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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50
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10answers
28k views

Can a piece of A4 paper be folded so that it's thick enough to reach the moon?

While procrastinating around the web I stumbled on a page that contained the image below, from cracked.com. I can't help but believe that this is false… Even though the article header says: ...
3
votes
4answers
355 views

Successor of 0 is 1

Using the Peano axioms as the foundation for arithmetic (but further elementary structure can be developed), where S is the successor operation and 0 is an element of what we will call the set of ...
0
votes
1answer
51 views

Help with Geometric or Arithmetic progression

Evaluate $$2004\cdot\left(\frac{1}{1\cdot2} + \frac{1}{2\cdot3} + \frac{1}{3\cdot4}+\dots + \frac{1}{2003\cdot2004}\right)$$ I think that this is based on either geometric or arithmetic progressions ...
1
vote
1answer
106 views

The first odd multiple of a number in a given range

As a part of a programming problem I was solving, we were required to find the first offset of a range at which the number is a odd multiple of another number. For e.g: Take the range $100$ to $120$. ...
1
vote
4answers
145 views

Cancelling out square roots gives 2?

Question: If $$N = \frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}$$Find N (This is a subset of a larger question) My approach: After rationalizing the denominator, by ...
8
votes
2answers
115 views

Is $\frac{0}{0}$ different from $\frac{1}{0}$?

In my mind, zero divided by zero answers the question of what $a$, when multiplied with zero, equals zero: $a * 0 = 0$ Obviously, any real number will satisfy this equation. However, one divided by ...
2
votes
0answers
511 views

The set of all natural numbers is closed under addition

I'm trying to prove the theorem described in the title, but my proof is so obvious I doubt it is sufficient. Here's my way of proving it: Definition of addition: Let a, b, and c be natural numbers. ...
3
votes
1answer
155 views

Show that the last four digits of $2013^k$ are 0001

Show that a natural $k \ge 1$ exists s.t the last four digits of $2013^k$ (written as a decimal) are 0001. I understand that k must be of the form k=4m. The last digit of 2013 is 3 and only when ...
1
vote
0answers
151 views

Finding possible numbers to yield a certain arithmetic mean (average)

I'd like to know how I could find the possible numbers to yield a certain average number (arithmetic mean), given that: the arithmetic mean will be calculated from 20 integer numbers, each having a ...
-2
votes
1answer
208 views

Conflict between $\pi$ and ($\sqrt2/81) \times 180$

Conflict between ${\pi}$and ($\frac{\sqrt2}{81})\times 180$. $\frac{\sqrt0.5}{40.5}$ = $\frac{\sqrt2}{81}$. If I have a number 486 per example and I divide 486 by 40.5 and then by $\sqrt2$ ,I would ...
0
votes
1answer
36 views

Given a natural number $a$ find its index in a set of structural descriptions

Looking at orbits of the collatz-like $(5x+1)/2^X$ - map I come to a useful structural description for all odd integers $a$. If I write $$ {5a+1 \over 2^A} \to b \qquad \qquad \text{for odd positive } ...
0
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2answers
78 views

for a friend's birthday, a special birthday card

My question is particulary, my friend will celebrate 27 years (March 19, 1987) and we will offer him the game Diablo 3 : The reaper of Souls . So, I would write on the card all the coincidences ...
7
votes
2answers
178 views

Mental Arithmetic

This is very possibly not the best place to ask this, however it's the best I could find but please suggest anywhere else that might be better suited. I'm building a sort of challenge revolving ...
0
votes
1answer
43 views

Can't come up with the correct result.(order of operations) Could you please help?

I have the following exercise: $$2\cdot \{100\cdot 3-3\cdot [100-3\cdot (100-3\cdot 33)]\}$$ I've looked into the text book and the correct answer is $18$ but I keep getting $-99$. Here's how I ...
3
votes
3answers
284 views

Why does $\sqrt{x^2}=|x|$? [duplicate]

By convention, we say that: $$\sqrt{x^2}=|x|$$ In fact, the above statement is how we define absolute value. We would not write $\sqrt{4}=-2$. Although logically it is correct, by convention it is ...
0
votes
2answers
87 views

Rationalising the Surds

Please help me rationalise and simplify: $$ \frac{1}{\sqrt[3]{2} - 1} \ - \ \frac{2}{\sqrt{3} - 2} \ . $$ I have tried using the cube of the denominator and the square of the denominator on the ...
1
vote
1answer
165 views

Why does an odd number plus one, not necessarily entail it being even?

