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

learn more… | top users | synonyms (1)

1
vote
1answer
49 views

A strain of bacteria doubles every 14 h. If there are 100 bacteria cells to start with in a colony, how many will there be in 7 days?

A strain of bacteria doubles every $14$ h. If there are $100$ bacteria cells to start with in a colony, how many will there be in $7$ days? This is a sequence question. My answer: We start with ...
15
votes
5answers
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 ...
6
votes
1answer
74 views

Why is multiplication treated differently to addition?

I am a grade 11 student in South Africa. Just so you know, this is my first time posting here. My understanding is that multiplication is simply a shorter way of writing addition problems. E.g. ...
3
votes
2answers
43 views

How do we find out angle from x & y coordinates?

I found the following sentence. To find the angle you use the arctangent function like this, angle $=\tan^{-1}\left(\frac{y}{x}\right)$. But I am curious, is this the only way to know the angle? ...
6
votes
2answers
180 views

How to find out the greater number from $15^{1/20}$ and $20^{1/15}$?

I have two numbers $15^{\frac{1}{20}}$ & $20^{\frac{1}{15}}$. How to find out the greater number out of above two? I am in 12th grade. Thanks for help!
0
votes
2answers
63 views

Paradox - minus one equals one using square roots [duplicate]

I was looking on Howard Eves's book "An Introduction to the History of Mathematics" and I stumbled upon a demonstration on how $-1 = 1$. The demonstration follows: $$ \sqrt{-1} = \sqrt{-1} $$ $$ ...
0
votes
3answers
20 views

Regarding the simplest multiplying methods

I got something method like the simplest multiplying methods when I googling. If you had a number, like 123.456 and you wanted to multiply by 100 you'd just ... Move the decimal point to the ...
0
votes
0answers
28 views

Modulus to a range -x to x

I'm trying to solve positions of the planets as described in this paper. Step 3 of the computation starts with "Modulus the mean anomaly so that $-180^o \lt M \lt +180^o$." I understand what that ...
2
votes
4answers
111 views

How does one explain addition?

What is $1 + 2$? The question may seem dumb but how can one prove the answer? I heard there is a proof but don't know where to find it so please help. Thanks in advance.
53
votes
17answers
16k views

Why is 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) ...
1
vote
1answer
23 views

Multiplication and binary xor

I have to prove one thing that combines logical xor and arithmetical sum of binary representation of some numbers. Could you direct me what can I read on this topic? Specifically, I need to prove ...
0
votes
2answers
37 views

Why negative times negative is positive? [duplicate]

I know that many people would say I don't even know this. But I know it very well that negative × neagtive = positive. But I don't know Why? So kindly give a logical answers.
2
votes
1answer
67 views

How can one make sense out of a negative number?

We know that if you have 3 apples and somebody gives you 4 apples, you then have 7 apples but then if we deal with negative numbers and we have -3 apples and somebody gives us -4 apples, things can ...
0
votes
0answers
18 views

Question about the sums of the entries in an infinite array

Imagine you have an infinite array of numbers. You can divide this array in columns with labels of opposite signs that go to infinity and negative infinity starting from the center of the array. Each ...
7
votes
6answers
1k 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 ...
1
vote
2answers
57 views

Why do Smith numbers have to be composite numbers?

As you may know, a Smith number is a number that if all the digits are added together that answer is equal to the sum of its prime factors' digits. Why are 2 and 3 not Smith numbers?
1
vote
2answers
20 views

Problem in substitution

I have a very stupid question, it seems that I've forgotten most of my math and can't figure this out. Considering the following, ...
0
votes
1answer
34 views

Link between two products

Could someone help me to solve this problem : Let's denote by $A_i$ the following product, $$ A_i = \prod_{\substack{k=1 \\ k\neq i}}^n (a_k - a_i) $$ Is there any link or simple formula between ...
-2
votes
1answer
47 views

Integer value of cubic polynomial [closed]

I need help on the next problem. Let $a,b,c$ be real numbers, consider $f(x)=x^3+ax^2+bx+c$. If $f(2013), f(2014), f(2015)$ are all integers, then $f(n)$ is an integer for all integers $n$. I ...
4
votes
5answers
209 views

What is the remainder when $213987654213473846989272654857367287454572836418486364$ is divided by $48$? [closed]

Can it be done by hand i.e. to find the remainder when $213987654213473846989272654857367287454572836418486364$ is divided by $48$?
-2
votes
1answer
2k views

brain teaser that has me totally confused [closed]

A man stole \$50 from a shop owner. He came back and used the same \$50 to purchase a bread that cost \$40 and received \$10 change. How much money in all did the shop owner lose?
1
vote
5answers
4k views

Absolute values of 1-10 in a pyramid form

_ _ _ _ \/ \/ \/ _ _ _ \/ \/ _ _ \/ _ you have numbers 1-10. you can only use each number once and the number below is equal to the absolute ...
2
votes
1answer
20 views

Tools for dealing with a divisibility problem with powers of 2 and 3?

