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

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Adding/Subtracting in binary and hexadecimal number systems?

I have two numbers(in decimal): M = 3892.74 N = 9341.65 I am trying to add and subtract them in binary numbers and then in hexadecimal numbers. I manage to ...
2
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1answer
42 views

Field Completions

Let $(K,v)$ be a number field with an absolute value. Denote $K_v$ to be a completion of $K$ and $\overline{K_v}$ to be an algebraic closure of $K_v$. Let $E$ be a finite extension of $K$. Every ...
0
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1answer
29 views

why are these two intuitive ways of understanding division equivalent?

The elementary school example of division, say 12:4 is saying that you have to share out 12 cookies to 4 kids. However, another (only slightly less intuitive) way would be to ask how many times 4 ...
2
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3answers
364 views

Finding product without working it out

What's the easy way to find the solution for the below problem without actually multiplying the numbers: $$(24 * 24) - (16 * 16)?$$ I tried multiplying the numbers but that is a long way. The ...
2
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0answers
33 views

Why have multiplicative operators precedence over additive operators?

Considering that addition is (in my understanding) a more basic operation than multiplication, would it not make sense to give it higher priority? That is to say, we would expect to encounter more ...
0
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1answer
25 views

Minimize g(x, y)=max{12-x,8-y} over x+y=10

Let $g (x, y)=\max\{12-x,8-y\}$. Find the minimum value of $g(x,y)$ as $(x, y)$ varies over the line $x+y=10$. 1.5 2.1 3.7 4.3 My attempt Without use of Lagrange method of multiplier , I see ...
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2answers
39 views
1
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0answers
12 views

Upper bound on function defined by induction involving divisions by two

Let $A=\lbrace (x,y)\in{\mathbb N}^2 | 0<x<y \rbrace$. For positive integers $u,v$ let $\rho(u,v)=(\textsf{min}(u,v),\textsf{max}(u,v))\in A$. It is easy to see that there is a unique map ...
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0answers
35 views

How many possibilities of sequences are there to have averages of adjecent two in the sequence will be as provided

Given: Sequence of Averages of adjecent two numbers in list i.e. (n-1) integers Output: how many non-decreasing sequences of n elements are possible? for example: Given: 2 4 Possibilities: 1> 0 4 ...
4
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2answers
88 views

Is $\Delta_0=\Delta_1$ in arithmetical hierarchy?

I have seen a definition (e.g. http://www.math.ubc.ca/~bwallace/ArithmeticalHierarchy.pdf) of an arithmetical hierarchy in computability starting with: "let $\Delta_0=\Sigma_0=\Pi_0$ be the set of all ...
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2answers
140 views

How to solve $\sqrt{9-4\sqrt{5}}=$?

Need some hints how to solve this: $\sqrt{9-4\sqrt{5}}=$ ? Thanks.
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2answers
52 views

What is it called and how it works?

If I borrow from two of my parents 50 dollars and spend 45 dollars at the store, I am left with 5. On my way home, I borrow to my friend 3, now I am left with just 2. I return home and give 1 to my ...
2
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4answers
81 views

find $z$ that satisfies $z^2=3+4i$

Super basic question but some reason either I'm not doing this right or something is wrong. The best route usually with these questions is to transform $3+4i$ to $re^{it}$ representation. Ok, so ...
0
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1answer
38 views

roots of equation $ e^{2x}\sin (2x) +7=0$

Let a,b,c be roots of equation $ e^{2x}\sin2x -7=0$ then roots of equation $ e^{2x}\sin2x +7=0$ lies between p and q where Both p and q $\in$(a, b) Both p and q $\in$(b, c) p $\in $(a, b) and q ...
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2answers
49 views

Problem approximating for a chemical problem:

Solve using suitable approximation by hand: $$s(s-\alpha)=5\times10^{-13} \\ \frac{\alpha}{(s-\alpha)(0.4-2\alpha)^2}=10^8$$ Now to solve this I tried assuming $s\approx\alpha\approx0.2$ and then ...
1
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1answer
18 views

Mathematical arithmetic rounding $1$

What is an example of $4$-digit arithmetic rounding: $ \text{ }\\ \text{a)}\\ 11.2468 = 11.25\\ \text{ }\\ \text{b)}\\ 0.25632 = 0.256\\ \text{or}\\ 0.25632=0.2563\\ $ Can you explain what is ...
3
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2answers
41 views

Solving an integer equation

Is it true that if: $x$, $y$, $z$ and $t$ are integers such that: $xz + 7yt = 0$ $and$ $yz + xt = 0$, then $x = y = 0$ $or$ $z = t = 0$? Why or why not? Unless I have miscalculations somewhere ...
0
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1answer
20 views

Arithmetic Time and Work related question

8 men can complet a piece of work in 20 days. 8 women can do the same work in 32 days. In how many days will 5 men and 8 women together will complete the same work? All I have is: Men's one day work ...
1
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4answers
226 views

Reversing the digits with a subtraction [closed]

How many 3-digits numbers possess the following property: After subtracting $297$ from such a number, we get a $3$-digit number consisting of the same digits in the reverse order.
0
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1answer
31 views

Why do the denominators of two fractions with numerators $1$ add up to a third fraction that have the special things below?

