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

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Hi I'm stuck trying to find square footage

Thank you for looking at my question. We're supposed to paint the walls of a room and ceiling twice (x2), the room is 15 ft long by 10 ft wide and 8 ft tall. The teacher is asking us to provide the ...
0
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2answers
79 views

Calculating percentages with weights

I've done a search for the answer but still couldn't figure it out. Say for example: Year 1 Result = 80% (Weight:20%) Year 2 Result = 70% (Weight:10%) Year 3 Result = Unknown ...
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2answers
327 views

Three numbers that multiply to ten (It gets harder)

I am working on a problem that involves the following: One must find three numbers, integers and/or decimals, that multiply to ten. Here's the catch: You must use all integers, $0-9$, in the ...
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2answers
290 views

Primes in nonstandard models of PA

What is known about prime numbers in nonstandard models of PA? Restricted to true natural numbers the sets are identical, but does there always exist nonstandard primes? Can we explicitly define one ...
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2answers
807 views

Schönhage-Strassen multiplication

I am trying to implement the Schönhage-Strassen algorithm (SSA) for multiplying large integers, but it only gives the right result if all $\delta_j$ are zero. I'll explain what I mean by this: SSA ...
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1answer
111 views

Infinitely many simple groups with conditions on order?

If $G$ is a non abelian finite simple group, we know that $4$ divides $|G|$. More precisely there are infinitely many finite simple groups $G$ such that $v_2(|G|)=2$, just consider ...
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2answers
181 views

What does a nonstandard proof of Con(PA) look like?

As in Godel's incompleteness theorem natural numbers encode proofs of theorems. Due to Godel's completeness theorem there is a natural number (in some nonstandard model) that proves $Con(PA)$. What ...
6
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2answers
274 views

What's the maximum possible score in this mathy solitaire puzzle?

Consider a deck of 52 cards in four mathy suits --two red: "adds" ($+$) and "subs" ($-$); and two black: "muls" ($\times$) and "divs" ($\div$)-- and thirteen numerical values --"A" (1), 2, 3, 4, 5, 6, ...
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5answers
423 views

Why is the math for negative exponents so?

This is what we are taught: $$5^{-2} = \left({\frac{1}{5}}\right)^{2}$$ but I don't understand why we take the inverse of the base when we have a negative exponent. Can anyone explain why?
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6answers
552 views

Proof of dividing fractional expressions

For dividing two fractional expressions, how does the division sign turns into multiplication? Is there a step by step proof which proves $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot ...
1
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1answer
209 views

Division by zero [duplicate]

Possible Duplicate: Division by $0$ Everyone knows that $(x/y)\times y = x$ So why does $(x/0)\times 0 \ne x$? According to Wolfram Alpha, it is 'indeterminate'. What does this mean? ...
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1answer
68 views

Confused about exponents and imaginary/real answers

I am confused about some exponent behavior. $$(-2)^{7.6} = (-2)^{\frac{76}{10}} = ((-2)^{76})^{\frac{1}{10}} = ((-2)^{\frac{1}{10}})^{76}$$ Is there something wrong in this logic? When I plug the ...
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2answers
558 views

How do you simplify the addition of square root

$2\sqrt{x} + \sqrt{3}$ How do I simplify this?
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2answers
1k views

Understanding Strategy:Minimum number of weighing to find the faulty bag

If Mr M buys $n$ bags of sands, each weighing a unit each except one bag. What is the minimum number of weighing is required to determine the faulty bag when: a two pan balance is used? ...
0
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1answer
57 views

Growth rate question

Something grows at an annualized rate of 5% for 4 months and then declines at an annualized rate of 4% for the next four months. What would be the annualized growth rate over the entire 8 month ...
0
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1answer
66 views

Which loan type is cheapest?

I have a 4% loan that spans 20 years, where I pay a fixed amount every three months. If I make an extra payment, I then can choose between two options keep the duration of the loan constant, and I ...
5
votes
5answers
813 views

The $3 = 2$ trick on Google+

I found out this on Google+ yesterday and I was thinking about what's the trick. Can you tell? How can you prove $3=2$? This seems to be an anomaly or whatever you call in mathematics. Or ...
2
votes
1answer
245 views

what does $-2^2$ evaluate to?

