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

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0
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1answer
83 views

Determine concentration

How would I go about solving a problem that goes roughly as such? Solution A: .1% Solution B: .15% ...
6
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2answers
1k views

Proving there is no natural number which is both even and odd

I've run into a small problem while working through Enderton's Elements of Set Theory. I'm doing the following problem: Call a natural number even if it has the form $2\cdot m$ for some $m$. Call ...
4
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3answers
2k views

How much faster is the Trachtenberg system?

How much faster are various mathematical operations using a Trachtenberg method rather than a conventional method?
1
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1answer
620 views

what is “average increase percentage” and how to calculate it?

What exactly it is meant by "average increase in percentage"? I stumble upon this term in while solving this problem: The average monthly income and expenditure of a person in the year $1995$ is $ \$ ...
2
votes
2answers
816 views

Can you encode if-then-else in arithmetic

Is there a general way to encode if-then-else/ITE in arithmetic, i.e. using the usual mathematical operators? Example: let $f(x) = x^2$ if $x < 10^{30}$ and $log x$ otherwise, shortly written as ...
0
votes
1answer
523 views

Suggest quicker method for finding rate percent per annum

$1$.The compound interest on certain sum for $2$ years is $\$410$ and simple interest is $\$400$. Find the rate of interest per-year. $2$.A sum of money invested at compound interest amounts in 3 ...
0
votes
2answers
109 views

On profit loss (II)

It seems like I am having troubles while dealing with dishonest merchants! Here is another problem: A cloth merchant says that due to slump in the market, he sells the cloth at $10\%$ loss but he ...
-1
votes
2answers
141 views

Solving $x$, $y$ and $z$

If I have $22x = 23y = 24z$ and $x+y+z = 3865$ how to obtain the values of $x$,$y$ and $z$ ?
9
votes
1answer
613 views

How to Compare powers without calculating?

Is there any rule for powers so that i can compare which one is greater without actually calculating? For example ...
11
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2answers
632 views

Is long division the most optimal “effective procedure” for doing division problems?

(Motivation: I am going to be working with a high school student next week on long division, which is a subject I strongly dislike.) Consider: $\frac{1110}{56}=19\frac{46}{56}$. This is really a ...
5
votes
1answer
3k views

Riddle (simple arithmetic problem/illusion)

I'm not sure how well known this "riddle" is but here it goes. 3 people go to a restaurant, each buy food worth 10.00. When they're done, they give 30.00 to the waitress. She gives the money to the ...
7
votes
6answers
817 views

How to Compare two multiplications without multiplying?

How to check if two multiplications are equal to each other or greater or lesser without actually multiplying them? For example, compare (254)(847) and (383)(536) EDIT: While trying to find a rule i ...
3
votes
3answers
156 views

Subsets of natural numbers generated by two generators

Let $m$ be a positive integer. Define $N_m:=\{x\in \mathbb{Z}: x>m\}$. I was wondering when does $N_m$ have a "basis" of two elements. I shall clarify what I mean by a basis of two elements: We ...
1
vote
3answers
343 views

Count number of values between two numbers

I am finding with some formulas for my web application. I need a formula that counts the number of values between two number, e.g. there are four numbers (3,4,5,6) between 2 and 7
0
votes
4answers
711 views

I'm totally confused about this addition problem [closed]

how does 1+1 = 3? I've seen it around and I mean the obvious response is that its just wrong but people say stuff like there's just some special way to look at it or something. any ideas?
1
vote
2answers
113 views

detecting 2 n bits integer addition overflow

Can somebody prove that when we add 2 bit integers and if there is an overflow then the result always will be lesser than the 2 operands used??
1
vote
1answer
207 views

Earth and Sun - fast question

Guys is my logic correct? If Earth travels around the Sun in $29.78$ km/s and I have to calculate how long will it take to travel $1$km I did following: $1s / 29.78 = 0.03358$ (to $5$ d.p) I think ...
2
votes
1answer
187 views

General form for $(\sum\limits_{i=1}^n a_i)^n$

Does anybody know where I can find a general form, in terms of n, of the sum $\left(\sum\limits_{i=1}^n a_i\right)^n$. What I mean is, there appears to be some sort of pattern, if you look at ...
4
votes
2answers
865 views

Algorithm (cryptarithm) question, yes it is homework, but I can't get it

The following is a multiplication problem in traditional base ten notation. Each letter represents a different digit. What digit does each letter represent? How did you get your foot in the door?
4
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5answers
1k views

Why does X divided by zero not equal X?

