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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2answers
189 views

the relationship of subtraction and division

I think addition, multiplication and exponents comes naturally in a mental way. Let's say I have the number 133 in the decimal base 10 system. We know that 1 is in the hundred's place. We know that 3 ...
3
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2answers
65 views

Calculating the square root of an integer as an integer with the smallest error

I was recently asked to write an algorithm to find the square root of a given integer, with the solution expressed as an integer with the smallest error. It was unclear to me whether this meant I ...
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4answers
86 views

compare an integer number without using calculator

we have $\displaystyle a=2^{12}$ and $\displaystyle b=3^8$ and I wonder if exist method to compare them without using calculator.
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2answers
120 views

Alternating sign square sum

It can be seen that $6² - 5² + 4² - 3² + 2² - 1² =21 = T_6$, the sixth triangle number. Prove that the $n$ th triangle number, $T_n = n^2 - (n - 1)^2 + (n - 2)^2- \cdots + 1²$. well my solution is : ...
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1answer
48 views

Nice proof for $\lim_{h\to 0}\frac{f(x+nh)-f(x)}{h}=nf'(x)$ besides LHR

Why is $$\lim_{h\to 0}\frac{f(x+nh)-f(x)}{h}=nf'(x)?$$ A cheap answer would be L'Hospital's rule, but I think there should be a more direct way to prove it, appealing to the first principles of the ...
0
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1answer
177 views

How to calculate a comparative percentage

We have 1002 seats in Head Start (all full) and 287 waiting for Head Start We have 48 seats in Early Head Start (all full) and 256 waiting for Early Head Start I'm trying to express to the directors ...
0
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2answers
169 views

sum of dedekind cuts

The sum of Dedekind cuts alpha and beta is defined to be {a+b : a in alpha and b in beta}. But why does this correspond to the intuitive notion of sum? Why is sum defined this way? Spivak's book says ...
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2answers
34 views

Modular arithmetics

I am having a question specific for this video on Youtube: https://www.youtube.com/watch?v=3QnD2c4Xovk They seem to explain that shared encryption concept pretty well, but I seem to get some incorrect ...
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1answer
80 views

Is $\left((-1)^2\right)^\frac12 = (-1)^\left(2\cdot\frac12\right)$? [duplicate]

I'm feeling confused. If I square 1 and -1, the answers should be equal: $1^2 = (-1)^2$ Then I take both sides to the power of $\frac12$: $\left(1^2\right)^\frac12 = \left((-1)^2\right)^\frac12$ ...
1
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1answer
217 views

Integral Involving Square Roots

Find the integral from 7 to 8 of $(x/(x-6))^(1/2)dx$ The questions hints that you should use that the integral of $1/(x^2-a^2)^1/2$ is equal to $ln(x+(x^2-a^2)^1/2) + C$ So I manipulated the ...
2
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2answers
51 views

Rounding up to $3$ significant figures when adding

If $a,\ b$ and $c$ are real numbers and you are required to find $a + b + c$ to $3$ significant figures, to how many significant figures could $a,\ b$ and $c$ be rounded up to to give the result?
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1answer
41 views

Proving an existence

I am completely lost on where to go with this one. Can someone provide help with how to do this? I am trying to understand uniqueness. Here it is: ...
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1answer
46 views

Find $x;y;z\in \mathbb{Z}^+$ such that : $\left\{\begin{matrix} (xy+1)\vdots z & \\ (xz+1)\vdots y & \\ (yz+1)\vdots x & \end{matrix}\right.$

Find $x;y;z\in \mathbb{Z}^+$ such that : $\left\{\begin{matrix} (xy+1)\vdots z & \\ (xz+1)\vdots y & \\ (yz+1)\vdots x & \end{matrix}\right.$ Thanks :) I have tried that : ...
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2answers
82 views

Can $7 + 4 \times 8$ have multiple answers?

