Questions on basic arithmetic involving numerical quantities only. Questions involving variable values (other than the result of the operation) should be placed under the (algebra-precalculus) tag.

learn more… | top users | synonyms (1)

3
votes
3answers
66 views

multiplication and addition fractions

Try to visualize process of multiplication fraction addition is obvious, need to split each part to the same size - "reduce to a common denominator" for example $$\frac23 +\frac24 = \frac{8}{12}...
2
votes
1answer
72 views

Prove that $2+2\sqrt{12n^2+1}$ is perfect square

Problem: Let $n \in \mathbb{N}$ such that $2+2\sqrt{12n^2+1}$ is the integer. Prove that $2+2\sqrt{12n^2+1}$ is perfect square. I tried to found $n$ such that $\sqrt{12n^2+1}$ is integer, i.e. $...
0
votes
2answers
32 views

How to resolve this proportion/equivalence calculation? [simple one]

Let's suppose I have one cat and when buying food for him I have to take into account this: 1 cat eats 2kg of food each 20 days How can I get a formula to know how many days my food will last based ...
2
votes
1answer
60 views

What's the numerator and the denominator of a fraction called?

Just a quick question, is it right to call the numerator and the denominator of a fraction by "terms"? I don't think that "terms" is the right word here, but i don't know any alternatives. Can any ...
0
votes
1answer
9 views

combining 3 ratio together with no equal volumes

An Alloy A contains copper and tin in the ratio of 3 : 5 by weight. Another Alloy B contains tin and zinc in the ratio 3:7 by weight . Find the ratio of copper : tin : zinc in a new alloy containing ...
1
vote
1answer
27 views

The future and present value of an annuity of $100 payable at the start of each quarter for 15 yrs if the rate is 12% compounded quarterly is?

What are the future and present value of an annuity of $100 payable at the beginning of each quarter for 15 years if the interest rate is 12% compounded quarterly?
0
votes
2answers
39 views

What amount can be paid at the end of every month in perpetuity from an endowment of $350,000 which is earning 5.4% compounded monthly?

What amount can be paid at the end of every month in perpetuity from an endowment of $350,000 which is earning 5.4% compounded monthly? Am trying to apply the compound interest formula but it isn't ...
0
votes
2answers
38 views

Convert the following between octal, decimal and hexadecimal

(a) Convert $61502$ from base $8$ to decimal. (b) Convert $EB7C5$ from base $16$ to octal. My answer: a) $6\times8^4+1\times8^3+5\times8^2+\times8^1+2\times8^0=25410$ b) not sure: converting $E=14$,...
3
votes
2answers
50 views

Football:What is the minimum number of points to guarantee qualification in a group of 4 teams?

In a group of 4 teams, each team plays 3 matches ( against the 3 other teams). A win gives a team 3 points, a draw 1 point, and a loss 0 points. In the end the top two teams of the group qualify. It ...
1
vote
2answers
30 views

For some $w$,$x$,$y$,$z$ it holds that $w+x>y+z$. Does that mean that $\sqrt w+\sqrt x> \sqrt y+\sqrt z$ and the other way around?

For some $w$,$x$,$y$,$z$ it holds that $$w+x>y+z. \quad \quad (1)$$Does that mean that $$\sqrt w+\sqrt x> \sqrt y+\sqrt z \quad \quad (2)$$ and the other way around, so if (2) holds then (1) ...
0
votes
0answers
15 views

The representation of finite and infinite ternary's

In my notes I came across a sentence that says "every ternary may also be written as an infinite ternary with infinitely many trailing 3's". I dont understand this statement, what does it mean?
0
votes
1answer
30 views

Evaluating an arithmetic abstract syntax tree [closed]

This might be very simplistic for this forum (apologies, if so). How does one evaluate the tree below. I am not looking for a solution, just assistance in how to evaluate it: I assume I start at ...
2
votes
2answers
90 views

How to remove parentheses from $x/(y-z)$

To remove parentheses from $x(y-z)$ I reword it to $xy-xz$. How do I remove parenthesis from $x/(y-z)$?
1
vote
3answers
51 views

$25$ men are employed to do a work

$25$ men are employed to do a work, which they could finish it in $20$ days but the drop off by $5$ men at the end of every $10$ days. In what time will the work be completed? My Attempt In $20$ ...
0
votes
2answers
60 views

Finding the min/max of consecutive numbers which equal a given sum

Given a consecutive list of numbers of size $n$, and a total sum figure $t$, what is the simplest way of finding the minimum $min$ and maximum $max$ numbers of that consecutive list? For example, $...
27
votes
9answers
7k views

What is the purpose of Stirling's approximation to a factorial?

