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

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3
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3answers
234 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
62 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 ...
0
votes
1answer
46 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
60 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
58 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
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2answers
50 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
37 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} = ...
1
vote
0answers
21 views

Help with Calculating amount in pages by 2 working days

I need help with the following, I think I got this right, but wanted to pass it by the gurus/experts first: ...
2
votes
1answer
75 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
72 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
0
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7answers
1k views

What is wrong in this proof?

\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} \\ &= ...
13
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
78 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
59 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
47 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
244 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
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1answer
109 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
42 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
2answers
57 views

Fractions and division [closed]

well i am really stuck at division in school and i don't really under stand so how can you help me so i can learn better..so i really need help with rounding as well like if you round 69707 to the ...
-5
votes
1answer
164 views

“The Escalator” Question

The mathematician Henry wants to find the amount of steps visible at one time. For every step he takes, a volunteer takes one step. Henry reaches the top after 28 steps and the volunteer reaches the ...
0
votes
1answer
86 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
35 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
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4answers
338 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
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1answer
25 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
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1answer
60 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
234 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
75 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
96 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 ...
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0answers
92 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 ...
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1answer
74 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
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1answer
81 views

An easy question with integer numbers

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 ...
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2answers
38 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
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3answers
79 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
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1answer
47 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
77 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
votes
2answers
356 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
2k 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 ...
1
vote
3answers
46 views

How is HCF (c, d) = HCF (d, r), where c = dq +r (by Euclid's division lemma)?

I read this in a math textbook, stated as obvious fact. I cannot wrap my head around why this works. I understood the division lemma, and also got the algorithm to work: but the proof of why the ...
1
vote
4answers
72 views

Finding number $n$ times larger then a given negative number

This is an interesting question, and I can't really answer it. The number which is $5$ times larger than $2$ is $10$ ($2 \times 5 = 10$) But, which number is $5$ times larger then $-2$?
1
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1answer
43 views

Number of couples of positive integers whose LCM is d

Let $d$ be a positive integer with $t$ prime factors, and without any square factor. (I translate that as $d=p_1p_2...p_t$, with $p_i$ prime, with exponent always equal to $1$). Show that the number ...
0
votes
2answers
47 views

How to prove that 12:3 will always be 4

I got this riddle that I just couldnt solve. It's simple, how can you prove that a:b will always be C ? (a, b and c are natural numbers) For example 12:3=4, 4 will be the only solution.
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2answers
85 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
votes
2answers
52 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 ...
0
votes
4answers
73 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.
0
votes
2answers
89 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 : ...
0
votes
1answer
46 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
votes
1answer
48 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
votes
2answers
78 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 ...
0
votes
2answers
32 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 ...