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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. 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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General formula for the numerators?

Suppose that $a$ is a natural number. The numerator of $\dfrac {1}{a}$ is $1$. The numerator of $\dfrac {1}{a} + \dfrac {1}{a+1}$ is $2a+1$ [Note: Here for our purpose we don't cancel common factors of the numerator and denominator]. The numerator…
user231343
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Does the order of operations matter with just addition and subtraction?

Had a debate on whether you could do addition/subtraction in any order you want. Specifically, for the following: $9 - 4 + 3$ We both agree that the answer is 8. I argue that, by giving addition a higher priority than subtraction (rather than the…
user290079
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Why does $x$ divided by zero not equal $x$?

Why does $x$ divided by zero not equal $x$? After all, $x$ is not being divided by anything.
Moshe
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Mersenne primes

A Mersenne prime is a prime number of the form $2^p-1$ where $p$ has to be a prime number. Now, let $p_0$ be a prime number, and let us define the sequence $p_n = 2^{p_{n-1}}-1$. Is there a $p_0$ such that the sequence $p_n$ is a sequence of primes…
sure
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Mean/Median/Mode question?

I came across the following problem: A list of 11 positive integers has a mean of 10, a median of 9, and a unique mode of 8. What is the largest possible value of an integer in the list? From the information, I got the following information: 11…
jj172
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Subtraction by addition

Can anyone explain to me "subtraction by addition" in a visual way? The steps say: Take the "complement" of the number we are subtracting Add it to to the number we are subtracting from Discard the extra "1" on the left Example: $9 - 7$ …
afgphoenix
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Is "applying similar operations from left to right" a convention or a rule that forces us to mark one answer wrong?

I saw this photo on my social network. The ambiguous expression $6\div2\times3$ yielded 2 different answers. The difference is the order of operations. If the division's done first then the answer is 9. If the multiplication was first then the…
842Mono
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can you disprove this rule PEDMSA?-(division before multiplication, subtraction before addition)

I know the proper teaching of PEMDAS/PEDMAS/BODMAS/BOMDAS.. is that multiplication and division have equal priority and are evaluated going through the arithmetic expression left to right (So, doing division first if division is left of…
barlop
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Would the answer of the square root of a square root be positive or negative?

I have this problem: $$\sqrt{\sqrt{16}}$$ would it be positive 2 or it would be $\pm$2? In this class we do not deal with complex numbers, so all the square roots are positive, thus for the class the answer is 2. However, I am asking this…
yiyi
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calculate order of magnitude difference

Say if I have two Areas of size a = 6 km$^2$ and b = 0.1 km$^2$ how would I find how many orders of magnitude one is greater or less than the other. So, the way I would work this is by saying that 0.1*10 = 1 and 1*10 = 10, making a roughly 2 orders…
KatyB
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If the mean of four of six given numbers is known, what is the mean of the other two?

Four of the six numbers $$1867,\quad 1993,\quad 2019,\quad 2025,\quad 2109,\quad \text{and}\quad 2121 $$ have a mean of 2008. What is the mean of the other two numbers? I would like to get help for this problem because i want to find a way to…
Briana791
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Can roots be thought of as a repeated arithmetic operation?

Multiplication can be thought of as repeated addition, where we add something up a certain number of times. Division can be thought of as repeated subtraction, where we subtract something from the dividend a certain number of times till we get zero…
DrZ214
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If the first 10 positive integer is placed in a circle(any order), 3 integer in consecutive locations around the circle that have a sum > 17?

If the first 10 positive integer is placed around a circle, in any order, there exists 3 integer in consecutive locations around the circle that have a sum greater than or equal to 17? This was from a textbook called "Discrete math and its…
Jun Hao
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Solve $n^m+m^n=n!+m!$

Determine all $(n,m) \in \Bbb N^2$ such that $n^m+m^n=n!+m!$ Clearly $(1,1), (1,2), (2,1)$ are solutions and they seem to be the only ones (At least they're the only solutions if $n\le 1000$ and $m\le 1000$ ) I've been thinking for quite sometime…
Tengen
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Possible pattern on sum of first $n$ $l$-th powers.

While discussing on some question with fleablood, we questioned ourselves on a possible pattern for the following sequence: $$F_n(l):=\sum_{k=1}^n k^l$$ Using Wolframalpha (and well-knows results) we…
b00n heT
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