Stirling approximation to a factorial is $$ n! \sim \sqrt{2 \pi n} \left(\frac{n}{e}\right)^n. $$ I wonder what benefit can be got from it? From computational perspective (I admit I don't ...
-1
votes
1answer
25 views

Speed Distance Time(RACES) [closed]

PLEASE GIVE THE DETAILED SOLUTION. Tom, Jerry and Snoopy participate in a race. Tom covers the same distance in $49$ steps as Jerry covers in $50$ steps and Snoopy in $51$ steps. Tom takes $10$ steps ...
0
votes
1answer
32 views

A,B and C can do a piece of

A can do a piece of work in $10$ days, B in $20$ days and C in $30$ days. If A is assisted by B and C turn by turn in alternate days, in how many days the work might have been completed? My Attempt: ...
3
votes
6answers
478 views

How to determine the remainder of $ \frac{7^{369}}{350} $?

How to determine the remainder of the following : $$ \frac{7^{369}}{350} $$ Is there any tricky way to determine this? I start as $$\frac{7^{368}}{50} \ \ , $$ This type of problem are highly ...
5
votes
5answers
391 views

Division with 4 digit number in denominator

I've got a question in my task sheet. The question is as follows. $$ \frac{43\cdot93\cdot47\cdot97}{3007}=X $$ Find the exact value of $X$. I've tried a lot, but couldn't find easier way to do it ...
1
vote
2answers
79 views

Basic arithmetic - trick question.

I have the following question: A baker filled a measuring cup with $3/4$ cup of water. He poured $1/2$ of the water into the batter, and then spilled $1/8$ of the water on the floor. How much ...
0
votes
0answers
21 views

Convert double precision number to rational fraction plus exponent

I have a double precision quantity (either pixels per cm or pixels per inch) that gets converted into pixels per meter. I then need to convert this number into a rational fraction, with numerator and ...
1
vote
3answers
39 views

The digits of a positive

The digits of positive integer having $3$ digits are in A.P and their sum is $15$. The number obtained by reversing the digits is $594$ less than the original number. Find the number. My Attempt ; ...
2
votes
1answer
18 views

how many ways to multiply n-tuples?

Let $G$ be a group and $a,b,c,\ldots$ elements of $G$. How many different ways are there to multiply elements in $G$, preserving the order? I mean, two elements ----> 1 way: $ab$ three elements ---->...
0
votes
1answer
402 views

First digit of a very long number

Suppose I have a set of numbers eg:{1,8,9,6,5,10} I want to keep a track of the first digit of the number obtained by multiplying the above numbers. 1*8*9*6*5*10 the answer is 21600 ,the first digit ...
-1
votes
2answers
87 views

Math's puzzle school problem

I got this weird homework situation and i can't find out what the answer is. I got to find out how to get $828$ using the numbers $8, 6, 8, 3, 75$ and $9$. Moreover, I can use all the operators $*, -,...
2
votes
5answers
8k views

negative number divided by positive number, what would be remainder?

my question is If $-27$ is divided by $5$, what would be the remainder?
4
votes
0answers
66 views

Sorting prime numbers on two sets of equals weights

Lets denote $(p_n)$ the sequence of all prime numbers $(p_1=2, p_2=3,\ldots)$. The conjecture is the following. For infinitely many $n\in \mathbb N_{\geq 1}$ $$\exists I \subset \{1,\ldots n\...
2
votes
4answers
242 views

Is $3+2=5$ a equation?

Problem: Is $3+2=5$ a equation ? Solution As we know that that $3+2$ is a arithmetic expression. So $3+2 = 5$ is a arithmetic equation. But my friend said that $3+2=5$ is not a equation as it ...
1
vote
3answers
18 views

Subtraction non-associativity when presented as addition

It's well known that the action of subtraction isn't associative: $(7-4)-1 \neq 7-(4-1)$ However, subtraction is simply the addition of negative numbers... so the inequality above can be ...
0
votes
0answers
36 views

Is any simple formula to find impact of new value addition on total

Sorry for my poor math skills. Please down vote after stating the reason. I have 4 values A, B, C and D. Following is the calculation. $(A + B + C) - D = Total.$ Later any of $A,B,C$ or $D$ will ...
0
votes
2answers
28 views

Sum of an unknown sequence (perhaps arithmetic or geometric)

The problem is stated as thus: Given a sequence $(a_n)_{n\geq 1}$, $$ a_1+a_2+\dots+a_n = 1 + 2^{n+1} $$ for all $n$. Find $a_5$. This is all the information that is given.
3
votes
4answers
76 views

How did we derive this general term for the series?

