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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Inequality involving $\sqrt{2}$

I need some help with the following problem: Show that for any pair $(a,b)$ of positive integers, $\dfrac{a+2b}{a+b} < \sqrt{2} < \dfrac{a}{b}$. I tried squaring both sides of the inequality, but I was not able to solve it.
yumiko
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Why do we multiply by 100 for finding percentage?

For example, if there are 50 boys in a school and the total number of students is $200$ then, for finding percentage of boys why do we do like this, $\left(\, 50/200\, \right)100\ \% = 25\ \%$ ?. Why does the fraction '$50/200$' represent ?. I know…
CandidFlakes
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Partitioning a Set so that the Sum is the Same

Let $M = \{1, 2, \dots , n\}$. What would be necessary and sufficient condition(s) for the number $m$, so that $M$ can be expressed as the disjoint union of $m$ subsets $A_i$, $(i = 1, 2, \dots, m$), such that (i) each $A_i$ contains the same number…
Raj Raina
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find a formula to explain this set:$\{3,7,-11,-15,19,23,...\}$

I want a formula to explain this set:$\{3,7,-11,-15,19,23,...\}$ Our teacher asked us to do.If they are one negative and one positive it was easy but now It become hard I think a lot, but no results.Please give me first some hints I want to solve it…
Taha Akbari
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Algebraic equation solving for X

Solve for x $1^x + 2^x + 3^x = 6^2 $ I have misconceptions here as I keep linking it to the laws of indices and therefore I do not know how to add $1^x + 2^x ... $ can I get a hint ? Thanks !
user307640
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Best method to add and subtract (Common Core-ish)

What's the best method for adding and subtracting? I have a son in the third grade so as a parent I'm smack dab in the middle of the common core debate (I'm hoping to avoid the Facebook politicization of Common Core and have a more "maths" oriented…
Just Another Justin
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Determining which number pair has greater product - without multiplying.

This is a 5x5 multiplication table. 1 2 3 4 5 =================== 1 | 1 2 3 4 5 2 | 2 4 6 8 10 3 | 3 6 9 12 15 4 | 4 8 12 16 20 5 | 5 10 15 20 25 Ordering all unique products by magnitude, you…
Cory Klein
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Simple property of power of -1

Is $(-1)^{a+b} = (-1)^{a-b}$ true $\forall a,b \in \mathbb{Z}$ ? My argument: $$ (-1)^{a-b} = \frac{(-1)^a}{(-1)^b} = \frac{(-1)^a}{(-1)^b}.\frac{(-1)^b}{(-1)^b} = \frac{(-1)^{a+b}}{(-1)^{2b}} = \frac{(-1)^{a+b}}{1} = (-1)^{a+b} $$ Any flaw?
Pranav Bisht
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Why $xb^x = a$ cannot be solved by arithmetic steps? (a formal explanation)

How do I solve the following equation? I understand it is not possible with regular arithmetic steps: $$xb^x = a$$ Provided $b \in \mathbb{R}^+$ and $a \in \Bbb{R}$. What would be the formal explanation telling this cannot be solved by regular…
Luis Masuelli
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What is this method of calculating int number times int number called?

I saw this video on Facebook and I'm curious about this. I have very basic questions on this because I can use it but I can't understand the technique. Link to the video explaining this method on Facebook:…
CodeShark
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Subsets of natural numbers generated by two generators

Let $m$ be a positive integer. Define $N_m:=\{x\in \mathbb{Z}: x>m\}$. I was wondering when does $N_m$ have a "basis" of two elements. I shall clarify what I mean by a basis of two elements: We shall say the positive integers $a,b$ generate $N_m$…
Timothy Wagner
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How do I find two integers - $x$ and $y$ - whose values satisfy the expression $x^2 + y^2 = z$, where $z$ is a perfect square?

I watched a YouTube video of an episode of Who Wants To Be A Millionaire?, in which a contestant was presented with a list of perfect squares. He was asked to choose the number that was also the sum of two smaller perfect squares. This video got me…
moonman239
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Adding $inches^2 + inches$?

At our school we have a "summer packet" we have to complete. In this packet was the following problem: At first the "sum" part puzzled me. I had no idea why they would quiz us on basic arithmetic in 6th grade. But then I realized, the exercise is…
user169330
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Is there a mathematical term for three orders of magnitude?

I've been playing this github game for a while called Swarm Simulator. I like it a lot and there are a bunch of other simulators going around either in-browser like Swarm or iOS apps, etc. These games use terminology centered on what I think of as…
Catija
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find nth term of a few sequences

first $4,-1,-11,-26,-46$ I found a recurrence relation of $U_{n-1} - 5(n-1)$ but I don't know how to find an explicit nth term formula second $0,3,8,15,24$ It goes up by $+3,+5,+7,+9$ I'm not sure how to find nth term for this
mathshelp
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