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.

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Difference between $\sqrt{x^2}$ and $(\sqrt{x})^2$

According to my logic, $$\large\sqrt{x^2} = x^{2\times \frac{1}{2}} = x = x^{\frac{1}{2}\times 2}={(\sqrt{x})}^2$$ But when I look at the graphs of these guys, they're totally different. Edit: Complex answers are okay, if you know what I mean.
Nick
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Percentages of $\$100,000$

$\$6,200$ is $6.2\%$ of $\$100,000$. That leaves $\$93,800$ as $93.8\%$ of that $\$100,000$. But when I take $\$93,800$. and multiply it by $6.2\%$, I get $\$99,615.60$ instead of $\$100,000$. Why is this? And how do I get back to my $\$100,000$. Do…
Myrna
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Negative × Negative = Positive... right?

The wife and I were doing homework together, and we noticed something really strange when charting quadratics with a TI-series graphing calculator: f(5) = -x^2 + 110x - 1000 f(5) = -5^2 + (110*5) - 1000 f(5) = -25 + 550 - 1000 f(5) = -475 // Wait a…
Dan
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A property of proportions: if $a/b=c/d$, then $(ma+nb)/(pa+qb)$ is equal to $ (mc+nd)/(pc+qd)$

If $\large\frac{a}{b}=\frac{c}{d}$ how we can obtain $\displaystyle{\frac{ma+nb}{pa+qb}=\frac{mc+nd}{pc+qd}}$? I can get $\large\frac{ma}{qb}=\frac{mc}{qd}$ and $\large\frac{nb}{pa}=\frac{nd}{pc}$ , now If we have $\large\frac{a}{b}=\frac{c}{d}$ and…
studentNk
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Did the ancient Sumerians calculate the square root of two?

This post makes the claim: Not bad you might think, but compare it to the Summerian Kù of 51.85cm of the copper of Nippur and its derived unit SAR of 3600 Kù being 1866.6 meter being only 0.77% off from an arc second of the meridian. Those…
hawkeye
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Simplifying Surd Fractions

can someone show me how to simple surd fractions such as: $$\frac{{8\sqrt 3 }}{2}$$ Can someone please help me here?
Rajesh
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How many new digits can appear in a multiplication?

When adding two positive integers, the result is sure to have at most the same number of digits as the largest of the two terms, plus one. What about multiplication? Can many more digits can the product have than its factors? I tried to look at a…
Paul Manta
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How can this equality be established by elementary algebraic means?

Let $x \geq 1$. Then is it true that $2x^3 - 3x^2 + 2 \geq 1$? If so, how can I show this using only elementary ideas such as factorisation? Of course, I can demonstrate this using the methods of single variable calculus. The outline is as…
Saaqib Mahmood
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Square root each term (clarification on polynomials?)

So I'm in Algebra 2, and right now we're learning about conic sections (circles/ellipse/etc). I thought some problems in the workbook looked weird, like this one: $\y^2 = x^2 + 16 By my understanding, I should be able to take the square root of the…
user164390
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Is it possible to have a mixed parentage of 10% 90%

Is it possible to have a mixed parentage such that you are, for example, 10% Dutch and 90% English? One generation up your mother would be 100% English and your father 20% Dutch and 80% English etc etc. How do you figure this out back up to the…
c4urself
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Square root of a squared number changes sign, which to apply first?

Heres something Ive always found interesting. Supose we have a variable $x$, and $x$ equals a negative number: Say: $$x=-17$$ Now, I can apply a square to both sides of the equation and preserve the equality: $$x^2=(-17)^2$$ Now I can apply the…
S.s.
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How many answers can be created using the elementary arithmetic operators?

If I gave you an amount of $n$ numbers, how many anwswer will you be able to create using the elementary arithmetic operators ($+, -, \times, /$)? These are the rules: All numbers $\in\mathbb{Q}_{0>}$. All numbers are different ($a\neq b \neq c…
Ellyjant
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How to calculate price for stamps?

I'm trying to create a programm that has the ability to calculate the most effective way of breaking down the number of stamps (3 and 5 cent) necessary for a consignment. That is - if a transmission costs, for example, 11 cents, it would take one 5…
Xeen
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The last digit of $n^5-n$

What will be the last digit of $$n^5 - n \bmod 1000,$$ where $n$ is a natural number and $m \bmod 1000$ is the remainder when $m$ is divided by $1000$.
Anamitra Palit
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Dumb question about the division algorithm.

The theorem about the division algorithm says: Given a, b $ \in \mathbb{Z}, b \neq{0}, $ there exist unique numbers q and r , $q,r \in \mathbb Z $such that $ a = bq + r , 0 \lt r \lt |b| $. Can q be zero?
Trux
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