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

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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 ...
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3answers
85 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
102 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 ...
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0answers
132 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
50 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
50 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. ...
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1answer
5k 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 ...
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1answer
65 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 ...
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3answers
56 views

How to do long division $1.068 / 40$ without using a calculator?

1.068 divided by 40. 1.068 / 40 = ? How would you do this problem by long division and any other methods to figure this out without using a calculator. Just pencil and paper.
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2answers
73 views

solve ratio word problem without algebra

Four gallons of yellow paint plus two gallons of red paint make orange paint. I assume this makes six gallons. So the ratio is 4:2, or 2:1. Question: how many gallons of yellow paint, and how many ...
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1answer
55 views

First-Grade Maths o.O Percentage of number, then out of 100.

I'm rewriting http://209.141.38.179/mcstatus_v1/ and need an equation. Basically, I have a game server. I know that there are 10 players on that server (Max ...
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1answer
36 views

How to convert one number range to another? (Prioritizing a list of skills based on current familiarity and usefulness)

I'm trying to come up with a formula to prioritize a list of skills that a learner should tackle based on: current familiarity with the skill, and the usefulness of the skill. Familiarity is a $1$ ...
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5answers
75 views

Change or cancel flight?

This is a simple problem, but I wanted to hear an answer from someone else. I had a round-trip flight that cost 135 dollars for a recent trip. At the last minute, plans changed and I decided not to ...
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3answers
59 views

How do i prove this inequality?

Let $a,b,c,d,e,f$ be positive reals. Then how do i prove the below inequality? If $ac-b^2≧0$ and $df-e^2≧0$, then $(a+d)(c+f)-(b+e)^2 ≧0$. I hope someone answers this specifically.. Thank you ...
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1answer
85 views

Converting division by a constant into multiplication

Given a small integer constant $N$, how can I find a fast to compute expression for $\lfloor \frac xN \rfloor$, working for each integer $x \in [-2^{31}, +2^{31})$? Here, "fast to compute" means that ...
3
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1answer
73 views

What is the condition for example $(number^c)^b=number^{cb}$ to be true?

What is the condition for $(\text{number}^c)^b=\text{number}^{cb}$ to be true? I can't find it on google.ze so I asked it here on math.stackexchange.com.
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2answers
90 views

How does $\frac{1}{n^4} = \frac{1}{(2n-1)^4} + \frac{1}{(2n)^4}$

I need to find the sum of $\displaystyle\sum_{n=1}^\infty \frac{1}{n^4}.$ In the solution document it written: $$\displaystyle\sum_{n=1}^\infty \frac{1}{n^4} = \sum_{n=1}^\infty \frac{1}{(2n-1)^4} + ...
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1answer
52 views

Odd way to do arithmetic

If I want to divide $9251$ by $29$, the methods taught in elementary school suffice. Now suppose I want the prime factorization of $9251$. The square root of that number is between the consecutive ...
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1answer
31 views

Need help proving an equality

I'm looking for help proving this equality: $\forall m:m \times 0 = 0 = 0 \times m$ Any help would be greatly appreciated. Thank you very much.
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3answers
131 views

Why is $12\cdot 12=144$ but $8 \cdot 16=128$? (I was asked by a co-worker)

Why is $12\cdot 12=144$ but $8 \cdot 16=128$? a friend thinks it should be the same because $12+12=24$ and $8+16=24$. He said it is only $4$ that is moved to the other side. Please give some sort of ...
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3answers
115 views

Addition composition problem?

I'd like to know how you go about solving the problem below. Does a trick exist other than evaluating substituted values until a solution is found? Furthermore, is there a generic name for such ...
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4answers
185 views

Representing $\frac{3 + \sqrt{5}}{2}$ as a square of a quadratic surd

How can I represent $\frac{3 + \sqrt{5}}{2}$ as square of a quadratic surd? Actually, I was solving a question where $\frac{3 + \sqrt{5}}{2}$ was converted to $(\frac{1+\sqrt{5}}{2})^2$. How did the ...
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1answer
28 views

How many quarter horses?

The rent-a-stall horse barn has stalls for 1000 horses. Forty percent of the stalls are for ponies. On Tuesday, there were 200 ponies and a bunch of quarter horses at the horse barn. The horse ...
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2answers
52 views

Combinations from a finite pool of objects

We've got a pool containing 5 A-balls, 4 B-balls, 3 C-balls, 2 D-balls and one E-ball. How many ways are there to pull out 5 balls? I thought of dividing off from the formula: $\frac{15!}{10!}$ but ...
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1answer
65 views

division and remainders

When you divide, it will not always result in whole number. Sometimes there will be numbers left over. You can either end the problem with a remainder or use decimal points to get a decimal number. ...
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1answer
56 views

What am I not understanding? Given 9 integers, choose 4 a, b, c, d such that a + b − c − d is divisible by 20.

What am I misunderstanding? A question on this site asks Given any nine integers show that it is possible to choose, from among them, four integers a, b, c, d such that a + b − c − d is divisible by ...
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2answers
1k views

Set Addition vs. Set Union

Given two sets $A$ and $B$, what is the difference between $A + B$ and $A \cup B$? For example, if $A = \left\{ a, b, c \right\}$ and $B = \left\{ d, e, f \right\}$, what are $A + B$ and $A \cup B$, ...
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2answers
75 views

How many inches are in 7.94 feet?

