Questions on basic arithmetic, e.g. addition, subtraction, multiplication, division, powers, roots, etc.
8
votes
3answers
76 views
Why are the order-of-operations conventions good?
Children are sometimes taught silly mnemonics like "PEMDAS" to remember conventions on order of operations. (I never heard of "PEMDAS" until long after graduating from college, as far as I can ...
1
vote
8answers
133 views
What is $2 - 1 + 1$? [duplicate]
$2-1+1$; a fairly straightforward question, but I (well, not me, but Henry Reich) found something strange.
Most people would evaluate it as $2+(-1)+1 = 2$; however, this goes against the famed, and ...
0
votes
1answer
34 views
How to derive the sum of an arithmetic sequence?
I'm attempting to derive a formula for the sum of all elements of an arithmetic series, given the first term, the limiting term (the number that no number in the sequence is higher than), and the ...
3
votes
2answers
53 views
real mechanism behind addition, subtraction, multiplication, division
we all know the basic rules for operations of addition, subtraction, multiplication and division.
but what i don't know is why these rules (of addition, subtraction, multiplication and division) ...
40
votes
5answers
2k views
Why is 987654321/123456789 = 8.0000000729?
Many years ago,
I noticed that $987654321/123456789 = 8.0000000729\ldots$.
I sent it in to Martin Gardner at Scientific American
and he published it in his column!!!
My life has gone downhill since ...
3
votes
5answers
126 views
Order of operations (BODMAS)
$$40-20/2+15\times1.5\\\hspace{.1in}\\40-20/2+15\times1.5=\\ 40-10+22.5=7.5$$
I'm studying and this is from an example.
In BODMAS, aren't addition and subtraction have same level?
So, in the ...
13
votes
3answers
343 views
Calculating $\sqrt{28\cdot 29 \cdot 30\cdot 31+1}$
Is it possible to calculate $\sqrt{28 \cdot 29 \cdot 30 \cdot 31 +1}$ without any kind of electronic aid?
I tried to factor it using equations like $(x+y)^2=x^2+2xy+y^2$ but it didn't work.
1
vote
3answers
57 views
How to sum numerator and denominator of a fraction?
I want to do sum over this. Can apply the summation to top and bottom separately?
$$\sum\limits_{i=1}^{n} \frac{-a(x_i-\mu)^2}{x_i}$$
...
4
votes
4answers
81 views
Definition(s) of rational numbers
The definitions of rational numbers are somewhat confusing for me. The definition of rational numbers on wikipedia and most other sites is:
In mathematics, a rational number is any number that ...
0
votes
1answer
21 views
(Follow Up) Checking the solutions of a quadratic polynomial
I'm following up from this question:
Solve a polynomial involving geometric progression?
I have had trouble with this question:
"Solve the equation $8x^3−38x^2+57x−27=0$" if the roots are in ...
0
votes
2answers
33 views
Prove that nearly all positive integers are equal to $a + b + c$ where $a | b$ and $b | c$, $a \lt b \lt c$
If a positive integer $n$ is equal to $a + b + c$ where $a | b$, $b | c$ and $a \lt b \lt c$, let it be called "faithful". Prove that nearly all numbers are faithful and list the non-faithful ...
1
vote
1answer
35 views
4 equations with specific set of numbers
I must make 1 addition (x+y=z), 1 subtraction (x-y=z), 1 multiplication (x*y=z), and 1 division (x/y=z) equation with the following numbers. All the numbers must be used to fill x, y, and z of each ...
4
votes
2answers
25 views
Counting Number of Objects - When to Add One Back
I know this might be a very basic question. Sometimes to count objects, we just subtract. For example -- If there are 5 apples and I take away 1, then remaining are $5 - 1 = 4$ apples.
But other ...
5
votes
1answer
184 views
Find the value of $x^3-x^{-3}$ given that $x^2+x^{-2} = 83$
If $x>1$ and $x^2+\dfrac {1}{x^2}=83$, find the value of the expression$$x^3-\dfrac {1}{x^3}$$
a) $764$
b) $750$
c) $756$
d) $760$
In this question from given I tried to ...
-1
votes
1answer
49 views
4 equations with set of numbers
I must make 1 addition (x+y=z), 1 subtraction (x-y=z), 1 multiplication (x*y=z), and 1 division (x/y=z) equation with the following numbers. All the numbers must be used to fill x, y, and z of each ...
2
votes
1answer
56 views
Age is fraction of year man dies
My friend sent me a question from an olympiad and im not sure that we have followed the right method, we both did the same thing:
The age of a man was 2/61 of the year in which he died. How old would ...