My textbook says evaluate $7 + 4 \times 8$ in a revision course. Is it $7 + 4$, then multiply by 8 or $7 + (4 \times 8)$ ? The calculator automatically gives me the correct answer, so I am going to ...
0
votes
2answers
44 views

Simplify fractional exponents

I am aware of the following rule: $a^{\frac{b}{c}} = (a^b)^{\frac{1}{c}}$ AND $a^\frac{b}{c} = (a^\frac{1}{c})^b$ I have a problem as follows: $32^\frac{3}{5}$ I simplify it: ...
1
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1answer
107 views

Delete Some Numbers

Given an array that consist of $n$ integers $a_1, a_2,\ldots, a_n$. Now I want to delete some(possible none, but not all) elements from the array, such that arithmetical mean of all remaining numbers ...
0
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2answers
86 views

Why is n^(1/m) no valid way to calculate a root

So I came across a situation where a calculator only had square root, but I needed the cubic root. So I used the old $n^\frac13$ trick, and sure enough, the cubic root of n. So this got me thinking. ...
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2answers
57 views

word problem involving interest

Upon entering college, Meagan borrowed the limit of $5000 on her credit card to help pay for expenses. The credit company charges 19.95 % interest compounded continuously. How much will Meagan owe ...
10
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7answers
2k views

An equation, where the solution does not exist, but on solving the equation we got a solution. why this is happening?

The solution of the equation $\sqrt{(x+1)} -\sqrt{(x-1)}= \sqrt{(4x-1)}$ is $\frac{5}{4}$,but when we put $x=\frac{5}{4}$ in the given equation, then it does not satisfy the equation. Actually, if ...
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1answer
224 views

Average percentage formula

I have something like: Price Quantity Tax (%) 2.2 34 8 1.3 29 7 And so on... After that I get something like: ...
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5answers
1k views

who invented division and why we do division in those steps told?

i know how to divide but i dont quit understand why we use those steps told in schools. like for example ...
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1answer
58 views

It is possible to prove that $a=b \Longleftrightarrow a+m= b+m ,\,\,\, \, \{a,b,c\} \subset \mathbb{R}$, or this is just an axiom?

It is possible to prove that $a=b \Longleftrightarrow a+m= b+m ,\,\,\, \, \{a,b,c\} \subset \mathbb{R}$ , or this is just an axiom? I'm curious if there is any demonstration of this simple statement. ...
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1answer
132 views

Maintain relationship between two numbers, when their sum equals 1

I have a question that I hope won't seem too silly. I have four numbers that add up to one: A= 0.4 B= 0.3 C= 0.15 D= 0.15 Now, assume that numbers C and D are removed and that I want to maintain ...
4
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2answers
16k views

Modulo 2 binary division (XOR not subtracting) method

I have attached an image showing a Modulo 2 binary division. I can roughly understand the working below which is using XOR calculation but I am not sure how the answer (in red) is being computed ...
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2answers
43 views

Ratios of people to time on jobs

If it takes three persons to complete a job in 30 hours, how long will it take for one person to complete the same job?
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2answers
327 views

Rationalizing the denominator 3

It is a very difficult question. How can we Rationalizing the denominator? $$\frac{2^{1/2}}{5+3*(4^{1/3})-7*(2^{1/3})}$$
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1answer
69 views

If the cost per minute is $\$0.032$, is the cost per hour $\$1.92$ or $1.92$¢?

I hope someone can help me with this problem. The cost per minute to make a phone call is $0.032, I'm that multiplying this by 60 will get total cost per hour. ...
0
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1answer
60 views

(Basic Arithmetic) Multiple number questions: 34 + 54 + 54.

Basic question here but I might aswell get it checked out. I've gone through the multiplication, division, subtraction and addition sections of Khan Academy but something he never went through were ...
2
votes
3answers
83 views

How to round $ 0.03446$ to three decimal places?

What is $ 0.03446 $ rounded to three decimal places? I think it is $0.035$ but someone told me that it should be $0.034$. I think $0.035$ because the $6$ would change the $4$ into a $5$, which ...
4
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3answers
74 views

Divisibility in base $7$ problem

Find all integers between $0 \leq a \leq 2400$ such they are divisible by $8$ and that their base 7 development has at least $3$ equal digits.
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2answers
78 views

How many seconds are there in 7 3/8 minutes? [closed]

$7 \text{ minutes} \cdot 60 \frac{\text{seconds}}{\text{minute}} = 420 \text{ seconds}$ What about the other $\frac{3}{8}$ minute?
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2answers
297 views

SAT #1 Arithmetic Sequence

Every Sunday Graham jogs 3 miles. For the rest of the week, each day he jogs 1 mile more than the preceding day. How many miles does Greg jog in 2 weeks? (A) 42; (B) 63; (C) 84; (D) 98; (E) 117.
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6answers
15k views

Why is the square root of a negative number impossible?

