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

learn more… | top users | synonyms (1)

1
vote
0answers
36 views

Is $\sum_{i=1}^n i = \sum_{i=n}^1 i$

When I enter these expressions into wolfram I get that they're not equal. Why is this? Essentially I'm trying to say $$ 1+2+\cdots+n = n+(n-1)+\cdots+1 $$
0
votes
1answer
29 views

From an expression raised in a power of 2 to an expression raised in the power or 10

Is there a simple/"easy" way to convert a big number from a power of $2$ to a power of $10$ equivalent. Example: I had $2^{127}\cdot 1.9999999$ which I did the multiplication got the result and from ...
15
votes
3answers
2k views

In primary school I was showed this. Why does it work?

When I was in primary school a teacher showed us the following exercise in arithmetic. Take any 3 digit number between 201 and 998 provided that the hundreds digit is bigger than the ones digit and ...
-1
votes
0answers
12 views

arithmetic calculations [on hold]

A work detail of nine people consisted of eight laborers and one supervisor. The supervisor instructed five laborers to plant shrubs along a portion of a highway. The supervisor instructed the rest ...
0
votes
2answers
40 views

Multiplication of repeating decimal $0.3333\overline{3}$ by $3$ [duplicate]

Let's start considering a simple fractions like $\dfrac {1}{2}$ and $\dfrac {1}{3}$. If I choose to represent those fraction using decimal representation, I get, respectively, $0.5$ and ...
1
vote
0answers
48 views

Types realized in ultrapowers consisting of definable functions

Let $\mathcal{M}$ be a nonstandard model of arithmetic and let $M$ be its universe. Let $U$ be a nonprincipal ultrafilter over $M$ and let $\mathcal{N}$ be the ultrapower $\mathcal{M}^M / U$. Let $F$ ...
-2
votes
1answer
17 views

length of the fence in feet? (12 inches = 1 foot) [on hold]

A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following could not be the ...
4
votes
4answers
65 views

Rationalize $\left(\sqrt{3x+5}-\sqrt{5x+11} -\sqrt{x+9}\right)^{-1}$

I was trying to find if there a method similar to multiplying and dividing by the conjugate $$\frac{1}{\sqrt{3x+5}-\sqrt{5x+11} - \sqrt{x+9}},$$ but that doesn't seem to work here. Also, is there a ...
0
votes
1answer
17 views

SAT Math Problem about decimal

In the decimal representation of $\frac{1}{k}$, where $0 < \frac{1}{k} < 1$. the tenths digit is $1$, hundredths digit is $3$ and at least one other digit is nonzero. What is the tenths digit ...
5
votes
4answers
1k views

Why exactly does the distributive property work?

Suppose I have this expression that needs to be simplified: $$4(2x + 4)$$ It can be simplified down to this: $$8x + 16$$ In this case, this expression has been simplified down using the ...
0
votes
1answer
32 views

General formula for a series

I am trying to solve series of the form, T(n) = T(n/4) + clog(n) I am able to formulate a general formula for the T(n) term for the nth term. Its of the form ...
0
votes
1answer
29 views

Formula for the floor of $n/2$, to be proved by induction

How do you compute this when the base case is all wrong?
0
votes
1answer
9 views

Operations on a set of numbers to leave the median unchanged

Set Q contains 14 distinct numbers. Which of the following operations would decrease the average of set Q while leaving the median unchanged? A. Decreasing all 14 numbers by 2 each B. Increasing the ...
0
votes
2answers
38 views

Inversing fraction

I'm having a little trouble understanding the logic behind solving the following equation: $(24/25)\times a = b \times \cos(12)$ we need to seperate a from the equation so it becomes $a = (b \times ...
1
vote
3answers
47 views

How to find $n$-th value in a series

Let $(x_n, y_n, z_n) = (3, 1, 0)$ for $n=0$ For $n \ge 1$, $$\begin{align} x_n &= x_{n-1} +3 z_{n-1}\\ y_n &= x_{n-1} +2 z_{n-1}\\ z_n &= 5 y_{n-1} \end{align}$$ Please let me know the ...
4
votes
4answers
259 views

Mean/Median/Mode question?