Why does X divided by zero not equal X? After all, X is not being divided by anything.
0
votes
4answers
5k views

How to reverse percentage?

If I have a value of 25%, and I want the value as it would be on the opposite side of the halfway point (75% in this case), what is a formula that can calculate this? I don't know the appropriate ...
1
vote
3answers
546 views

What will be the remainder?

I'm stuck with this problem I'm trying to solve from about an hour. Here's the question. What is the remainder when (3^202)+137 is divided by 101? There are 4 options -> 36, 45, 56, 11 I want to ...
1
vote
2answers
282 views

quick basic math equation question

I've got a solution to a economy class calculation, but I can't figure out how they came to the answer. Could you help me? -5p + 80 = 8p +-50 .......? = ......? 120 = 12p p = 10 Extra: do you ...
40
votes
14answers
11k views

Why negative times negative = positive?

Someone recently asked me why a negative * a negative is positive, and why a negative * a positive is negative, etc. I went ahead and gave them a proof by contradiction like so: Assume $(-x) * (-y) ...
20
votes
15answers
14k views

How do I explain 2 to the power of zero equals 1 to a child

My daughter is stuck on the concept that $$2^0 = 1,$$ having the intuitive expectation that it be equal to zero. I have tried explaining it, but I guess not well enough. How would you explain the ...
2
votes
3answers
2k views

How to find next prime number?

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the 10001st prime number?
2
votes
3answers
261 views

$2^{k} \mid {2k \choose 0} \cdot 3^{0} + {2k \choose 2} \cdot 3^{1} + \cdots + {2k \choose 2i} \cdot 3^{i} + \cdots + {2k \choose 2k} \cdot 3^{k}$

I have to prove this question: $$2^{k} \,\left|\, {2k \choose 0} \cdot 3^{0} + {2k \choose 2} \cdot 3^{1} + \cdots + {2k \choose 2i} \cdot 3^{i} + \cdots + {2k \choose 2k} \cdot 3^{k}\right.$$ What ...
3
votes
9answers
682 views

What is $57^{46}$ divided by 17?

$$\frac{57^{46}}{17}$$ What is best and quickest way to evaluate an approximate answer to this by hand?
5
votes
4answers
590 views

Long division notation (census of nations)

The Wikipedia article on long division explains the different notations. I still use the European notation I learned in elementary school in Colombia. I had difficulty adapting to the US/UK notation ...
9
votes
4answers
1k views

Proving that an integer is the $n$ th power

I have not been able to solve this problem. Any insights would be appreciated! Let $x, n > 1$ be integers. Suppose that for each $k > 1$ there exists an integer $a_{k}$ such that $x − a_k^n$ is ...
2
votes
5answers
1k views

Why is two to the power of zero equal to binary one?

Probably a simple question and possibly not asked very well. What I want to know is.. In binary, a decimal value of 1 is also 1. It can be expressed as $x = 1 \times 2^0$ Question: Why is two to ...
1
vote
2answers
119 views

How do I transform an inequality on $n$?

I have an inequality: $$ n \ge C\log^k n \times (A\log(n^r\log^l n) + B)$$ I want to turn it into an inquality $$n > F(A,B,C,k,l,r)$$ that implies the first inequality, while making it $F$ as ...
1
vote
1answer
378 views

What's a Multiple?

A quick question-Something that I learned that I forgot throughout the years. If a question asked you for a multiple of 9 and 12, which would be less than 40, would "36" be an answer, as both 9 and ...
-1
votes
2answers
3k views

Converting a radical to a mixed radical

Say I have the square root of 2/9. How would I convert this to a mixed radical where the radicand is a whole number? I can convert the square root of 8 to a mixed radical easily (2 sqrt 2) but this ...
3
votes
2answers
391 views

Arithmetic? Logical/Boolean/Bitwise operations?

