Mathematics Stack Exchange
Mathematics Stack Exchange

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. Questions about number theory (sometimes called "arithmetic") should not use this tag and should instead use (number-theory) or (elementary-number-theory).

Arithmetic is defined as operations upon numbers using $4$ main operations along with many others:

addition - the sum of two numbers

subtraction - the difference of two numbers also defined as the addition of negative numbers

multiplication - the area of a rectangle with sides of lengths equal to the two operands

division - the number of times one number can be subtracted from another before equaling zero. Sometimes it will allow decimals and in other cases there will be a remainder left over when a number doesn't go into another evenly

See Arithmetic.

6283 questions
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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 without calculator, which of course, is not allowed…
Electrifyings
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What is the difference between $0$ and $-0$?

Why is there a $0$ and a $-0$? I thought zero meant nothing, so how can we have negative nothing?
user1762507
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Discrete Mathematics Power of 3

If m is a power of $3$, n is a power of $3$, prove that $m+n$ is never a power of $3$. This is the question that I was given, unfortunately, my teacher doesn't like to teach and I' left reading a $1000$ page book by myself answering these random…
Karl
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Summing cube roots in fractions

I found this problem, and understand the solution, but do not understand why they made the first assumption. The problem: The first line of the solution says that: The cube root of $1$ plus the cube root of $2$ plus the cube root of $4$ is a…
Jamminermit
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Arithmetics ; $p-1 \mid q$ equivalent to $(p-1)^2 \mid p^q - 1$

I have a problem with this exercise : prof that $p-1|\space q \iff (p-1)^2|\space p^q - 1$ I succeed to prof that $(p-1)^2|\space p^q - 1 \implies p-1|\space q$ thanks ^^
Sherloek holmes
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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?
StuntHacks
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For dual numbers, what does $\epsilon^\epsilon$ equal?

$$\epsilon^\epsilon=?$$ Where $\epsilon^2=0$, $\epsilon\notin\mathbb R$. There is a formula for exponentiation of dual numbers, namely: $$(a+b\epsilon)^{c+d\epsilon}=a^c+\epsilon(bca^{c-1}+da^c\ln a)$$ However, this formula breaks down in multiple…
Plungerdz
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Conversion to base $9$

Where am I going wrong in converting $397$ into a number with base $9$? $397$ with base $10$ $$= 3 \cdot 10^2 + 9 \cdot 10^1 + 7 \cdot 10^0$$ To convert it into a number with base $9$ $$3 \cdot 9^2 + 9 \cdot 9^1 + 7 \cdot 9^0 = 243 + 81 + 7 =…
Sanjay Mohan Bhatnagar
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Is my result accidental?

I explored the value of PI up to 10 million digits with the following link http://pi.karmona.com/ From here I realized that it included many scientific constants. Below are some examples • …1618033… Where 1.618033 ~ golden ratio to be used in…
Thinh Nghiem
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find the least $k$ such that any subset of order $k$ contains 4 terms in arithmetic progression.

Question: Let set $A=\{1,2,\cdots,100\}$ ,find the least $k$ such that any subset of order $k$ contains 4 terms in arithmetic progression. It seem interesting problem. Now I have found $k$ must $k\ge 43$,because I found following set has $42$…
math110
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When a 4 digit number is multiplied by 3/2 or 1.5, that number is reversed.

When a 4-digit number is multiplied by 1.5, the order is reversed. What is the number? I did several things. Here is my work. $1.5(1000a+100b+10c+d)=1000d+100c+10b+a$ $1500a+150b+15c+1.5d=1000d+100c+10b+a$ $1499a+140b=998.5d+85c$ I know $d$ must be…
Matthew Tang
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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 far: \begin{align} 1000 &= (8888 - 888) / 8\\ …
Svend Tveskæg
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Can two sets have same AM, GM, HM?

Can two set of numbers(same size) have same arithmetic , geometric, and harmonic mean ? When I say different set they must differ by at-least $1$ element and also what if set is not be of distinct elements?
user35690
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How much faster is the Trachtenberg system?

How much faster are various mathematical operations using a Trachtenberg method rather than a conventional method?
Zaz
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Will Division by Zero be Defined Eventually?

Possible Duplicate: Division by $0$ I've always been inclined to believe that x/0 = NaN is a placeholder for a character or constant that no one has created yet. I know assume that none of you can tell the future, but is there an expectation…
Sonic42
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