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

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0
votes
1answer
27 views

Simplifying sum of sort

I want to know that simple method of sqrt sum I have 10 values of some information. Let these be $d_1 , ... , d_{10}$ And I want to calculate $\frac {\sqrt d_1+...+\sqrt d_{10}}{10}$ in computer ...
-3
votes
0answers
33 views

I guess I have found a possible explanation of “Collatz conjecture”. So, how can I publish it? [duplicate]

Please anyone help me in this. This is going to be my first one. So, can anyone good me in this.
8
votes
4answers
120 views

Is there $n$ such that $n,n^2,n^3$ start with the same digit ($\neq 1)$

From the 2015 Moscow Mathematical Olympiad: Is there some $n>2$ such that $n,n^2$ and $n^3$ start with the same digit (this digit being different from $1$) Using a computer I found that $99$ ...
0
votes
1answer
48 views

Finding square of cube? [on hold]

A cube is built using $64$ cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in square units) after ...
0
votes
1answer
22 views

Problem on Time and Work

$A$ can do a piece of work in $10$ days, $B$ can do in $20$ days and $C$ can do in $30$ days. If $A$ is assisted by $B$ and $C$ turn by turn in alternate days respectively, in how many days the work ...
3
votes
2answers
73 views

Fraction Sum Series

This question was asked in (selection) IMO for 8th graders. $1/2 + 1/6 + 1/12+ 1/20 + 1/30 + 1/42 +1/56 + 1/72 + 1/90 + 1/110 +1/132$ I have noticed that it can be written as $1/(1*2) + 1/(2*3) ...
-1
votes
0answers
15 views

How to subtract fractional numbers using complements.

I know how $10$'s and $9$'s complements are used, but I don't know how to use complements to subtract two fractional numbers. For example $108.32-26.30$ . How will we solve it using $10$'s and $9$'s ...
-1
votes
2answers
49 views

How calculate the rest of the division 2/7 [on hold]

How can I calculate the rest of division about two / seven? According to this video (https://youtu.be/Nu-lW-Ifyec?t=113) the result of this division is two. But how can I know that? In calculator the ...
0
votes
3answers
43 views

Complex Addition

Solving a question, I need to find the value of following in between the solution. $$(\frac{i+\sqrt3}{2})^{200} + (\frac{i-\sqrt3}{2})^{200}$$ The only useful thing I got was ...
0
votes
2answers
36 views

A reduction of $10\%$…

A reduction of $10\%$ in the price of sugar would enable a man to buy $2\,\rm{kg}$ of sugar more for Rs. $125$. Find the reduced price per kg. My attempt: Let the initial price of sugar be Rs. $x$ ...
0
votes
2answers
36 views

How is unique factorization of integers related to computing greatest common divisors?

Source: Discrete Mathematics with Applications, Susanna S. Epp. What does the unique factorization of integers have to do with gcd $2^{10}$ of ($10^{20}, 6^{30}$) in Example 4.8.5.b? ...
7
votes
3answers
97 views

What is the sum of all the natural numbers between $500$ and $1000$.

What is the sum of all the natural numbers between $500$ and $1000$ (extremes included) that are multiples of $2$ but not of $7$?
0
votes
1answer
36 views

Solve this simple problem of Simplification [on hold]

Simplify $14-\frac{21}{7}+4*2$ Answer given is $3$ but mine is $19$. Where am I doing wrong?
0
votes
3answers
36 views

Which of the following integers cannot be expressed as the sum of two prime numbers? [on hold]

Please help me with this problem. I'm stumped! which of the following integers cannot be expressed as the sum of two prime numbers? A) $8$ B) $9$ C) $10$ D) $11$ E) $12$ According to the GRE ...
0
votes
0answers
43 views

Standard name or notation for the “even part” of an integer?

\begin{align} 0 & \mapsto 0 \\ 1 & \mapsto 0 \\[6pt] 2 & \mapsto 2 \\ 3 & \mapsto 2 \\[6pt] 4 & \mapsto 4 \\ 5 & \mapsto 4 \\[6pt] 6 & \mapsto 6 \\ 7 & \mapsto 6 \\ ...
0
votes
1answer
46 views

Why does lattice multiplication work?

My brother (who is currently in 4th grade) is learning a technique called Lattice multiplication in school. It is a technique that involves taking two numbers, placing them on the outside of a square, ...
0
votes
0answers
16 views

Approximate ratio with a small fraction so that numerator multiplied by denominator give enough rectangular area?

