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Questions tagged [arithmetic]

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.

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2answers
32 views

Finding sum of terms in a sequence

A sequence has $a_1=-2$ and $a_2=4$ and in the sequence, when $n>2$, $a_{n}$= $\dfrac {a_{n-1}}{a_{n-2}}$. Find the sum of the first $99$ terms of sequence. I tried to deduce from the patterns ...
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1answer
39 views

Basic mathmatical concepts( multiplication) [duplicate]

Here is a conundrum I pondered upon while solving an equation - 2x2 , generally means we are adding 2 two times , that is , 2+2 Then , (-2)x(-2) , should go like this (-2)+(-2)=-4 , But , that's ...
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0answers
31 views

help with how to distribute data using various variables

I'm working on a problem that involves distributing data (national) to the state level using a number of variables.. Among these variables, I'm considering the state population size, how many schools ...
2
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1answer
24 views

Is there a way to solve this equation arising from a weighted sum?

If I have a weighted finite sum that is equal to a known real value $x$, and I also know the real-valued and non-negative weights $a_i$, and I have unknown but also real and non-negative elements $b_i$...
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2answers
33 views

Absorbing bounded quantifiers, formal proof?

Intuitively I get in arithmetic aka the natural numbers that: $\exists n\,\exists m\,(m < n \wedge P(m)) \Leftrightarrow \exists k\,P(k)$ But I am having problems finding a formal proof. What I ...
2
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4answers
67 views

What method for mentally computing 2-digit multiplication problems, minimizes the amount of mental steps?

So I've been practicing alot of mental math recently and ofcourse as a part of that, multiplying a double-digit number by another double-digit number. I have been doing some research into what the ...
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0answers
21 views

Can rational points on algebraic varieties have a homological interpretation? [on hold]

This question is based on a curiosity I have to see whether finitely generated ring extensions can be used to reveal some interesting properties of general algebraic varieties. Thank you in advance!! ...
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1answer
23 views

Operator precedence in addition and subtraction

Customary operator precedence has addition prior to subtraction. Apart from historical convention and notational consistency, is there a rationale for this?
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1answer
50 views

Could there be an $\omega_1^{CK}$th hyperoperation?

If addition is the first hyperoperation, multiplication is the second, and the $(\alpha+1)$th hyperoperation is repeated occurrences of the $\alpha$th one. Is it possible for a limit ordinal (for ...
4
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2answers
69 views

Division using only addition and multiplication?

I need to perform a division operation using only addition and multiplication. I can't use substraction. Is it somehow possible to do that with only these two operations?
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1answer
58 views

Algorithms for elementary operations using other elementary operators

The question asks to provide an algorithm to compute $(i)$ The product of $n$-bit numbers using reciprocation operation and addition operation but not using multiplication and squaring. $(ii)$ The ...
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1answer
29 views

Sum manipulation

my question is if these two sums are equal: $\sum_{j=1}^n \lambda u_jx_j + \mu v_j x_j = \sum_{j=1}^n \lambda u_jx_j + \sum_{j=1}^n \mu v_jx_j$ Thank you for your help.
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1answer
52 views

Series with lower limit greater than upper limit

I was under the impression that a summation of the form $\sum_{i=j}^{k}a_i$ where $j>k$ is regarded as an empty sum and so equal to $0$. My TI-89 Titanium calculator seems to disagree. It gives$$\...
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1answer
66 views

Even polynomial having multiple with odd coefficients

Let $Q \in \mathbb{Z}/2\mathbb{Z}[X]$ be a non constant polynomial such that all coefficients of odd order are $0$, i.e. $Q = \sum a_k X^{2k}$. Show that if $P \in \mathbb{Z}/2\mathbb{Z}[X]$ is such ...
2
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0answers
40 views

Explanation about integer being $l$-th power modulo every prime

Let $l$ be a prime number and let $x$ be an integer which is an $l$-th power modulo every prime. The claim is that $x$ is the $l$-th power of some integer. I've read the following proof, but I don't ...
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1answer
33 views

What is the time in the afternoon problem

I have been reading Ray's Intellectual Arithmetic and I stumbled upon the following problem: What is the time in the afternoon, when the time past noon is equal to $1/5$ of the time past ...
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1answer
30 views

Decelerated summation of X [closed]

Disclaimer: I'm a 19 year old who didn't pay enough attention in math class, so there is likely a very simple solution to this that I just can't think of. I'm writing an algorithm that will run ...
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1answer
56 views

How to do 21/2 on paper

I looked at online tutorials and im stuck at this case. 21/2 First, 2 goes into 2 once, so put 1 in the quotient, 2*1 = 2 so 2-2 = 0. Now we bring the 1 in 21 down. 2 doesnt go into 0, so what do we ...
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0answers
50 views

Which mathematical property prevents reducing equations to 0 = 1?