I came across the following problem: A list of 11 positive integers has a mean of 10, a median of 9, and a unique mode of 8. What is the largest possible value of an integer in the list? From the ...
-1
votes
3answers
38 views

How to find the total amount from given percentage

I am trying to answer this question from internet for my mathematics practice. ...
0
votes
1answer
25 views

Check whether an image is proportional to a given one

I wonder how can I test whether the size of an image is proportional to $250\times 167$. For example, I have an image size of $1000\times 668$ and would like to see if it is proportional to ...
0
votes
1answer
20 views

Find base of numbers in a sum?

is there an easier way to find the base A in the following without essentially brute-forcing it with different conversions until I get the result? Again, trying to find base A such that the following ...
0
votes
3answers
41 views

How to find the total investment from interest received

Dave Horn invested half of his money at $5$%, one-third of his money at $4$%, and the rest of his money at $3.5$%. If his total annual investment income was $\$530$, how much had he invested? I found ...
-2
votes
2answers
72 views

What is $\sqrt{x^2}$ when $x<0$? [closed]

$x\in \mathbb{R}$\ $\{0\}$ $$\frac{\sqrt{x^2}}{|x|}+1 =?$$ What is the answer when $x \lt 0$? $2$ or $0$?
0
votes
3answers
27 views

Generiloze: the difference of two squares is equal to a odd number.

For example, 3 = 2^2 - 1^2 5 = 3^2 - 2^2 7 = 4^2 - 3^2 ... Is there a general formula to explain this phenomenon?
0
votes
1answer
34 views

$ \sqrt[5]{x^3} = (\sqrt[5]{x})^3 $?

$ \sqrt[5]{x^3} = (\sqrt[5]{x})^3 $ ? I would suppose so given that $ x^{3/5} = x^{3(1/5)} = \sqrt[5]{x^3} $ or $ x^{3/5} = x^{(1/5)3} = (\sqrt[5]{x})^3 $
0
votes
2answers
52 views

Is there a general way to do arithmetic involving binomials more quickly?

I'm talking about exercises like these for example: $ (a+2b)^3 - (a-2b)^3 $ $(a+b+c)(a+b-c)(a-b+c)(a-b+c)(-a+b+c)$ Of course these can be done the time-consuming and mentally easy way, but are ...
0
votes
2answers
31 views

Simplifying $0.300 (1 \pm 0.0633)$

This problem had to do with finding area with uncertainty, I got this far but I'm not sure how to go on. The answer to the next step is $(0.300 \pm 0.0190)$. How do they get this? What do we do with ...
0
votes
0answers
20 views

when to use ( end point/date - start point/date + 1) , and when to use end point /date - start point /date?

This is a simple question on difference. I have seen the following situation - for example how many day you spend on a travel when the travel date was 14-Aug-2014 till 25-August-2014. The answer for ...
2
votes
1answer
23 views

Shared groceries expenses between roommates to be divided as per specific consumption ratio and attendance

My apologies if this question is in the wrong section. Couple of my roommates & I (total 5 people) share the groceries expenses. We record the purchases in an Excel sheet, and also have the ratio ...
1
vote
2answers
49 views

How to reduce large combinations?

The result of a hypergeometric distribution question that I posted about earlier this evening is what follows: $$\frac{{30 \choose 10}{20 \choose 5}}{{50 \choose 15}}$$ This becomes: ...
4
votes
1answer
72 views

What is $\sqrt{-x^3}$?

What is $\sqrt{-x^3}$, assuming $x \in \mathbb R$ and $x < 0$? It seems as if there are two possibilities: $\sqrt{-x^3} = \sqrt{-x\times x \times x} = \sqrt{-x \times x^2} = x\sqrt{-x}$ ...
1
vote
5answers
45 views

Not clear on what we mean with numbers with infinite digits

I am confused on a rather simplistic question. 1/3 = 0.333333333333 to infinity. So it has infinite digits. How is it possible to multiply such a number with another one and get a finite number? 6/3 = ...
6
votes
5answers
2k views

Arithmetic mean. Why does it work?

I've been using the formula for the arithmetic mean all my life, but I'm not sure why it works. My current intuition is this one: The arithmetic mean is a number that when multiplied by the number ...
-1
votes
0answers
17 views

divide amount spent equally

Me and my friend needs to divide the amount spent equally. He brought food worth of 20 dollars and I brought worth of 130 dollars. Now I need to divide this money equally so that we both spend equal ...
5
votes
2answers
83 views

Efficiently factoring polynomials over $\Bbb F_2$

I am attempting to write some software which is intended to generically answer the question of which Cyclic Redundancy Code (CRC) generating polynomial is used for a given set of sample messages using ...
1
vote
1answer
30 views

Yet another product of irrational numbers

Let $~\alpha~$ and $~\beta~$ be irrational numbers such that $$~\alpha \notin \{\beta, -\beta\}$$ and $$~\alpha \notin \left\{\frac{1}{\beta}, -\frac{1}{\beta}\right\}$$ I suppose that in this case ...
0
votes
2answers
93 views

Evaluate $\sqrt{1 + 2\sqrt{1 + 3 \sqrt{1 + \dots}}}$ [duplicate]

I was asked to show that the answer is 3. I don't have any idea on how to proceed. Thanks!
3
votes
4answers
334 views

General formula of repeated roots.