I would like to layout given number of objects (like plots) into rectangular area (like computer operating system window on screen). I would like to calculate the width and height of the window (in ...
0
votes
1answer
20 views

Doling out money constantly arithmetic progression [on hold]

okay, if an enterprise want to pay to $10$ best workers and could distribute $\$35,000$ among them to tenth worker receives $\$1,500$ and if the difference among each is constant. how much money ...
1
vote
1answer
20 views

Convert base y to base 10

I have a problem to find base y. The equation given is ($1111011$)gray + ($123$)y + ($211.1$)3 + ($34.4$)$6$ = (CD)$16$ + ($40$)y - ($10010$)BCD. I am able to simplify by converting everything ...
0
votes
0answers
13 views

How to visualize the product of two segments lengths? [duplicate]

So there seems to be easy ways to visualize addition. If three points a, b, and c are on the same straight line respectively, we can say that the sum of the lengths of ...
0
votes
2answers
32 views

Q: Quadratic Division - How to divide two quadratics?

My studies into graphs and models following examples from Khan Academy has helped me on my goal to learn how to chart and model via the quadratic formula However while I have been successful in ...
1
vote
0answers
17 views

Money-Business Stocks [closed]

Let's say I work in retail and at the beginning of the month, my stock ownership is \$350,000.00. Over time, my sales are \$78,000.00 and my stock is reduced by \$32,000.00 worth of markdowns. my ...
0
votes
2answers
34 views

What is one possible distance (in km) at which I live from Arun’s place?

Michael lives $10$ km away from where I live. Ahmed lives $5$ km away and Susan lives $7$ km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the ...
-1
votes
1answer
16 views

Signed binary number [closed]

What is the range of number that can be represented by a 16 bit signed binary numbers ? How many are negative and positive numbers ? Thanks.
2
votes
2answers
40 views

What is the property of addition called when you break 97 into 100 - 3?

Sometimes it's easier to add numbers when you recognise that they're close to some round number, and then add the differences separately. $$97+198$$ $$=(100-3)+(200-2)$$ $$=(100+200)+(-3-2)$$ ...
1
vote
0answers
22 views
+50

Computing Bessel functions in complex interval arithmetic

Does anyone know any resource of algorithms for evaluating the Bessel function of the first kind and second kind under interval-valued domains? In particular, I am interested in complex interval ...
1
vote
3answers
31 views

For how many days will the food last in garrison?

A garrison has sufficient food for $75$ soldiers for a period of $90$ days. After $10$ days, one third of the soldiers leave. After another $10$ days, $5$ soldiers return, From this day on, ...
-3
votes
0answers
39 views

Optimal solution and Answer [closed]

Batman has devised a plan to lure Superman to a high rise building. His brilliant plan is to pour concrete over him to immobilize him, and then throw him off the building so that the concrete breaks ...
-1
votes
5answers
61 views

Can a decimal multiplied by another decimal ever equal an integer? [closed]

Any decimal number between 0 and infinity that multiplied by itself or another decimal number. Like 0.4 times 0.25, 2.425 times 2.425 and so on.
9
votes
6answers
835 views

Squaring both sides when units are different?

Given $((9) \text{inches})^{1/2} = ((0.25) \text{yards})^{1/2}$, then which of the following statements is true? $((3) \text{inches}) = ((0.5) \text{yards})$ $((9) \text{inches}) = ((1.5) ...
0
votes
2answers
24 views

Binary arithmetic - overflow and carryout at same time?

In binary arithmetic, When you subtract 2 signed numbers you must discard the carry out. My question is, is it possible for overflow to occur and a carry out? So, on paper there would be two extra ...
29
votes
16answers
4k views

How did the rule of addition come to be and why does it give the correct answer when compared empirically?

I'm still a high school student and very interested in maths but none of my school books describe these kind of things, and only say how to do it not the whys. My question is very simple, for example: ...
3
votes
1answer
17 views

Relationship between operations of a ring

Is there any requirement that the two operations of a ring have to be related to each other, excluding the requirement of distributivity? We all know from grade school that multiplication of integers ...
2
votes
2answers
29 views

Irreducible vs. reducible fractions

Let $a,b,c,d$ be positive integers. Suppose that $$\frac cd=\frac ab.$$ I want to prove that if $a$ and $b$ are relative primes, then $c/a=d/b$ is an integer. That is, the only way a fraction can be ...
1
vote
3answers
122 views

Book on foundational reasoning of standard arithmetics “curriculum”

I am interested in a book that is about arithmetics but the presentation is not just the known to all formulas but the foundational logic behind it. The closest example I can think about is the way ...
3
votes
1answer
38 views