I found out that the denominators of two fractions with numerators $1$ add up to a third fraction that has the sum in the numerator and the product in the denominator. For example, ${1\over ...
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1answer
54 views

How to divide by negative numbers? [closed]

How to divide by negative numbers? Like what is the quotient and remainder when 24 is divided by $-5$ or $-24$ is divided by $5$?
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2answers
29 views

Why do consecutive triangular numbers in pairs like $6$ and $10$ always add up to a perfect square?

I was a bit surprised by this when I thought of it. Look here: $$001, 003, 006, 010, 015, 021, 028, 036, 045, 055$$$$004, 009, 016, 025, 036, 049, 064, 081, 100$$As you just saw, $15$ and $21$ add to ...
0
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1answer
17 views

Polynomial with integer values

I'm looking for a polynomial $P \in \mathbb Q[x]$ with $P(\mathbb Z) \subset \mathbb Z$, with $P \notin \mathbb Z[x]$ I found that $f_n := \frac{1}{n}x(x-1)(x-2)\dots(x-(n-1))$ is such an element. ...
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2answers
70 views

Can you recommend a book with techniques for solving hard algebra/arithmetic problems?

I'm a university student who never really studied maths in high school (I did the basic courses, but because I'm dyslexic I was to embarrassed to try the harder courses) now I'm getting back into it, ...
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2answers
32 views

what is the default order and direction of operation?

I have a division like this 16/8/4/2 what is the default way to do calculations when the bracket is not specified . Method 1 : Is it correct to go from right to left like [16/ (8 / { 4 / ...
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2answers
50 views

How many numbers end with $0,2,9$?

The question is very simple: How many positive integers from $900$ and down end with $0,2$ and $9$? I think it is either $270$ numbers or $271$ numbers, but I am not sure which one.
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1answer
47 views

What do I do after this?

The question goes.. In a recent marathon, $\frac{1}{10}$ of the participants finished in less than $3$ hours. $\frac{1}{3}$ of the remaining participants finished in $4$ hours or less. Out of those ...
0
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2answers
41 views

Splitting sum into two sums

Assuming that $f$ is a multiplicative arithmetic function. Let $n_1,n_2\in \mathbb{N}$ with $gcd(n_1,n_2)=1$. Consider the sum $$\large S=\sum_{a\mid n_1n_2}f(a).$$ Can I split the sum $S$ into two ...
2
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2answers
71 views

Is there another way to prove $(x-n)^2 = (n-x)^2$

Let's say $n$ is $4$. So, I came up with the solution below. $(x-4)^2 = (x-4)(x-4) = x^2 - 8x + 16$ $(4-x)^2 = (4-x)(4-x) = 16 - 8x + x^2 = x^2 - 8x + 16$ I was wondering if there is another way ...
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3answers
143 views

Convert 1-5 Grading Scale to 1-100 Grading System

I am creating a formula in Excel to convert 1-5 Grading Scale to 1-100 Grading System Suppose that I have the following table: 97-100 = 1.00 94 - 96 = 1.25 91-93 = 1.50 88-90 = 1.75 85-87 = 2.00 ...
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0answers
5 views

Creating a Performance Formula Which Awards Longevity

I have a website where I'm grading user performance on a certain metric. Each year, users can earn a grade of 0-100. However, I'm trying to determine an 'all-time' leaderboard for users which ...
3
votes
2answers
147 views

How to simplify this arithmetic expression

I'm trying to simplify: $\left[(\frac{3}{4}\right)^{7}\cdot$ $\left(\frac{3}{4}\right)^{-4}]^{2}$ $\cdot4^5$ The only advance that I have done is $\left[(\frac{3}{4}\right)^{14}\cdot$ ...
3
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1answer
70 views

Proof that $\sum_{i=1}^n{1} = n$ for all $n \in \Bbb Z^+$

It seems obvious that $$\forall n \in \Bbb Z^+, \sum_{i=1}^n{1} = n $$ However, I'm having trouble coming up with a formal proof for this. Given a concrete number like $4$, we can say that ...
3
votes
1answer
101 views

Is it possible to express addition as repeated multiplication?

