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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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Silly question about properties of operations

This is a very frivolous question about basic arithmetic. In a precalculus book I'm going through substraction and division are informally defined as the "opposites" of addition and multiplication, and an "inverse" to a number is defined with…
nek28
  • 153
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Calculating Lower and Upper Bounds of 100 to 2 Significant Figures

I'm trying to help my daughter with the concept of lower and upper bounds of a number when given a specific accuracy, but I'm starting to realise how many holes there are in my own knowledge! For a specific number of decimal places this is…
Richard Day
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Why is an equation that originally had a division through 0, still not defined in that point - after it was removed

Relearning the basics. When I have the equation: $$2x^2+2x+2=2x^2+2x+2$$ $$0=0.$$ I can say that x is any number. But when i simplify this equation from the following one: $$2x(x+1+ \frac{1}{x})=2(x^2+x)+2$$ $$\iff 2x^2+2x+2=2x^2+2x+2.$$…
Agorf
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How do I create an index where a low number equals a high score, as below?

Can you help? If $0.6 = 10$ and $30 = 1$, what does $3.3$ equal and what does $1.62$ equal? Is there a formula to this and if so what is it, please? This would enable me to calculate any number between $0.60$ and $30.00$ (to two decimal places) and…
Steve B
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How is division comparable to subtraction?

I was watching a lecture where the professor was describing the mathematics of the ancient Greeks and said they had division because "that's just fancy subtraction." That line got me thinking because it doesn't seem to be quite true. Multiplication…
user284549
  • 21
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Tips on counting length of intervals

I'm studying for an actuarial exam and it always confuses me when I'm trying to count intervals in annuities. For example, if I want to know how many payment periods there are from period 13 to period 27, what is the length of this interval? A more…
David South
  • 2,508
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How can calculate this: $ n=\pm\frac{1}{400} \mp\frac{16}{400} $ (multiple Plus-Minus operators)

This is a problem from a book i'm reading. The $ \pm\frac{1}{400}$ and $\mp\frac{16}{400}$ represent tolerances of some quantities and i'm looking to find the total tolerance/sensitivity in the quantity $n$. So i'm confused here. The book gives the…
KeyC0de
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Are there any $x$ for which $x ^2= (x-1)(x+1)$?

$x^2 = (x-1)(x+1)$. Does anybody know if this is true for any numbers (specifically the larger the better)? Because: $256^2 = 255 \cdot 257 + 1$ It's very very close, just an interesting thing I noticed when dealing with 2-byte integers in…
Wyllow Wulf
  • 143
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Check algebraic transformation with trial numbers?

I did some algebraic transformations on equations with multiple real variables $x_i$, and I'd like to check whether the transformed equation is still valid. The equations are basically only rational functions with rational coefficients. I found…
Gere
  • 2,117
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Order of parsing + and -

This seems like an absurdly simply question, and is possibly below the level of this forum, but it seems the most sensible place. I'm building an arithmetic equation parser, and currently working on parsing + and - operations. I know that (leaving…
wyatt
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How to calculate fuel cost and mpg?

A car has a mileage of "5 miles per litre" and traveled a distance of 573 miles. The cost of fuel is £1.09 per litre. How do I compute the miles per gallon(mpg) and the total cost of fuel for the trip? A formula or example would be great, so that…
user892134
  • 123
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Order of operation to get total

Does anyone know the answer for this equation: $$((6.2 * 4) * ((0.00019106 * 2,715,297.4673) + (0.00226263 * 4,500) + 0.55))\\ * (1 + 0.1 + 0.02 ) / 150 * 10 = ?$$ I also do not understand how it is answered step by step, if you could provide how it…
user256816
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Do negative signs count as subtraction or multiplication?

Would $-x$ count as $0 - x$ or $(-1)\times x$?
James Wu
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detecting 2 n bits integer addition overflow

Can somebody prove that when we add 2 bit integers and if there is an overflow then the result always will be lesser than the 2 operands used??
chappar
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How can one make sense out of a negative number?

We know that if you have 3 apples and somebody gives you 4 apples, you then have 7 apples but then if we deal with negative numbers and we have -3 apples and somebody gives us -4 apples, things can get confusing and nonsensical. How can we make…
Jesus Christ
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