Prove that $$\underbrace{\sqrt{k\sqrt{k\sqrt{k\sqrt{\cdots\sqrt{k}}}}}}_{n\text { times}}=k^{1-1/2^n}$$ How do I derive this formula?
2
votes
2answers
38 views

Square grid , sum of elements

I am trying to solve the following problem : Find all the positive integers $n$ and $k$ such that it is possible to write integers in an $n \times n$ grid so that the sum of all elements in the grid ...
0
votes
2answers
46 views

How do break down this addition?

I've been given the following expression: $2(a + b) + (n + 1)(2a + c) + 2n(2a + d + b) + (a + r)$ And I've been told that it can be simplified to: $n(6a + 2b + c + 2d) + (5a + 2b + c + r)$ I've ...
5
votes
3answers
131 views

The proof of $\sqrt{2}$ is not rational number via fundamental theorem of arithmetic.

I assume that $\sqrt{2}$ is positive number satisfies $(\sqrt{2})^2=2$. proof) Let $m$, $n$ as natural number,$\ $ $M$ is the number of prime factor of $m$,$\ $ $N$ is also the number of prime ...
0
votes
1answer
78 views

Divisibility rule for 22

Divisibility rule for 22: Under what conditions a natural number $N$ is divisible by $22$ ? My thought is The divisibility rule for $22$ is that the number is divisible by $2$ and by $11$. ...
1
vote
1answer
17 views

Calculation of a value for number divisible by 11

Calculates the value $x$ for the number $M=5278x$ is divisible by 11 my attempt, $11\mid M=5278x \Longleftrightarrow (5-2)+(7-8)+x=2+x$ is multiple of $11$ $ 2+x$ is multiple of $11 ...
2
votes
2answers
57 views

Divisibility rule of 11

Let $M$ be a natural number with $n+1$ digits; represented by $M=a_{n}a_{n-1}\cdots a_{2}a_{1}a_{0}$ Show $M$ is divisible by $11$ if and only if ...
19
votes
10answers
3k views

Get $5$ by doing any operations with four $7$s

How can one combine four sevens with elementary operations to get $5$? For example $$\dfrac{(7+7)\times7}{7}$$ (though that does not equal $5$). I am not able to do this. Can you solve it or prove ...
2
votes
0answers
56 views

What was babylonians estimation for square root 3?

We see a lot of papers and talk about ancient Babylonians exactness of calculating the value of square root of 2. For example: ...
2
votes
1answer
32 views

Represented in basis X

Let ABCD represent the digits of the starting number. The four digit number would be represented in basis $X\in \mathbb{N}$ by : $$\textrm{ABCD}=X^{3}.A+ X^{2}.B+ X^{1}.C+ X^{0}.D$$ Am I ...
1
vote
2answers
81 views

How to simplify $\sqrt{\sqrt{5}+1} \cdot \sqrt{\sqrt{5}-1}$?

This is the original problem: $\sqrt{\sqrt{5}+1} \cdot \sqrt{\sqrt{5}-1} = x$. I'm really confused about how to solve this problem, I come as far as saying this: $\sqrt[4]{5} + \sqrt{1}\cdot ...
3
votes
4answers
39 views

What's the intuition for why repeated div and mod converts a number to another base?

This guide here tells how to base 10 number to binary. For example, for the first bit, you take $356_{10} \div 2 = 178 \, R \, 0$. Because the remainder was 0, the first bit is $0$ and we recurse ...
2
votes
1answer
134 views

Turing machines that compute $\pi$

For each $K > 0$ there is a brut force Turing machine $\pi_K$ that "computes" the first $K$ digits of $\pi$ starting on the blank tape (all $b$s) with $K+1$ states $S \in \mathsf{S} = ...
0
votes
3answers
71 views

Particular number is divisible by 11

Let $\mathcal{N} \ $ be a natural number of the form $\mathcal{N}=\textrm{dcba}$ ($a$ being the number of units $b$ the tens digit $c$ the hundreds digit and $d$ the thousands digit). On what ...
0
votes
0answers
16 views

add 5 nos such that ans is 30 from following nos and nos can be repeated [duplicate]

use five nos from the following: 1,3,5,7,9,11,13,15 such that by adding them result is equal to 30 ++++_=30 nos can repeat themselves according to the question we ...