I'm trying to convey to some folks some logical and bitwise operators such as AND, OR, XOR, &c in programming languages such as C &| Java. Though these I guess could be considered "boolean" ...
0
votes
1answer
194 views

About a certain signed sum of consecutive integers ($\sum_{k=1}^n k\cdot \varsigma(k)=\sum_{k=n}^{2n} k\cdot \varsigma(k)$)

I hope you will excuse my vague title. Let's define $$\varsigma \ \colon\ \mathbb N\to \mathbb Z\ \colon\ k\mapsto (-1)^{\lfloor \frac{k-1}{2}\rfloor}$$ and $$S(m,n)=\displaystyle\sum_{k=m}^n k\cdot ...
7
votes
2answers
6k views

How to calculate the number of decimal digits for a binary number?

I was going to ask this on Stack Overflow, but finally decided this was more math than programming. I may still turn out to be wrong about that, but... Given a number represented in binary, it's ...
2
votes
4answers
311 views

How to reduce lower one number, while another number increases goes up increments

This is such a basic question I'm sure, but I've been trying to find a robust solution to it for a while. Lets say I have the numbers 0-100 in series. As the number increases, I want another number ...
13
votes
4answers
3k views

Aunt and Uncle's fuel oil tank dip stick problem

This problem first came to me in high school, and a couple times since, and I even assigned it for extra credit in one of my calculus classes after I became a teacher. So I know the solution. What I ...
0
votes
1answer
254 views

Problem related with equation consisting square root

Here's the question I've been thinking for $2$ days and couldn't find an answer why. If $Y = \sqrt{X}$, where both $X$ and $Y$ are real numbers then which of the following is true? a) $X\geq 0$; ...
9
votes
1answer
5k views

Rules for rounding (positive and negative numbers)

I'm looking for clear mathematical rules on rounding a number to $n$ decimal places. Everything seems perfectly clear for positive numbers. Here is for example what I found on math.about.com : ...
1
vote
1answer
206 views

Difference between Percentage value calculation

Here's one more question I need help with. Samir has some amount of rupees with him, the difference between 45.45% and 36.36% of which is Rs. 789435689. Find the amount. a) 8683792579 b) ...
2
votes
2answers
284 views

(PQ)²=RSP, where P,Q,R,S are distinct single digit natural numbers, then R=?

I have a problem I tried to solve, but couldn't because I don't know the method to solve it and I've never come across such problem. Here's the problem. $(PQ)²=RSP$ Where $P, Q, R, S$ are distinct ...
5
votes
5answers
339 views

Division with 4 digit number in denominator

I've got a question in my task sheet. The question is as follows. $$ \frac{43\cdot93\cdot47\cdot97}{3007}=X $$ Find the exact value of $X$. I've tried a lot, but couldn't find easier way to do it ...
5
votes
5answers
35k views

How to convert a hexadecimal number to an octal number?

How can I convert a hexadecimal number, for example 0x1A03 to its octal value? I know that one way is to convert it to decimal and then convert it to octal ...
6
votes
8answers
4k views

Need faster division technique for $4$ digit numbers.

I have to divide $2860$ by $3186$. The question gives only $2$ minutes and that division is only half part of question. Now I can't possibly make that division in or less than $2$ minutes by applying ...
10
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6answers
6k views

What calculation shortcuts exist to help or speed-up mental (or paper) calculations?

Anything to speed up or simplify calculations. A simple example might be to get a multiple of $19$, for instance, $38 \cdot 19 = 38 \cdot 20 - 38$. (This is hard to tag with so few tags in play!) ...
23
votes
6answers
2k views

$-1$ is not $ 1$, so where is the mistake?

I know there must be something unmathematical in the following but I don't know where it is: \begin{align} \sqrt{-1} &= i \\ \\ \frac1{\sqrt{-1}} &= \frac1i \\ \\ \frac{\sqrt1}{\sqrt{-1}} ...
3
votes
2answers
207 views

Faulty logic when summing large integers?

This is in relation to the Euler Problem $13$ from http://www.ProjectEuler.net. Work out the first ten digits of the sum of the following one-hundred $50$-digit numbers. ...