Which mathematical property prevents taking an equation, this one for example: $r = -0.5\cdot a \cdot t^2$ and moving all terms to one side to make it equal to zero... $\Longrightarrow 0 = -r - 0.5\...
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7answers
6k views

Why can we multiply by breaking up the factors as sums in different ways?

My friend and I were discussing some mathematical philosophy and how the number systems were created when we reached a question. Why can we multiply two different numbers like this? Say we had to ...
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2answers
40 views

Finding the number of days between two dates given specific methods

Let's say I have two input dates of the format dd/mm/yyyy. The first is the current date and the second is the future date. I have methods getDay, getMonth, and getYear, which return to me integer ...
2
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3answers
113 views

Show that $A = a^{pq} - a^{p} - a^{q} + a$ can be divided by $pq$

Let $p$ and $q$ be two different prime numbers, and $a$ a positive integer. Show that $$A = a^{pq} - a^{p} - a^{q} + a$$ can be divided by $pq$ I started by rewriting $A$ as $((a^{p})^{q} - a^{p}) - (...
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3answers
105 views

How to prove $(-3) \times (-4) = 12$?

How to logically understand the multiplication of two integers ? Eg: 3 x 4 = 12 (is understandable) -3 x4 = -12 (is also somewhat understandable) But , 3 x -4 = -12 (is NOT understandable) -3 x -...
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1answer
36 views

Is ordinal multiplication commutative?

DISCLAIMER I am sure this is a duplicate yet I coudn’t find an answer I was looking for so I’m probably going to ask and then eventually flag it as a duplicate. Is every instance of ordinal ...
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2answers
58 views

Counting the number of sums of two powers of two below 2000

In this question, $x^y$ stands for $x$ raised to the power $y$. For example $2^3=8$ and $4^1.5=8$ Find the number of positive integers $n<2000$ which can be expressed as $n=2^m+2^n$ where $m$ and $...
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1answer
62 views

Pandigital number divisible by the most prime numbers and other properties [closed]

Of all ten-digit pandigital numbers, that is numbers containing each of the ten digits 0 to 9 precisely once: Which is divisible by the most different primes? How many are divisible by just two ...
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2answers
23 views

I need help proving $2-\frac{2(j+2)}{2^{j+1}}+\frac{j+1}{2^{j+1}}=2-\frac{2j+4-j-1}{2^{j+1}}$

This seems simple, yet I just can't figure out how the LHS equals the RHS. Why do the terms $j$ and $1$ suddenly become negative? $$2-\frac{2(j+2)}{2^{j+1}}+\frac{j+1}{2^{j+1}}=2-\frac{2j+4-j-1}{2^{j+...
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2answers
38 views

Proving $1-(-2)^{n+1}+3(-2)^{n+1}=1-(-2)^{n+2}$

I have this equality $$1-(-2)^{n+1}+3(-2)^{n+1}=1-(-2)^{n+2}$$ Can anyone show me how the LHS can be equal to the RHS here? I can't really see it.
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1answer
31 views

I know the average rate of change formula, but I'm not sure if my arithmetic is current for the problem (find the average rate of change of…)

I know that the average rate of change formula is: $$\frac{f(b) - f(a)}{b-a},$$ but I'm not sure if my arithmetic is current for this problem: Find the average rate of change on the interval $(1/100,...
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3answers
715 views

The volume of a child's model plane is $1200~\rm{cm}^3$ & that of a full size plane is $4050~\rm{m}^3.$ Find the scale of the model in the form $1:n.$

The volume of a child's model plane is $1200~\mathrm{cm}^3.$ The volume of a full size plane is $4050~\mathrm{m}^3.$ Find the scale of the model in the form $1:n.$ I thought of first converting the $...
4
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3answers
52 views

Negative Value in Modular Arithmetic

How can $ -2 \mod 26 = 24$? I can not understand it properly. In my view point: -2 mod 26 = .7.What is totally wrong. the real out put is 24, but how can anybody explain it clearly?
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7answers
3k views

Is $9-4+1$ not equal to $4$? [closed]

I ran across the following math problem where there is arithmetic involved: $$9-4+1$$ Supposedly the answer is $6$? I entered into my computer and calculator and got the same result so I realized ...
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0answers
17 views

Product over empty set

Assuming some kind of function $f(x)$, what is the value of $\prod\limits_{x \in \varnothing}f(x)$? https://www.wikiwand.com/en/Empty_product suggests that it is equal to $1$ but I wasn't sure if it ...
2
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1answer
27 views

Given a finite set of primes $(q_i)$ is the set of all primes reachable by common differences finite?