We have this series of numbers: $1, 3, 6, 10, 15$ The general term can be described wit: $\frac{r(r + 1)}{2}$ Apparently the following series: $1, 4, 10, 20, 35$ Can be described with $\frac{r(r + 1)(...
9
votes
1answer
114 views

Calcule $\gcd(0!+1!+\ldots+n!, (n+1)!)$

I have to compute $d=\gcd(0!+1!+\ldots+n!, (n+1)!)$, so let $a=0!+1!+\ldots+n!$ and $b=(n+1)!$. Then: $a=0!+1!+\ldots+n!=3!+0!+1!+2!+4!+...+n!=6+4+4!+...+n! \equiv 2 \mod 4$ Thus, $a$ and $b$ are ...
0
votes
4answers
100 views

Why is $-3^4 = -81$ and $(-3)^4 = 81$?

How do you express $-3^4$ to get an answer of $-81$. And how is $(-3)^4$ expressed to get the answer of $81$?
1
vote
1answer
22 views

How to find miles per gallon given the following situation?

Fred drives an average of $15,000$ miles per year, and his car gets $20$ miles per gallon of gasoline. The average cost of gasoline is $\$3.25 $ per gallon. He buys a new car. In his new car Fred ...
1
vote
1answer
75 views

nth root function

I want to write code for a nth root function, so I need to be sure, that the underlying mathematical function is correct. From another post over at SO, I wrote the following definition: $ \sqrt[x]{y} ...
2
votes
2answers
204 views

Prove that gcd(n, mp) = gcd (n, m) if n and p are relatively prime

Let $n, m$ and $p$ non-zero natural integers, with $n$ and $p$ relatively prime. Prove that $\gcd(n, mp) = \gcd (n, m)$. This problem had three questions. First, to prove that if $d$ divides $n$ then ...
0
votes
2answers
555 views

Drove 238 miles and used 27.3 litres of petrol: find upper bound for consumption per mile, considering measurement errors

X drove 238 miles, correct nearest mile. They used 27.3 litres of petrol, to the nearest tenth of a litre. $Petrol Consumption =$${Miles}\over Petrol Used$ Work out the upper bound. I used $238.5\...
-66
votes
9answers
5k views

Unique Representation and The Fundamental Theorem of Arithmetic [closed]

While reading this thread Why 1 is not considered to be a prime number?, I recalled that The Fundamental Theorem of Arithmetic (FTA) which says that every positive integer greater than $1$ can get ...
733
votes
26answers
115k views

How long will it take Marie to saw another board into 3 pieces?

So this is supposed to be really simple, and it's taken from the following picture: Text-only: It took Marie $10$ minutes to saw a board into $2$ pieces. If she works just as fast, how long ...
1
vote
1answer
25 views

Structure of the proof of the fundamental theorem of arithmetics

Fundamental theorem of arithmetics: A principal ideal domain is factorial. i.e: Any non zero element of a principal ideal domain can be decomposed in a unique product of irreductibles. The structure ...
0
votes
0answers
45 views

Studying mathematics concretely, axiomatically & philosophically

I see mathematics as structures made up of numbers & shapes and actions done with them, like additions-multiplications-exponentiations, or divisions in pieces, translations, rotations, or some ...
1
vote
4answers
88 views

Determining parity of a number

I have this function: $$f(n) = \frac{(-1)^n + 1}{2}$$ For $n \in Z$ It seems be equal to $1$ if $n$ is an even number and $0$ otherwise: $$ \begin{array}{c|c} n & -3 & -2 & -1 & 0 &...
1
vote
0answers
42 views

The art of arithmetic [closed]

People doing arithmetic in a high level usually agree that there is an inherent beauty in numbers. They also often have trouble to find the words to describe how they feel and why they find arithmetic ...
4
votes
2answers
145 views

Creating arithmetic expression equal to 1000 using exactly eight 8's and parentheses

I would like to find all the expressions that can be created using nothing but arithmetic operators, exactly eight $8$'s, and parentheses. Here are the seven solutions I've found (on the Internet) so ...
5
votes
4answers
116 views

Find the last two digits of $2^{2156789}$

Find the last two digits of $2^{2156789}$. My try: As $2156789 = 4* 539197 + 1$ The unit digit of $2^{2156789}$ is similar to the unit digit of $2^{4n+1}$ which is equal to 2. But I'm unable to find ...
51
votes
11answers
29k views

Can a piece of A4 paper be folded so that it's thick enough to reach the moon?

While procrastinating around the web I stumbled on a page that contained the image below, from cracked.com. I can't help but believe that this is false… Even though the article header says: ...
2
votes
0answers
22 views

Bending a horizontal from 0 to infinity real number line, ninety degress counter-clickwise at 1.

Can the real number line from 0 to infinity, which of course is often represented as a horizontal straight line, also be represented as being bent ninety degrees counter-clockwise at 1? I.e., if such ...
1
vote
2answers
287 views

Addition in Cantor expansion

How to add two integers in their Cantor expansion?