What does $-2^2$ evaluate to? My wife is upgrading her math & I'm quite uncertain how to answer. is it the same as $(-2)^2$ or is it the same as $-(2^2)$? at the heart of this is whether the ...
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2answers
381 views

Isn't base 27 more adapted to express numbers with letters?

I thought about the importance of 0 in numeral systems, and base 26 doesn't have one, for example those numbers in base 10 are the same: 0342 342 000342 In ...
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0answers
75 views

Percentage to obtain for Net salary

Gross Amount Given Salary = Rs. 1000 (Gross) Annual Income (AI) = Salary x 52 Annual Tax (AT) = 30% of AI Levy = 2.04% of AT This is simple I got this point ...
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2answers
7k views

Calculate Gross amount when only percent is known

Consider Rs.1000 as my Gross salary and suppose 20% is PF. so the simple thing is my NET amount is Rs.800. But when I know only my NET amount i.e. Rs.800 and I know that my 20% PF is already ...
2
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1answer
422 views

Simplify a surd expression

I won't lie, I have the following questions in my maths homework but I have no idea how to solve it and I wondered if you could help me here! My teacher has taught us, what seems to be the basics of ...
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1answer
963 views

Multiplying exponents by fractional exponents and whole numbers to the power of fractional exponents

I am trying to understand the different rules for multiplying exponents by fractional exponents and raising whole numbers by the power of fractional exponents. I have an idea but I'm trying to assure ...
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1answer
289 views

Question about significant figures

I was taught that there are two different methods for obtaining results for multiplication/division or addition/subtraction with decimals. For multiplication/division the result will have the least ...
21
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1answer
791 views

Is it possible $n(n+1)(n+2)…(n+k)$ is a square?

Let $n,k$ two integers greater than $1$, is it possible that $n(n+1)(n+2)...(n+k)$ is a square $m^2$, with $m$ an integer ? Thanks in advance.
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1answer
3k views

How to determine if a binary addition/subtraction has an overflow

From what I understand from my lecture notes, overflow occurs when: $C_{in} \neq C_{out}$ Change in sign For $C_{in} \neq C_{out}$: suppose $111+111=1110=110$. In this case $C_{in}=0, C_{out}=1$, ...
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3answers
148 views

Remembering multiplication of these two numbers

I have almost mastered multiplication table up to 9x9 however, I'm having problems with the following two. 7 x 8 = 56 and 9 x 6 = 54 For some reason my brain thinks that 56 and 54 are somewhat the ...
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3answers
1k views

Calculator for Arithmetic in Alternate Bases

In the course I'm currently teaching, we're testing our understanding of elementary school arithmetic algorithms by working in base 5. Each day, I write up several example problems for them to try ...
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3answers
242 views

Actual process for fractions to decimals?

Alright. I want to get a fraction into decimal. Without a calculator. $\frac{15}{7} = 2.14285714$ Basically, what are the steps for manually getting that decimal result?
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7answers
651 views

$\frac{a}{b} = \frac{c}{d} $ if $ad = cb$, how to intuitively understand this?

This works if you multiply both sides with $bd$ and cancel stuff out... But how does it work? When I look at it, I would never guess something like that is valid without resorting to the established ...
7
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1answer
694 views

How can I visualize division of negative numbers

$$-4 / 4$$ I have trouble because I don't know what's happening. I can do positive because I can see in my head with $$10 / 2$$ $$2, 4, 6, 8, 10 = 5$$ But with negative numbers, I can't see anything ...
16
votes
6answers
2k views

If multiplication is not repeated addition

What is it? How do you define multiplication? All of us had to memorize the multiplication table in elementary school, but how did they come up with it if so many people claim that it is wrong to ...
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0answers
301 views

How do I calculate cost savings and profits in this example?