Let $Q =(q_i)$ be a finite set of prime numbers in $\Bbb{Z}$. Define $\hat{Q}$ to be the unique largest set of primes reachable by adding an offset to $Q$: $$ \hat{Q} = \bigcup_{a \in \Bbb{Z} \\ Q + ...
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1answer
39 views

Integers whose multiples contain a specific digit

In base 10 (or any other base, for that matter) is there an integer all whose multiples contain a specific digit, say 1?
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1answer
15 views

Intuition behind hexadecimal subtraction result

By doing hexadecimal subtraction i got $(BA)_{16}-(AB)_{16}=(F)_{16}$ similarly $(CB)_{16}-(BC)_{16}=(F)_{16}$ $(DC)_{16}-(CD)_{16}=(F)_{16} $ $(ED)_{16}-(DE)_{16}=(F)_{16}$ $(FE)_{16}-(EF)_{...
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4answers
179 views

Prove that $T_n = 3n^2 -60n + 301$ is positive for every $n$

I recently did a Mathematics exam from a previous year, and I stumbled across a question's answer I struggled to fully understand. It is given: The quadratic pattern $244 ;~ 193 ;~ 148 ;~ 109;~ \...
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2answers
48 views

A question of arithmetic regarding erection cost of a structure. [closed]

The current erection cost of a structure is Rs. $13,200$. If the labour wages per day increase by $\frac 1 5$ of the current wages and the working hours decrease by $\frac 1 {24}$ of the current ...
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2answers
36 views

Multiple divisions

I was confused a bit with a little arithmetic here. For instance $1÷1÷2$ and $2÷3÷7$. BODMAS isn't effective in this case. My question is this: $2÷3÷7$ Am I to divide $2/3$ by $7$ or divide $2$ by $3/...
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1answer
25 views

Arithmetic way to get the number of decimal digits in a number [closed]

There is any general formula to get the number of decimal digits in a decimal number? For example in 8.888, there are 3 decimal digits. Thanks for any reply!
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2answers
66 views

Suppose that $a$ and $b$ are relatively prime natural numbers such that $ab$ is a perfect square. Show that $a$ and $b$ are each perfect squares.

Is there any other way of proving this besides showing that all of their respective factors or representation have an even number of exponents?
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1answer
105 views

A math riddle involving sums of digits

When I was in highschool I became obsessed with this strange combination I discovered. I don't really know a lot about math but I've recently re-discovered it and believe I have found an answer, but ...
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3answers
74 views

Prove that there is a digit that appears infinitely often in the decimal expansion of $\sqrt{7}$. [closed]

Prove that there is a digit that appears infinitely often in the decimal expansion of $\sqrt{7}$.
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0answers
21 views

Is there a Hamiltonian path? (i.e. can the general associative law be solved with Graph Theory?) [duplicate]

Consider the different bracketings of the summation $$1+2+3+4+5\,.$$ I've listed them all below: $$ 1+(2+(3+(4+5)))\,,\quad (1+((2+3)+4))+5\\ 1+(2+((3+4)+5))\,,\quad (1+(2+(3+4)))+5\\ 1+((2+(3+4))+...
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1answer
42 views

Find tax percent given tax amount and total amount [closed]

First, I will start with example ... for example meal price is : 105  and meal total price + the tip is : 120 so left with : 15 how I can tell how much % the 15 is from the 105 (meal price)?
2
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2answers
108 views

Number of ending symbols of prime numbers written in different bases

In base $b=10$, all prime numbers (except $2$ and $5$) end with one among the four symbols $1,3,7,9$. Therefore, between $10\cdot k$ and $10\cdot (k+1)$, there can be found $0,1,2,3$ or $4$ prime ...
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4answers
67 views

What's the fuss about performing operations from left to right?

When I learned about BODMAS / PEMDAS rules in mathematics. I was told to follow certain rules. For example if I have this expression: $3 − 2 + 4 − 1$ and to solve it I was told to always go from left ...
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4answers
819 views

Wrong solution for solving $ 3x^2 - 6x - 9 = 0 $ [closed]

Very Easy question, but I wasn't actively doing the question and I got it wrong. I was looking at it & didn't know which step was wrong? It looked like all the individual steps are correct but the ...
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1answer
30 views

Is it possible to get the solution 14 using only the numbers 2, 5 and 6, using each number only once? [closed]

Is it possible to use the basic arithmetic operations and exponents on the numbers 2,5 and 6 each used only once to produce 14. Akin to the game 24. Concatenation is not allowed.
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1answer
25 views

2 series questions (arithmetic)

So if I borrow money and, to pay it back, I pay 50 for my first month and then 25 more each additional month for 12 months, How much am I paying in total after 12 months? I’m thinking $a_1=50$ and $d=...