What is the algorithm to get the square root of a number? Why does it not accept / allow for negative numbers? I've always been told that the square root of minus one does not exist by my maths ...
0
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1answer
60 views

How can I determine least common multiple for a given number and all numbers before it?

The wikipedia article on least common multiples only talks about determining the least common multiple between 2 numbers. I'm looking for an algorithm that will determine it for a set of numbers 1 .. ...
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1answer
83 views

I have simple multiplication confusion, any help would be great

$(\mathbf60\times\mathbf60)$ Seconds = $3600$ Seconds or $60$ Minutes while $(1\times 1)$ Minute = 1 Minute What am I missing? and sorry about formatting i am new here on math network
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2answers
70 views

Calculate mode of 2 numbers with the same base !!!!

I have 2 numbers with same base(not necessary 10). I want to calculate the mode(Remainder of the division) of this 2 numbers without changing the base of them.The base of this 2 number can be ...
0
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1answer
139 views

Simplification of a simple expression

I'm going through an answer on this site, and I can't see how $7−2(31−4(7))$ simplifies to $9(7)−2(31)$ What rule is being used here? source: How to find the inverse modulo m?
3
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1answer
1k views

Average of products VS. product of averages

I have a problem at work where prices of things are determined by multiplying together a series of factors. For example assume each price is made up of three factors, $A, B, C$, so that $\text{Price} ...
1
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1answer
245 views

How to solve for getting average of them

I am trying to solve this problem If x+y= 6, y+z= 7 , and x+z= 9 , what is the average of x , y and z ? Well how i am trying to do is getting the value of 'X' , ...
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1answer
349 views

How I got this answer

Well i am new to this forum but old to stack exchange but i don't know much about mathmatics tags so sorry for the wrong tags if any. I have a question, but i want to know how i got its answer as 'D' ...
6
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1answer
73 views

Prove that no four positive integers $a, b, c $ and $d$ with $ab = 2d²$ can satisfy the equation $a² + b² = c²$.

Prove that : No four positive integers $a, b, c$ and $d$ with $ab = 2d²$ can satisfy the equation $a² + b² = c²$. Thank you...
1
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1answer
206 views

Primes created by “n + digital-root(n)” sequences

I've looked at the sequences created by repeatedly adding the digital root of a number to the number until it becomes prime. This is the pseudo-code for the program I've used:   n = 0 ...
0
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2answers
92 views

Right to left and order of operations

Reposting since I am unable to validate the previous account,I asked the same question Right to Left order Can someone please clarify unable to understand this basic math :( I am sorry if this too ...
2
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3answers
130 views

Prove $\lim_{(x,y) \to (0,0)} \frac{x^3y}{x^4+y^2} = 0$

How would you prove the following limit? $$\lim_{(x,y) \to (0,0)} \frac{x^3y}{x^4+y^2} = 0$$ I think the best way is using the squeeze theorem but I can't find left expression. $$0 \le ...
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3answers
160 views

How does ZFC describe addition?

Surprisingly, the Wikipedia article on addition doesn't contain the answer. I looked elsewhere online for it, but didn't find it. Intuitively, the cardinal of the union of two sets seemed ...
2
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0answers
168 views

Inserting +/- into 123456789…

I'm looking at a generalization of the problem of inserting + and/or - into the blocks $123456789$ and $987654321$ to create a formula for $100$, like this: $$123 - 45 - 67 + 89 = 100$$ $$9 - 8 + 7 ...
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1answer
64 views

arithmetic of the binomial

\documentclass[12pt]{article} \usepackage{amsmath} Bonjour à tous ! Let us have some integers n, k, r satisfiying:: $n/2 \geq \ k \geq 4, r>1$ Let's suppose that there exist an integer a such ...
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2answers
62 views

Multiplying two numbers

I've come across this technique to multiply two numbers of multiple digits and its not long multiplication. I'd appreciate it if someone could throw some light on why it works or the logic behind it. ...
1
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1answer
18k views

What is zero times infinity? [duplicate]

If any number times zero is zero and any number time infinity is infinity, then what do you get when you multiply zero times infinity? Do they cancel one another out and equal any number since any ...
0
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1answer
219 views

Base 10 arithmetic

The characters in the ascii codes have a decimal equivalent: http://www.asciitable.com/. Let's assume the decimal value of each ascii code requires to be 3 digits. So the NUL character is 000. The ...