Simple property of power of -1

Is $(-1)^{a+b} = (-1)^{a-b}$ true $\forall a,b \in \mathbb{Z}$ ? My argument: $$ (-1)^{a-b} = \frac{(-1)^a}{(-1)^b} = \frac{(-1)^a}{(-1)^b}.\frac{(-1)^b}{(-1)^b} = \frac{(-1)^{a+b}}{(-1)^{2b}} = ...
0
votes
1answer
20 views

Possible Typo in Manipulation of Expressions

Someone claimed that the following two expressions are equal. But after much manipulation, I cannot establish their equality. Is there in fact a typo somewhere? $C(x_1^2+x_2^2)^{-(a+p)/2} x_1^p$ ...
0
votes
1answer
22 views

Formula for monetary amounts with equal taxes

My colleague ran into the following problem while writing billing software. Suppose you have a monetary amount $M$ and a tax rate $t$. For example, $M = 20.1253$ and $t = 0.07$. The question is ...
4
votes
5answers
69 views

Why is the solution to $\sqrt{6-5x}=x$ only $x=1$ and not $x=-6$? [duplicate]

I solved the equation $\sqrt{6-5x}=x$ as follows: $$(\sqrt{6-5x})^2=x^2$$ $$6-5x=x^2$$ $$0=x^2+5x-6=(x+6)(x-1)$$ $$x=-6 \quad \text{or} \quad x=1$$ If I plug in $x=-6$ into the original equation, I ...
0
votes
1answer
38 views

Is $\displaystyle\lim_{h \to 0} H_n(f(h), g(h)) = H_n(\displaystyle\lim_{h \to 0} f(h), \displaystyle\lim_{h \to 0} g(h))$ true for all $n$?

Consider the limit $\displaystyle\lim_{h \to 0} H_n(f(h), g(h)), $ where $H_n(a, b)$ denotes the $n$th hyperoperation $H_n(a,b) = a \uparrow^{n-2}b$ with both $f(x)$ and $g(x)$ being continuous and ...
1
vote
3answers
65 views

Problematic square root [duplicate]

Ok, here is what I think. Please correct me if I am wrong. $$\sqrt{9} \neq 3$$ and also $$\sqrt{9} \neq -3$$ Now let's assume, that above statements are false, then we have $-3 = \sqrt{9} = 3$ and ...
1
vote
1answer
21 views

Inverting the equality which contains the operation of taking integer part

I was recently presented with the following equality $$ n = \left[\frac{w}{2d+a}\right]\cdot \left[\frac{h}{2d+b}\right] $$ where all participating variables are non-negative integers, and $[\ldots]$ ...
1
vote
1answer
28 views

Integer Y with N Repeating Digits of X?

I have a single Base 10 digit X. I want to return number Y where Y is digit ...
0
votes
0answers
25 views

Are there clear, formal definitions for “terms” in subtraction operation?

I tutor children of all ages in Mathematics and I've noticed so many different words thrown around regarding binary operations, particularly with subtraction. For example, when working with a 2nd ...
1
vote
1answer
38 views

How many non-negative integers less than $10000$ are there such that…

I am stuck with the following two problems : How many non-negative integers less than $10000$ are there such that the sum of digits of the number is divisible by $3$ ? The options are : ...
7
votes
3answers
164 views

Variety of proofs of a simple proposition in arithmetic

I have a couple of simple proofs of a simple proposition and I'm curious to see the variety of different approaches others would take to prove the same thing. Definition: The dilation of a sequence ...
1
vote
3answers
55 views

Is $p-t(p+q)$ the same as $p+t(q-p)$

This might be a silly question, but is $p-t(p+q)$ the same as $p+t(q-p)$? Not that it matters, but this is a formula in linear algebra called two-point form. The original formula is $(1-q)p+tq$ and I ...
1
vote
2answers
25 views

Sum based on sub-sums

Let's say, we have three numbers: $a, b, c$ but we know only their sums: $x = a + b, y = b + c.$ Is it possible to find sum $z = a + b + c$? edit - $a, b, c$ are natural numbers
0
votes
1answer
67 views

How can I average two integers digit by digit?

I would like to take two integers of similar size (about the same number of digits) and average them, without having to first add them, and then divide the result by two. Let's say I have the ...
-4
votes
3answers
50 views

What will be value of 0/0? [duplicate]

We know $\frac{\text{equal things}}{\text{equal things}}=1$,$\frac{\text{anything}}{0}=\text{undefined}$, and $\frac{0}{\text{anything}}=0$. Then why does $\frac{0}{0}=0$. Could it also be $1$ or ...