Why does an odd number plus one, not necessarily entail it being even? For example, $\sqrt{5} + 1$ is not even.
0
votes
1answer
70 views

Using induction to prove $\sum\limits^n_{k=1} 9^k = 0.5 \cdot \sum\limits^{2n}_{k=1} (-1)^k \cdot 3^{k+1}$

$$\sum^n_{k=1} 9^k = 0.5 \cdot \left[\sum^{2n}_{k=1} (-1)^k \cdot 3^{k+1}\right]$$ I have tested both with a python script and it seems to be correct. For the life of me, I am unable to unwind the ...
1
vote
2answers
76 views

What is the name for finding biggest two multipliers of a number?

Excuse my English please. I am looking for the name in Mathematics (/English) for finding the biggest two numbers that form an array that can contain at minimum ...
1
vote
1answer
66 views

How to solve equations with modulus in them

For e.g. (100 * X) % 35 = 25 gives X = 2 and on similar note (100 * X) % 360 = 80 gives X = 8 and it can be possible that there is no X which satisfy this for e.g. (100 * X) % 360 = 70 there ...
3
votes
2answers
57 views

Arithmetic Problem Prime numbers

Let $p\equiv 2\mod 3$ an odd prime number. Prove that: $p \mid (x^3+y^3) \implies p \mid (x+y)$ , for any integers $x,y$ $p\mid (x+y)(x^2-xy+y^2) \implies p\mid (x+y)$ or $p\mid (x^2-xy+y^2) $ ...
1
vote
1answer
40 views

Reducing simultaneously a pair of fractions $\frac{a^2}{b},\frac{ a^3}{c}$ using only gcds

Given three positive integers $a,b,c$ and I want to find the smallest positive integers $a', b', c'$ such that $$ \frac{a^2}{b} = \frac{a'^2}{b'} \quad \text{and} \quad \frac{a^3}{c} = ...
2
votes
1answer
106 views

Finding when the distances to three cities again have different digits

Very confused on this question. How would you solve it, and what would be the answer(s). Recently I was driving down the freeway and spotted the following freeway sign with the distances to three ...
0
votes
1answer
104 views

Column math please help

If I'm adding the sum of £100 +£320+£220+£20+£6+50p+20p+10p+5p+2p, how would I write that using column math. Thanks
2
votes
9answers
13k views

Can $\frac {100-100}{100-100}=2$?

\begin{align*} \frac{0}{0} &= \frac{100-100}{100-100} \\ &= \frac{10^2-10^2}{10(10-10)} \\ &= \frac{(10+10)(10-10)}{10(10-10)} \\ &= \frac{10+10}{10} \\ &= \frac{20}{10} \\ &= ...
14
votes
8answers
4k views

Meaning of $\dfrac{x-y}{y}$ versus $\dfrac{x}{y}-1$

I'm trying to understand what is probably a fairly simple math concept, but this is escaping me for some reason. Why are the results of these two expressions equal? Thanks for any responses. ...
1
vote
2answers
230 views

Loan repayment calculations when interest compounding frequency does not match repayment frquency

Is there a formula for calculating loan repayments where interest is compounded daily, but repayments are made only monthly, for instance? I would like to be able to calculate the repayment amount ...
2
votes
1answer
79 views

Need help finding closed form of finite product

Is there a closed form for this product? $$\prod\limits_{k=1}^n (n+k)$$ I checked it on wolfram alpha but it uses something called the Pochhammer symbol. Does anyone else know of a nice explicit ...
1
vote
1answer
51 views

If the sum of $-10.5$ and $+15.0$ is rounded down, it becomes $4$. How to distribute the effect of rounding among the summands?

This may seem a simple stupid question but its driving me crazy for 4 hours. I have two values $-10.5$ and $+15.0$ These values sum $4.5$. For whatever reason that doesn't matter the end result ...
3
votes
1answer
948 views

Can Pi prod be expressed using Sigma Notation?

My question is simple (but difficult for me): $\prod(x)$ be expressed interms of $\sum (x)$
1
vote
1answer
116 views

When can $a-(b-c) = (a-b)-c$?

What I'm asking is, when subtracting numbers is there any integers that make $a-(b-c) = (a-b)-c$? Besides $0$ of course. Thanks! Sorry for the stupid question.
0
votes
1answer
67 views

Distribution of liquid among different capacity cans

There are three cans A,B,C. The capacities of A,B and C are 6 liters, 10 liters and 16 liters respectively. Can C contains 16 liters of milk. The milk has to be divided in them using these three cans ...
0
votes
1answer
93 views

simplify $3x^2 \times x^2 + x^3 \times 2x$

Looking at an old assignment, and the function in the title is a derivative result of the product rule, but I've simplified it to $5x^4$, but I have forgotten how I got to that result. Anyone with a ...
0
votes
1answer
42 views

Cubing a Minterm

I've just been going over some stuff I should actually already know - and I've come to a question that has really stumped me, (my math skill are lacking) and I don't actually know where to begin on ...
1
vote
4answers
2k views

what is the best and esiest way to find Square root?