Question: the height on my land is 7.94 feet noted by a surveyor on a Certificate of Elevation form. In layman's terms, that is 7 feet and how many inches? or how much of an inch is it short of 8 ...
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2answers
56 views

finding percentages between several numbers

My question: if i had an account that yielded $\$60$ in interest annually and another that yielded $\$500$ annually, what percentage better did the second account perform? Is it 830% 60 • X% = 500 ...
2
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2answers
141 views

99 Ninja missions and a single lantern

From http://blog.liveramp.com/2014/01/30/the-case-of-ninety-nine-ninja/: A team of 99 ninja are each sent out on individual missions by their master. Their master tells the ninja that one of them ...
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248 views

cross-multiply with algebra word problems

I am using cross-multiplication here, but it is definitely giving me the wrong answer. Here is the question: If 1200 bits are transmitted in 1 second, how many milliseconds does it take to transmit 3 ...
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3answers
173 views

Why is this considered to be an AXIOM?

One of the axioms out there is: if n and m are integers and they have the same next integer then n=m But why is it considered to be an axiom since I can easily prove it: Have the same next integer ...
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2answers
386 views

Binomial Theorem Practical Problem

I have been studying the 'Binomial Series', Chapter 16, Pg.125 within the Engineering Mathematics Book by John Bird. After completing this section I have attempted to complete the exercises for ...
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2answers
99 views

Binomial Theorem - Proving

The viscosity $\eta$ of a liquid is given by; $$\eta = \frac{kr^4}{v*l}$$ Where $k$ is a constant. If there is an error in $r$ of $+2%$, in $v$ of $+4%$ and $l$ of $-3%$, what is the resultant ...
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1answer
52 views

Modeling viral growth

I'm trying to forecast the viral growth for a website I'm developing. I've arrived at some monthly growth rates I can expect per month, the difficulty is I'd like to model my growth per week instead. ...
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2answers
36 views

The Order of Operations with Brackets

How would one go about answering something like -8-(-2)[4-(-5)]? The problem here really isn't very complicated once one is used to getting down the right ...
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1answer
118 views

Long division differs from calculator

i have been helping my daughter with her long division homework. One of the questions was 172/6 she worked out the answer using the long division tree, and upon checking it found the answer differs ...
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2answers
83 views

Converting fractions / decimals to percentages

Can someone show me the methodology on how to convert 1.2794 to a percentage form? If I multiply it by 100, I get 127.94%, which is the correct answer. I'm not really sure 'why' I multiplied it by ...
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1answer
47 views

Calculation of working hours [closed]

When I was hired at Company $A$, I agreed I would work for them three days a week and be sent to work at Company $B$ for the other two working days. Company $A$ would then contribute to my wage for ...
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4answers
118 views

My grade so far?

Quizzes $20\%$ Midterm $40\%$ Final $40\%$ Can someone please help me calculate what I have in the class so far? I'm pretty slow when it comes to numbers. I'm getting the full $20\%$ from the ...
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1answer
27 views

Need an equation to measure frequency of a certain period over days, months, years.

Example) Curious as to how many times a certain song of 3:46 will repeat over a given amount of time. How many times over a day, month, year, and the remaining growing fraction of time left over.
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2answers
202 views

Adding sum of negative integers to the sum of positive integers - how would value look like?

I know that the sum of positive integers will diverge and that the sum of negative integers will diverge. I also know that "the sum of all integers" will likely be meaningless (it depends on the order ...
2
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2answers
65 views

True or false division algorithm problem

Let a,b,c be integers with a not equal to 0 and (b,c)=1. If a divides the product of bc, then a must divide b or a must divide c. My thoughts: I can prove this if (a,b)=1. but I believe it is false ...
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1answer
61 views

Is there a name for this theorem?

Theorem: If you have a number $x$ with $n$ number of decimal places and another number $y$ with $l$ number of decimal places, then $x \cdot y$ will never have more than $n + l$ decimal places. For ...
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4answers
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How would I solve this algebraically?

So I've got a small question: How do I solve this algebraically? $x^2=x+6$ It's easy to see the answer but how would you solve it algebraically?
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1answer
42 views

Determine $2$ missing digits for modulo $11$

An account number verification system works as follows: All digits in a 10-digit account number all multiplied by following weights: $$(6 \ 3 \ 7 \ 9 \ 10 \ 5 \ 8 \ 4 \ 2 \ 1)$$ Resulting numbers ...
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38 views

Average related question

Can some one please let me know how to solve this problem for my son's home work assignment which i am not able to understand. after taking 3 quizzes, your average is 72 out of 100. What must your ...
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3answers
265 views

formula for converting a very long number to a fraction

What is the average (arithmetic mean) of 8, 7, 7, 5, 3, 2, and 2? the answer is $4\frac{6}{7}$. The sum of numbers is 34 and when you divide by 7 it's 4.8571428..... How can I get the fraction of ...
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1answer
217 views

Reverse Polish Notation with power

Perhaps I'm just not understanding RPN correctly, but whenever I translate something like 2^2^3 then I get 22^3^ But if I try ...
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2answers
34 views

Which decimal can be multiplied by the result of $(x \times 1.15)$ to return $15$% of $x$?

Which decimal can be multiplied by the result of $(x \times 1.15)$ to return $15$% of $x$? For example, when I want to add $15$% sales tax to an item before tax, I would multiply by $1.15$. ...