1
vote
2answers
36 views
finding nth term
Let
3,8,17,32,57 . . . . .
be a pattern.How do we find the nth number?My brains are completely jammed.I do not even recognize any pattern.I calculated a few ways,but all I want is a little hint,not ...
4
votes
3answers
167 views
sum of ten squares
You are given an unlimited supply of $1\times 1,2\times 2,3\times 3,4\times 4,5\times 5,6\times 6$ squares.Find a set of ten squares whose areas add up to $48$.If not the whole solution,even a little ...
4
votes
7answers
151 views
Rational numbers $\mathbb Q$
$$\Bbb{Q} = \left\{\frac ab \mid \text{$a$ and $b$ are integers and $b \ne 0$} \right\}$$
In other words, a rational number is a number that can be written as one integer over another.
...
1
vote
0answers
35 views
Gold Ring Calculation
I have problem with gold ring weight calculation
I have below details to calculate gold ring calculation
...
20
votes
0answers
198 views
+100
Manual proof that ${\left(\pi^\pi\right)}^{\pi^\pi}$ is a noninteger
Conor McBride asks for a fast proof that $$x = {\left(\pi^\pi\right)}^{\pi^\pi}$$ is not an integer. It would be sufficient to calculate a very rough approximation, to a precision of less than 1, and ...
0
votes
5answers
90 views
Finding two numbers when having their sum and product
I have two numbers, their sum is 41 and their product is 238. What are the numbers?
I got during this far in my calculations:
$a+b=41,\quad ab=238,\quad 238=41-b.$
I appreciate answers or tips to ...
3
votes
7answers
124 views
I have difficulty counting
Take this example:
$$84 + 87 + 90 + 93 .. + 180 + 183$$
If we want to use Gauss' way of finding this sum, we have to find the number of elements in this. What I do is just take the difference of the ...
-3
votes
1answer
28 views
Multiply $11010_2$ with $1011_2$ by working through each step of the multiplication algorithm
I need to multiply 11010 in its binary form with 1011 also in its binary form with the steps in detail.
-1
votes
1answer
48 views
Convert $435_{10}$ and $220_{10}$ to both their hexadecimal and octal expansions
I need to convert 435 and 220 from their decimal form, to their hexadecimal and octal expansions.
0
votes
0answers
37 views
Calculate the distance between the points (1, 2, …, n) and (2, 3, … n, 1)
I know that the operation to find the distance between two vectors is:
$$\sqrt{(b_1-a_1)^2+(b_2-a_2)^2+...+(b_n-a_n)^2}$$
So:
The distance between $(7, 5, 3, 1)$ and $(1, 3, 5, 7)$ is:
...
1
vote
3answers
45 views
What have I done wrong in solving this problem with indices rules?
The question asks to simplify:
$$\left(\dfrac{25x^4}{4}\right)^{-\frac{1}{2}}.$$
So I used $(a^m)^n=a^{mn}$ to get
$$\dfrac{25}{4}x^{-2} = \dfrac{25}{4} \times \dfrac{1}{x^2} = \frac{25}{4x^2} = ...
1
vote
2answers
86 views
when the numerator is less than the denominator
when the numerator is less than the denominator the result is always between 0 and 1?
for example if I have a number like
x/y where x<y then the result will be ...
2
votes
5answers
69 views
Why do this expressions evaluate to different results?
$$\frac{12}{15} = 0.8\\
\frac{15}{12} = 1.25$$
If $15$ divided by $12 = 1.25$ shouldn't $12$ divided by $15$ be the same as $\frac{15}{12}$ and have the same result?
Can someone please explain this ...
-3
votes
0answers
65 views
Find the sum of all the multiples of 3 or 5 of 1000000000 [closed]
Find the sum of all the multiples of 3 or 5 limit $1<n<100000000$
0
votes
1answer
44 views
Length of DNA strand
The DNA molecule has a double helix structure. The radius of each helix is approximately $10$ angstroms ($1$ angstrom $=10^{-8}$cm). Each helix goes up by approximately $34$ angstroms every ...
0
votes
1answer
55 views
Math/Statistical analysis of a video on youtube
Say approx 6.3 billion people in the world:
6300000000
And the youtube video has 290 million views:
290000000
What percentage of people (of the world) have seen this video?
0
votes
3answers
66 views
Calculating overall grade from a partial grade
If I have a $76\%$ grade but I didn't do a project that was worth $15\%$ of my grade, what would my overall grade be?
Please I need to know and I suck at math.
3
votes
2answers
59 views
Patterns in the repetend in $1/121$
$$
\frac{1}{121} = 0.00\ \overbrace{8264}\ \overbrace{4628}\ 09\ \overbrace{91735}\ \overbrace{53719} \ldots
$$
The entire $22$-digit repetend appears here. It begins with the first digit after the ...