I'm trying to solve an equation with congruences: $$ \sum_{i=1}^{N}2^{\sum_{j=1}^{i} n_j}3^{N-i} \equiv 0 \; (\text{mod} \; 2^{\sum_{j=1}^{N}}-3^N) $$ The unpacked version (assuming ...
5
votes
4answers
48 views

How to determine the number removed from the list [duplicate]

One number is removed from a set of integers from 1 to n,the average of the remaining numbers is $\large{\frac{163}{4}}$. Which number was removed? I tried to find the mean of ...
2
votes
1answer
28 views

Last Value of an Arithmetic Sequence of a Particular Sum

I was able to derive the formula for summing consecutive integers: sum $= \dfrac{n(n + 1)}{2} \Longrightarrow n = 4$, sum $= 10$ Nothing difficult there, but then I would like a formula for giving ...
-1
votes
1answer
40 views

Finding the solution to an equation using trial and improvement. [closed]

Using trial and improvement to find this solution to 2 decimal places. The equation $x^3=10-3x$ has a solution such that $1 \le x\le 2$.
1
vote
1answer
41 views

Simple Interest Problem Ambiguity in Conventions

I am solving some simple interest problems. Following questions are creating ambiguity with conventions, hope someone will clarify what is going on. In what time does sum of money become 4 times ...
0
votes
1answer
757 views

Priority of parentheses and brackets in basic arithmetic.

Wolfram alpha is giving inconsistent results to this problem: When I enter: 16÷2( 8-3(4-2) )+1 the result is 17. When I enter: 16÷2[ 8-3(4-2) ]+1 the result is 5. and 16÷2*[ 8-3(4-2) ]+1 brings ...
4
votes
3answers
150 views

Why does $\frac{49}{64}\cos^2 \theta + \cos^2 \theta$ equal $\frac{113}{64}\cos^2 \theta $?

I have an example: $$ \frac{49}{64}\cos^2 \theta + \cos^2 \theta = 1 $$ Then what happens next: $$ \frac{113}{64}\cos^2 \theta = 1 $$ Where has the other cosine disappeared to? What operation ...
5
votes
2answers
212 views

Find $x;y$ such that: $\frac{x^2+y^3}{xy-1} \in \mathbb{Z}$ [closed]

Let $x,y \in \mathbb{Z}$ such that: $$\frac{x^2+y^3}{xy-1} \in \mathbb{Z}$$ Find $x,y$ I don't have any ideas about this problem.
0
votes
0answers
25 views

Uniqueness of finite continued fractions expansions

Under wich condition on $a_0, \dots , a_n$ the continued fraction expansion of a positive rational number $$r= a_0- \frac{1}{ \ddots -\frac{1}{a_n}}$$ is unique?
0
votes
5answers
489 views

Does the zeroth root exist?

Definition of Nth root: 3rd order inverse group 1 hyperoperation. Division is how many times you can subtract a certain divisor from the dividend before it becomes negative. Likewise Nth root is ...
0
votes
0answers
35 views

How to find the nth term of the merged Mutiplication Table of two numbers?

Given two numbers $x$ and $y$ both $\le 2000$ and $x\le y$. Multiplication table is build of $x$ and $y$ and merged and terms arranged in ascending order, removing the duplicates and finally, need to ...
0
votes
0answers
17 views

Clarifying Areas in terms of circles(Help Please) [duplicate]

Clara the Calculus Cow has been tied to a silo with radius r by a rope just long enough to reach a point diametrically opposite to the point where she is tied If she goes to the left side of the ...
0
votes
0answers
28 views

upper and lower bounds related to $\sqrt[3]{a^3 + b}$ with $b \ll a$

We can use Taylor series to approximate $a + \frac{b}{3a}\approx \sqrt[3]{a^3 + b}$ with $b \ll a$. However, what are precise upper and lower bounds for this quantity? $$ a + \frac{b}{3a^2} < ...
-1
votes
1answer
37 views