It is possible (and common when explaining multiplication) to express multiplication of positive integers as repeated addition like this: $$4\cdot5 = 5+5+5+5=20$$ And a general expression would be ...
0
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1answer
27 views

equality of two sums

Is $\sum _{t=1}^m \sum _{k=t}^m (a_{k+1}-a_k)b_t$ equal to $\sum _{k=1}^m \sum _{t=1}^k (a_{k+1}-a_k)b_t$? If not, then how to derive equations for temporal difference algorithm in machine learning: ...
0
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1answer
63 views

What is the contraposive of this statement?

I have to prove the negation of this statement: $$\forall a,b,c\in\mathbb{Z}{\;if\;a\;|\;b\} $$ But the fact that there is a "and" is very disturbing. I think that I am missing something because my ...
0
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1answer
41 views

How to determine significant figures involving radicals and exponents

How do you determine the significant figures for solving equations with radicals and exponents? For example, how do you evaluate $x = \sqrt{4.56^2 +1.23^2}$?
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0answers
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Among 10 packet each having weight 100grams 1 packet is defective and weight is 90 grams. How to find out the defective one in only one measurement?

I have 10 packets of cigars. Each packet consists of 10 cigar and weight of each cigar is 10 grams.So weight of each pack will be 100 grams.But Somehow my friend measures packets of cigars and said ...
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2answers
23 views

Computing an academic grade when relative weights are changed

My grade is 88.6% (High B) and we get 80%(Assessment Grade) and 10%(Homework). My teacher is now making this 70%(Assessment Grade) and 30%(Homework). I have done all my homework 100% and I've been ...
1
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2answers
37 views

How to recognise the digit multiplication, subtraction or addition when checking for divisibility by 7, 11, 13, 17 and 19?

I was studying this page Divisibility by prime numbers under 50 to check for the divisibility by 7, 11, 13, 17, 19 etc. Is there any way to recognise whether to add or sub the given times of unit ...
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3answers
51 views

The meaning of dot centered vertically, as in $3\cdot 5$

I just went to a site to practise some maths as I am studying some maths on my OU course in computing and IT and I ran into some symbols that I did not understand The questions were solve ...
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0answers
42 views

Are ratio notations always equivalent?

Is there any case where the following ratio notations are not equivalent? For cases where the notations are equivalent, under what circumstances would the first notation be preferred? First ...
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5answers
71 views

Manually obtainining a list of primes $\leq n$, by using the root of n?

In my abstract math class I learned that if we want to get a list of primes $\leq n$ manually, we have to calculate the root of n, and the floor of that result will be the greatest number for which to ...
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1answer
35 views

Calculating how much money I spent? (23-73 gives

I'm a very simple person with basic math knowledge. Recently I run into huge problems when calculating how much I spent. Sometimes to calculate how much I spent I do a calculation $final sum - start ...
0
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2answers
33 views

Use of arithmetic progression to find the sum of numbers

How can I find the sum of numbers divisible by 3 that are between 1 and 1000 if I don't know how many elements there are in the arithmetic progression?
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1answer
27 views

Bézout's identity on a polynome sequence

I'm stuck on an exercise which is split in 3 questions : 1) Prove that : $$\exists (U_n, V_n) \in \mathbb{R}[X]^2 \text{ s.t. } (1-X)^{n+1}U_n+X^{n+1}V_n=1$$ 2) Let $(R_n, ...
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3answers
156 views

Proving that $p_1p_2\mid n$ iff $p_1\mid n$ and $ p_2\mid n.$

Let $p_1$, $p_2$ be distinct primes. Using the Fundamental Theorem of Arithmetic prove that a natural number $n$ is divisible by $p_1p_2$ if and only if $n$ is divisible by $p_1$ and $n$ is divisible ...
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2answers
55 views

$\frac{1}{0}$ is undefined. Is $\frac{1}{0}-0.5$ undefined as well?

I know that $\frac{1}{0}$ is undefined. What about $\frac{1}{0}-0.5$ it's undefined as well?
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1answer
19 views

Covering deficits with values with different weights

SO I have a couple of assessments with specific weights as follows: Assignment 1: 5% => Mark 60% Assignment 2: 5% => Mark 53% Assignment 3: 5% Assignment 4: 5% Test 1: 30% => 47% Test 2: 30% ...
0
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1answer
30 views

What can you say about two expressions with same reminder?

I am working on Integer factorization problem and I came to those two interesting expressions: $a,b,c,x$ are non negative integers $a,b < c$ $$\frac{ax + b}{c-x}$$ and $$\frac{ac + b}{c-x}$$ ...