How are profits and cost savings calculated in this table? Is there enough given data to calculate these two? Here is what I ...
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2answers
337 views

two's complement encoding

I'm referring to this article: http://en.wikipedia.org/wiki/Two's_complement I want to convert the following number to two's compliment using 4 bits: Decimal: -6, 6, 1 hexadecimal: C,D,E In the ...
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0answers
89 views

Closed-form decimal to binary

I've searched around but can't seem to find anything relevant. Given a natural number $n$, is there a closed-form formula that gives a decimal number (whose digits consist only of ones and zeros) ...
2
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2answers
136 views

Simplify with no calculator

$\dfrac{(8^3)(-16)^5}{4(-2)^8}$ $\dfrac{8\cdot8\cdot8\cdot-16\cdot-16\cdot-16\cdot-16\cdot-16}{4\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2}$ ...
2
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2answers
86 views

Simplifying a simple fraction with exponent

I am trying to simplify this fraction : $ \dfrac{(3^2)(5^4)}{15^3} $ The answer is : $ \dfrac{5}{3} $ I am trying to do the following: $ \dfrac{3^2}{15^3} \cdot \dfrac{5^4}{15^3} $ so ... $ ...
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1answer
1k views

Decimal to negabinary conversion

I found in wikipedia that youy can convert base 10 to a negative base simple by dividing to a base and keeping reminder like this: Source: http://en.wikipedia.org/wiki/Negative_base Now I'm stuck ...
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4answers
182 views

How to think about multiplication with a number $0 <x < 1$?

To clarify my confusion: $88 \cdot 0.732$ is the same as $0.732 \cdot 88$ The latter being: 0.732 eighty-eight times: $0.732 + 0.732 + 0.732 + \cdots + 0.732$ But how to think about $88 \cdot ...
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1answer
316 views

Elliptic curve point addition

Are there any elliptic curves, that require computing GCD for point addition? I've an algorithm, that apparently adds two points on an elliptic curve, but it uses GCD, which is strange, because I ...
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1answer
217 views

How would I solve this fraction division problem?

5/8 ÷2 1/2 I understand how to divide it by flipping the numbers (reciprocal) and what not. I just don't know what to do with the 2 next to the division sign. Help?
0
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1answer
200 views

How is called roots parts?

I'm not sure how to ask but I hope you will understand. Let's say we have such root: $$m\sqrt[2] n$$ or $$2\sqrt[2]3$$ So could you please tell me how to call m or 2 and n or 3 and how to say ...
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1answer
324 views

Fast arithmetic, without a calculator?

This has been on my mind for quite a while now... Is it really crucial to be able to crunch numbers on the fly? I have considerate difficulty making out the quotient of $1 / 0.732 $ for example. I ...
3
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2answers
527 views

What's this function called: $a^2 + b^2 + 2(ab)$?

This is a formula for calculating the 2th power of a number, for example if you want to calculate the 2th power of 5: $\begin{align*} a&= 2\\ b&= 3 \end{align*}$ $ 5^2 = a^2 + b^2 + ...
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2answers
2k views

How can I calculate non-integer exponents?

I can calculate the result of $x^y$ provided that $y \in\mathbb{N}, x \neq 0$ using a simple recursive function: $$ f(x,y) = \begin {cases} 1 & y = 0 \\ (x)f(x, y-1) & y > 0 \end ...
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1answer
110 views

Casting nines in other bases (radix) and doing check sums for binary

I was showing my son how to cast out nines the other day. He noted that based on the way it worked, we should be able to cast out 7s when we work with octal. We tested this in several bases and it ...
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1answer
2k views

What is mathematical basis for the percent symbol (%)?

Percent means 1 part of 100 or 1/100 and is indicated with %. Per mille means 1 part of 1000 or 1/1000 and is indicated with ‰, so it seems that these symbols indicate the mathematical operations ...
6
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2answers
237 views

Quantitative aptitude

I'm not very good at maths, but I need help with a question. This one appeared in an aptitude test. Consider the sum: $ABC + DEF + GHI = JJJ$ .If different letters represent different digits, and ...
2
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2answers
50 views

Progressions| Existence of 1980 in the given progression

Given three infinite arithmetic progressions of natural numbers such that each of the numbers 1,2,3,4,5,6,7 and 8 belongs to at least one of them, prove that the number 1980 also belongs to at least ...
4
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1answer
329 views

How do I divide integers in a negative base?

What algorithm can I use to divide numbers in a negative base? To divide numbers in positive bases, I am accustomed to using short division: ...