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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Hexadecimal Sum

How do I go about finding the hexadecimal sum of 9A88 and 4AF6? I know how to find the decimal sum, but have little understanding of how to find the sum of a hexadecimals?
Adam
  • 21
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3 answers

How do I solve this square root problem?

I need to solve the following problem: $$\frac{\sqrt{7+\sqrt{5}}}{\sqrt{7-\sqrt{5}}}=\,?$$
SIBHI S
  • 123
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Show that the last four digits of $2013^k$ are 0001

Show that a natural $k \ge 1$ exists s.t the last four digits of $2013^k$ (written as a decimal) are 0001. I understand that k must be of the form k=4m. The last digit of 2013 is 3 and only when powered by multiply of 4 the result ends with…
Galc127
  • 4,451
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Need help finding closed form of finite product

Is there a closed form for this product? $$\prod\limits_{k=1}^n (n+k)$$ I checked it on wolfram alpha but it uses something called the Pochhammer symbol. Does anyone else know of a nice explicit closed form or some type of trick to calculate this…
homegrown
  • 3,678
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Arithmetic sets problem

I need help with a set problem Given: $$A=\{(\sqrt{n}+2) \in \Bbb Z \ /\ \ 16\le n^2 \le 1296 \}$$ $$B=\{({3m-2}) \in A \ /\ \ 4 \le 4m+3 \le 17 \}$$ Calculate the value of : $$n(A)\times n(B)$$ So far I've got into $$ A =…
Harry
  • 81
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How is HCF (c, d) = HCF (d, r), where c = dq +r (by Euclid's division lemma)?

I read this in a math textbook, stated as obvious fact. I cannot wrap my head around why this works. I understood the division lemma, and also got the algorithm to work: but the proof of why the algorithm works, just said "because of the equation"…
Aditya M P
  • 121
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Rounding up to $3$ significant figures when adding

If $a,\ b$ and $c$ are real numbers and you are required to find $a + b + c$ to $3$ significant figures, to how many significant figures could $a,\ b$ and $c$ be rounded up to to give the result?
Jojoba
  • 21
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How many seconds are there in 7 3/8 minutes?

$7 \text{ minutes} \cdot 60 \frac{\text{seconds}}{\text{minute}} = 420 \text{ seconds}$ What about the other $\frac{3}{8}$ minute?
listoff
  • 21
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1 answer

Simplify a surd expression

I won't lie, I have the following questions in my maths homework but I have no idea how to solve it and I wondered if you could help me here! My teacher has taught us, what seems to be the basics of surds now, but it no seems quite apparent that he…
Andy
  • 205
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Simplify with no calculator

$\dfrac{(8^3)(-16)^5}{4(-2)^8}$ $\dfrac{8\cdot8\cdot8\cdot-16\cdot-16\cdot-16\cdot-16\cdot-16}{4\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2}$ $\dfrac{8\cdot8\cdot8\cdot-16\cdot-16\cdot-16\cdot-16\cdot-16}{2\cdot2\cdot2\cdot2\cdot2\cdot2\cd…
Franck
  • 65
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Simplifying a simple fraction with exponent

I am trying to simplify this fraction : $ \dfrac{(3^2)(5^4)}{15^3} $ The answer is : $ \dfrac{5}{3} $ I am trying to do the following: $ \dfrac{3^2}{15^3} \cdot \dfrac{5^4}{15^3} $ so ... $ \dfrac{1^{-3}}{3} \cdot \dfrac{1^1}{3} $ But that's not…
Franck
  • 65
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New Year challenge

if i did one push up on Jan 1st 2014 and I did two push ups the next day Jan 2 2014 than 3 times on Jan 3rd 2014 what would I be at by the end of the year? How many pushups would I have done throughout the whole year?
Devon
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Show that $\frac{\sqrt[n]a}{\sqrt[n]{ab}+\sqrt[n]a+1}+\frac{\sqrt[n]b}{\sqrt[n]{bc}+\sqrt[n]b+1}+\frac{\sqrt[n]c}{\sqrt[n]{ac}+\sqrt[n]c+1}=1$

If $$\sqrt[n]{{abc}} = 1,$$ Prove that $$\frac{\sqrt[n]a}{\sqrt[n]{ab}+\sqrt[n]a+1}+\frac{\sqrt[n]b}{\sqrt[n]{bc}+\sqrt[n]b+1}+\frac{\sqrt[n]c}{\sqrt[n]{ac}+\sqrt[n]c+1}=1.$$
mehransalehi
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The arithmetic mean of $X$ when arithmetic mean of $X^2 = 29$.

Sorry if my question is a beginner because of my mathematical knowledge is low. arithmetic mean is : $$ \overline x=\dfrac{x_1+x_2+\cdots+x_n}n $$ What method can solve it? $$ \overline{X^2}=29\quad\Rightarrow\,\text{Not }\left(\overline…
user106557
  • 133
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how do we prove $p|q\cdot r \rightarrow p=q$ or $p=r$ (all primes)?

I know this is one of the most fundamental basis of arithmetic but I can't find the result by myself. how do we prove $p|q\cdot r\rightarrow p=q$ or $p=r$? ($p, q, r$ being prime numbers)
Thomas
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