0
votes
0answers
52 views
Arithmetic Coding Example
I have a question for static arithmetic coding which I have done in class but I can't seem to figure out where I got the answers. It's a bit hard to get in touch with my lecturer at the moment so I'm ...
1
vote
2answers
98 views
Are the propreties of arithmetic unproven?
For example, the property which says that $$a(b+c)=ab+ac$$ This is very clear for integers, but is it actually provable for all real numbers (and complex maybe). Or the commutative property which says ...
1
vote
1answer
47 views
Looking for name of theorem: “rational $\Leftrightarrow$ fractional part terminates or repeats”
I am looking for the name of the theorem that says that a number $x$ is rational if and only if its fractional part terminates or repeats (where "fractional part" refers to the representation of $x$ ...
3
votes
0answers
79 views
Square and reverse reading of an integer
For all $n=\overline{a_k a_{k-1}\ldots a_1 a_0} := \sum_{i=0}^k a_i 10^i\in \mathbb{N}$, where $a_i \in \{0,...,9\}$ and $a_k \neq 0$,
we define $f(n)=\overline{a_0 a_1 \ldots a_{k-1} a_k}= ...
5
votes
4answers
121 views
How to factor 5671?
The other day I wanted to factor 5671 in my head. (It turns out to be $53\cdot107$, but I did not know this at the time.) I quickly ruled out the easy divisors, 2, 3, 5, 7, 11, and 13. At this point ...
3
votes
0answers
44 views
How to find an expression whose value is 190
Given a set of numbers (in this case):
3, 7, 7, 100, 50
Either:
prove it is impossible to form the number k = 190 using ( ) + - * / operators between sub set of the these numbers ex: 1000 = ((3 + ...
0
votes
1answer
48 views
How does the difference quotient with a square root in the numerator end up with square roots in the denominator?
I don't understand when
I apply the difference quotient to: $f(x) = \sqrt{x} $ , to get:
$$\frac{\sqrt{x+h} - \sqrt{x}}{h}$$
To simplify it.. How does it end up like this?:
$$\frac{x + h - x}{h ...
2
votes
2answers
51 views
$\frac{1}{ab}=\frac{s}{a}+\frac{r}{b} \overset{?}{\iff}\gcd(a,b)=1$
$$\frac{1}{ab}=\frac{s}{a}+\frac{r}{b} \overset{?}{\iff} \gcd(a,b)=1$$
This seems almost painfully obvious because it is just $ar+bs=1$ in another form. This second form is the definition of ...
0
votes
1answer
55 views
Smallest Mersenne prime with 100 million digits?
As some of you are probably aware, the Great Internet Mersenne Prime Search (GIMPS) is managing the search for the largest Mersenne primes of the form $M_p=2^p-1$, where $p$ is itself prime (GIMPS ...
2
votes
2answers
41 views
Floor function inequality of multiplication
In a final step of a homework, I want to deduce that
$$n\lfloor(n-1)!e\rfloor+2\le \lfloor n!e\rfloor+1$$
I'm unable to see whether this is true in general that
$$n\lfloor a\rfloor+1\le \lfloor ...
2
votes
1answer
25 views
Proportionality In two Values Equal to $0$
If two values $m$ and $n$ are in direct variation, then
$m \propto n$
If the constant of proportionality is $q$ between them, then
$m = qn$
If $m$ and $n$ both are equal to zero or $m = ...
1
vote
3answers
63 views
How to manually calculate Roots
I have always used a calculator for determining roots
But I think it would be useful to know how to do this on paper. Are there different procedures for calculating square roots then cubic roots or ...
0
votes
1answer
58 views
Arithmetic and geometry [closed]
While $3^2 + 2^1 = 11$ arithmetically, geometrically aren't you adding a line of length $2$ to a square of area $9$, so wouldn't the geometrical answer be $9$, because adding a line to a square would ...
1
vote
2answers
72 views
Absolute Value of $|-3 -2|$
$|-3 -2|$ is the distance between the points $-3$ and $-2$. If we solve it further then,
in one way I get $|-5| = 5$. But $5$ is the distance between $0$ and $-5$ in this case. In other way,
$2 ...
0
votes
2answers
34 views
Absolute Value Problem, Solution and Method
Please check my method and also if I have solved the following problem correctly:
Problem: $f(x) = |x - \frac12| + |x + \frac12|$
If $x = -1$, then:
$f(-1) = |-1 - \frac12| + |-1 + \frac12|$
From ...
1
vote
2answers
68 views
How is the following arithmetic sequence solved?
Apologies to bother you with this, but how is the following arithmetic sequence solved?
$$\dfrac1n \left(\sum_{k=1}^{n-1}\dfrac{n-k+1}2\right)$$
