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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2 questions regarding solutions for $\sqrt{a+b} - (a-b)^2 = 0$

Here's two questions derived from the following question: $\quad\begin{matrix} \text{Is there more than one solution to the following statement?} \\ \!\sqrt{a+b} - (a-b)^2 = 0 \end{matrix}$ $\color{Blue}{(1)\!\!:\;}$How would one (dis)prove this?…
JohnWO
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What is the correct answer to this infamously ambiguous arithemetic problem 6÷2(1+2)?

I am going to make the case that $6÷2(1+2) = 1$. Many people often quote the PEMDAS rule and get the answer $9$ but look at this way: $$ 6 \div 2(1+2)= \frac{6}{2(1+2)}$$ Algebraically, we can treat the division operator(obelus or solidus) as a…
Mr X
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Best definition for distributive property of multiplication

I am teaching math for kids in Perú, however, I find so many different definitions for the distributive property of multiplication. Do you have a solid definition in words with a book reference? Thanks.
Matemóvil
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prove that the product of 4 consecutive positive integers is divisible by 24

How can I prove that prove that the product of $4$ consecutive positive integers is divisible by $24$, ie for any positive integer $n$ : $n(n+1)(n+2)(n+3)$ is divisible by $24$. I've noticed that: $24$ = $2^3 * 3$ $n(n+1)(n+2)(n+3)$ is divisible by…
sammy210
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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 he have been if he lived until 1992? Surly then…
simplton
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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 step by step thank you.
NelDoozy
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Number of carries in addition

A set of natural numbers $\{a_1,a_2,...,a_n\}$ are given. We add the numbers one pair at a time in some order. Is it true that the number of carries during our process is independent of the order? Example: $\{57, 82, 19\}$. $57+82 = 139$ (1 carry),…
tarthoe
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different ways to find middle point in a range

I've found that in some algorithms to find the middle point of a numeric range the next formula is used: middle = low + ((high - low) / 2) Yet, others use the next formula: middle = (low + high) / 2 I've done some test and both formulas yield to…
API_1024
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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 $m = 0$ and $n = 0$, then will they be called directly…
Samama Fahim
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For $x≠y$ and $2005(x+y) = 1$; Show that $\frac{1}{xy} = 2005\left(\frac{1}{x} + \frac{1}{y}\right)$

Problem: Let $x$ and $y$ two real numbers such that $x≠0$ ; $y≠0$ ; $x≠y$ and $2005(x+y) = 1$ Show that $$\frac{1}{xy} = 2005\left(\frac{1}{x} + \frac{1}{y}\right)$$ Calculate $l$: $$l = \frac{y}{y-x} - \frac{y-x}{y} - \frac{x}{y-x} -…
Entropistemologicality
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What's the difference between the correct time and the time shown on the clock in this question?

I came across a question in an ICAS exercise booklet for primary school in Australia. Ihe question is as follows: At midnight on Friday, Megan's clock showed the correct time as 0:00 am. At midnight on Saturday, her clock showed the time as 11:48…
Michael May
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Is it proven that the maximum carry in an addition is always 1 whatever the base?

From my understanding the standard algorithm for adding two numbers in base $b$ is the normal pencil-on-paper addition. For example, let's say with have two base $b$ numbers with digits $i$, $j$, $k$, $l$, $m$, $o$: $$ \begin{array}{rccccc} ( &…
Antoine Catton
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How come 1.000 - 1 = 999 and 1,000 + 1 = 2,000 to Germans?

I ask my german friend a math question: I expected my German friend to answer it as this: $$1.000 - 1 = 0$$ $$1{,}000 + 1 = 1{,}001$$ but instead my German friend says this: $$1.000 - 1 = 999$$ $$1{,}000 + 1 = 2{,}000$$ All of my German friend said…
5th grader math kid5
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Why can't you add terms with different exponents?

When evaluating algebraic expressions, 1) you can add together like terms. $3x^5 + 6x^5 = 9x^5$, but you cannot add together different terms: $2x^4 + 3x^5$, because these have different exponents. 2) you can multiple different terms: $2x^4 \cdot…
JohnMerlino
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If a repair on a vessel costs \$2 and fully repaired vessel is worth \$1 don't we need know worth of broken vessel to decide whether to repair or not

I skip "million" because the question would be the same without. I intentionally don't quote judgement, because the book beneath doesn't say what the value of the vessel is now. But don't we need to know the value of the current vessel to calculate…
user53259
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