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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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Rule for multiplying rational numbers

The rule for multiplying rational numbers is this: $\space\frac{a}{b}\cdot \frac{c}{d}=\frac{ac}{bd}$ Can the rule be proven or is it meant to be taken as a given? Edit: Where $b\neq 0$ and $d\neq 0$.
Sara
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Why is $n$ divided by $n$ equal to $1$?

I've understood how to apply this operation for many years but I recently was reminded that: $n^0 = 1$ Which in high school I accepted and just "solved for", but I'm now curious. Why is that true? So my own cursory research on the internet led me to…
Ixmatus
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5 answers

Is a negative number squared negative?

$-3^2 = -9$ I found this problem while doing an algebra refresher in the book The Complete Idiot's Guide to Algebra. I asked my engineer brother this problem and he got it wrong. A search on Google for why is a negative number squared negative I…
Mark
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which is larger number? $\sqrt{7}-\sqrt{6}$ or $\sqrt{6}-\sqrt{5}$

Which is larger number? $\sqrt{7}-\sqrt{6}$ or $\sqrt{6}-\sqrt{5}$? Squaring both sides will give me something but I could not go any further.
Sherlock Watson
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5 answers

Doing take aways

I am reviewing take aways. I am having trouble How do I do $342 - 58$? For the ones column I made the $2$ into a $12$ so I can do $12 - 8 = 4$ but I must take away one tens. So I get $3 - 5$ in tens column but I cant do $3 - 5$. What do I do now do…
user133894
18
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1 answer

How to get count of digits of a number

I need to get count of a number like 12346 it must get the count of digits = 5 One way is that divide the number by 10 until remainder equals to zero. Please tell me other approaches.
Hamed Kamrava
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Is there a way to prove that $2+2$ really equals $4$?

In elementary school, one learns that $2+2=4$ by experiment (putting two apples next to two other apples), and maybe also from some addition table to be memorized. But is there any approach that proves $2+2 = 4$? If so, an example of such a proof…
Anoni Moose
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How to explain that division by $0$ yields infinity to a 2nd grader

How do we explain that dividing a positive number by $0$ yields positive infinity to a 2nd grader? The way I intuitively understand this is $\lim_{x \to 0}{a/x}$ but that's asking too much of a child. There's got to be an easier way. In response to…
Marcus Junius Brutus
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6 answers

How do you find the number of multiples of a given range of numbers?

I know this sounds a bit stupid but this question always confounds me. Say that you are given a range of numbers like $20$-$300$. And it asks you to find how many multiples of $5$ are given in that range. How would you proceed? What would the…
beepbeepbeep
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Why is the square root of a negative number impossible?

What is the algorithm to get the square root of a number? Why does it not accept / allow for negative numbers? I've always been told that the square root of minus one does not exist by my maths teacher, but I don't really get why?
Ben Johnson mk2
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6 answers

Find the number of $X$ from start to end

If I wanted to figure out for example, how many tutorial exercises I completed today. And the first question I do is question $45$, And the last question I do is question $55$ If I do $55-45$ I get $10$. But I have actually done $11$…
K-Feldspar
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Is long division the most optimal "effective procedure" for doing division problems?

(Motivation: I am going to be working with a high school student next week on long division, which is a subject I strongly dislike.) Consider: $\frac{1110}{56}=19\frac{46}{56}$. This is really a super easy problem, since once you realize…
Matt Calhoun
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Does the negative apply before or after an exponent

I have been having an argument with a friend, and they claim $-8^0$ is $1$, and I claim that $-8^0$ is really $-(8^0)$ and is therefore $-1$. Who is right?
user144807
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Is there an numeric arithmetic with a single operator?

I remember reading a while back about arithmetics with only a single operator that did all the work of the familiar $+ - \times /$ operators. If there is such a thing, could someone point me to it? As background: I have a side project where I'm…
sea-rob
  • 381
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$ \sqrt{2-\sqrt{2}} $ simplified

So I have a (nested?) square root $ \sqrt{2-\sqrt{2}} $. I know that $ \sqrt{2-\sqrt{3}} = \frac{\sqrt{6}-\sqrt{2}}{2} $. I know how to turn the simplified version into the complex one, but not vice versa. What is $ \sqrt{2-\sqrt{2}} $ simplified in…
Gᴇᴏᴍᴇᴛᴇʀ
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