integer value of cubic polynomial [closed]

I need help on the next problem. Let $a,b,c$ be real numbers, consider $f(x)=x^3+ax^2+bx+c$. If $f(2013), f(2014), f(2015)$ are all integers, then $f(n)$ is an integer for all integers $n$. I ...
2
votes
1answer
18 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 ...