$|x+2|\ge 0.001$ at wolfram alpha [closed]

Shouldn't it be $x\ge -1.999$ and $x\le -2.001$? Why wolfram alpha says $x>-1.999$? http://www.wolframalpha.com/input/?i=|x%2B2|%3E%3D0.001 Sorry by the stupid question
10
votes
2answers
56 views

Interesting Array of Integers with Strange Pattern

I was experimenting and I found this pattern: Start with an (infinite) array with top row with all ones, and leftmost two columns also all ones. $$ \begin{matrix} 1 & 1 & 1 ...
3
votes
2answers
65 views

Is there a mathematical term for three orders of magnitude?

I've been playing this github game for a while called Swarm Simulator. I like it a lot and there are a bunch of other simulators going around either in-browser like Swarm or iOS apps, etc. These ...
0
votes
1answer
41 views

Interpreting predicate formulas in the structure of arithmetic

Given two formulas a) $(\forall x)(\phi(x)\rightarrow\varphi)\;\;\;\;\;\;$ b)$(\forall x)\phi(x)\rightarrow\varphi\;\;\;\;\;$ Let $\;\mathbb{S}=(\mathbb{N},+,\times,\le,0,S)$ (where $S$ stands for ...
2
votes
10answers
309 views

Difference between $\sqrt{x^2}$ and $(\sqrt{x})^2$

According to my logic, $$\large\sqrt{x^2} = x^{2\times \frac{1}{2}} = x = x^{\frac{1}{2}\times 2}={(\sqrt{x})}^2$$ But when I look at the graphs of these guys, they're totally different. Edit: ...
8
votes
8answers
1k views

Compare two powers of numbers without common divisor

Which of the numbers $2^{60}$ and $3^{43}$ is greater? There is no common divisor and it must be done without a calculator.
1
vote
3answers
169 views

Finding the square root of a big number, like 676? [closed]

I am having trouble understanding and finding the square roots of large numbers. How would I go about finding this number efficiently?
4
votes
2answers
90 views

Are $+, -,\times,\div$ the “base” calculations?

My friend told me that every equation possible with modern mathematical notation boils down to only $+, -,\times,\div$ What that means is that you can take any function and if you dive deep enough ...
0
votes
1answer
39 views

$ P\mid n \implies \exists (a,b)\in\mathbb{Z}^2 \quad an+b(p-1)=1$

show that $$ p\mid n \implies \exists (a,b)\in\mathbb{Z}^2 \quad an+b(p-1)=1$$ with p is the least prime dividing my attempts Indeed, Let $d=n\wedge (p-1)=gcd(n,p-1)$ and we try to show ...
0
votes
1answer
20 views

change from recurrence relation to iterative approach

An investment of 1,000,000 receives a 10% bonus every year. A total of $48,000 is withdrawn from the investment each year. Assume that you have got the 10% bonus before you withdraw each year. I just ...
1
vote
2answers
27 views

Four lots of sums using only $4$

You need to make exactly four sums using only the number $4$ each time. For example, $4+4+4+4 = 16$ or $4×4-4÷4 = 3$. You can use $+ - × ÷$, square, or square root. Another example: $4^2 × 4 + 4 ÷ ...
24
votes
11answers
2k views

Is there any way to define arithmetical multiplication as other thing than repeated addition?

Is there any way to define arithmetical multiplication as other thing than repeated addition? For example, how could you define $a\cdot b$ as other thing than $\underbrace{a+a+\cdots+a}_{b ...
3
votes
2answers
127 views

Why isn't the identity $\sqrt{ab}$ = $\sqrt{a} \cdot \sqrt{b}$ always true?

If we take $a=b=-1$ then the L.H.S. is $1$ but the R.H.S. is $-1$. Is this identity not applicable for complex numbers? How to prove this and prove that this is not applicable for some complex ...
2
votes
2answers
41 views

decimal to fractions

When being asked how to solve the Arithmetic Means of 8, 7, 7, 5, 3, 2, and 2, I understand that adding these numbers then dividing by 7 (the amount of numbers) gives me the decimal 4.85714... But ...
-1
votes
2answers
109 views

How do we add numbers?

How do we compute sums in general? How can we tell the result of the operation $A+B$? Even when we talk about very basic numbers like $\Bbb{N}$ I find it hard to understand the algorithm we use to ...