Hi to all I'm new this forum . I want to know easiest way to find squre root of large number with in a seconds without using calculator. Suppose I have 2601 and ...
2
votes
2answers
42 views

Arithmetic sets problem

I need help with a set problem Given: $$A=\{(\sqrt{n}+2) \in \Bbb Z \ /\ \ 16\le n^2 \le 1296 \}$$ $$B=\{({3m-2}) \in A \ /\ \ 4 \le 4m+3 \le 17 \}$$ Calculate the value of : $$n(A)\times n(B)$$ ...
0
votes
1answer
34 views

What percentage is the rest of the black cars in the parking lot

Ok so, Last Monday, a parking lot had 80 cars. Of those 80 cars, 25% were silver. 16 were red, and the rest were black. What percent of the cars were black
1
vote
1answer
70 views

$pq\mid (a - pq) \implies pq\mid a$?

This may be a dumb question. I'm not a math major, but, since I'm studying logic, I decided to learn a bit of number theory. I've just begun my studies (I'm reading Davenport's The Higher Arithmetic) ...
0
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3answers
259 views

negative exponent confusion

I am a bit confused with negative exponents so here is an example. Let $4$ to the $-3 = 1\div4\div4\div4 $ The thing which confuses me is the $1$, why we use $1$ before dividing. so if i do it ...
2
votes
1answer
92 views

very simple math question

I have this very simple math question: Each person starts working life on a salary of $5000$ dollars and then benefits form an annual increment of $250$ dollars over $40$ years of his career. My ...
0
votes
1answer
161 views

Why is (-1)(-1) = 1? [duplicate]

I apologize if this is too obvious, but I crave for a reasonable definition/explanation - why is $(-1)(-1)=1$? Something akin to the reason $a^{-1}=\frac{1}{a}$, I.e. because ...
1
vote
0answers
185 views

Why doesn't this base 10 number x mod 2^y work for converting base 10 to binary

Okay I tried to convert 1 million to binary by dividing by a power of 2 and taking the remainder and dividing that by a power of 2 and so on and I got this: 1111010000100100000 Google says 1 million ...
1
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1answer
88 views

Hyperoperations and $\mathsf{PA}$

I am very confused about the "role of the hyperoperations" in the peano arithmetic. For example addition's and multiplication's axioms are given. $A_1$ $\forall x(x+0=x)$ $A_2$ $\forall ...
0
votes
1answer
94 views

An easy question with integer numbers [duplicate]

I have an easy question of arithmetic. Let $a, b, N$ be integer numbers such that $\mathrm{gcd}(a,b,N) = 1$. Is it true that there exists an integer number $x \in \mathbb{Z}$ such that ...
1
vote
2answers
49 views

Approximating 'big' ratio with 'small' ratio

Given a ratio $ \frac{m}{n}, p \in N, q \in N $ where either $m$ or $n$ (or both) is a very big number, how can we find a ratio $ \frac{p}{q}, p \in N, q \in N $ which estimates $ \frac{m}{n} $ up to ...
0
votes
3answers
87 views

If I know that $S$ is a square but not its square root, how do I find the next square number?

Given a square number $s = n^2$, is there a way to find the next square $s'$ without knowing $n$? (That is, if you can't take the square root of $s$ to determine $n$, can you compute $s'$?)
0
votes
1answer
56 views

Are My Calculations right?

In My Program called More Realistic Galaxy I include all different kinds of stars and I can look up their solar mass limits. I also made it like a midnight blue instead of like black so that if a ...
0
votes
1answer
294 views

Parse Trees - Arithmetic Expressions

In regards to the right side of this expression (c * (a-b)) how is it factored to include (-) instead of * and then (-) again? I cant understand what steps my teacher made to do this.
6
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2answers
421 views

Is “applying similar operations from left to right” a convention or a rule that forces us to mark one answer wrong? [duplicate]

I saw this photo on my social network. The ambiguous expression $6\div2\times3$ yielded 2 different answers. The difference is the order of operations. If the division's done first then the answer ...
19
votes
10answers
3k views

Does there exist a system such that the additive identity is non-zero?

I am trying to explain how although the additive identity is written as $0$, it is not the same as the number $0$. For example for a $2\times 2$ matrix the additive identity is $\begin{pmatrix} 0 ...