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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What does it mean that multiplication and division have the same precedence?

I have read and heard in many places that multiplication and division are of equal precedence. So what is the value of: $$ 80 \div 10 \times 2 $$ Is it $$(80 \div 10) \times 2 = 16$$ or $$ 80 \div (10 \times 2) = 4 $$ ? The answer here seems to be…
jds
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How do you distinguish the difference between a negative sign and a minus sign in Algebra

Both the negative sign symbol and subtraction's minus symbol look the same, so how does anyone tell them apart?
Ethan
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Is my son's math book key in error?

My son's math book key gives a different answer than what my wife and I consider the right answer. We both worked independently with our son and I asked two other people (both of whom came to the same conclusion). What's important here is that…
Stonetip
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Does the zeroth root exist?

Definition of $Nth$ root: $3rd$ order inverse group $1$ hyperoperation. Division is how many times you can subtract a certain divisor from the dividend before it becomes negative. Likewise Nth root is the result of repeated division by a certain…
Caters
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The proof of $\sqrt{2}$ is not rational number via fundamental theorem of arithmetic.

I assume that $\sqrt{2}$ is positive number satisfies $(\sqrt{2})^2=2$. proof) Let $m$, $n$ as natural number,$\ $ $M$ is the number of prime factor of $m$,$\ $ $N$ is also the number of prime factor of $n$. For example, $m=12=2^2\cdot3$, $M$ is…
Rupert
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Subtraction of a negative number

Why subtraction of a negative number from a positive number is addition? Eg: $a - (-b) = a + b$ When looking through the number scale I am unable to relate this, please kindly clarify ?
wcs
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Solve equation with $x$ in the exponents

How can I solve $$8(9^x)+3(6^x)-81(4^x)=0 $$ for $x$ using elementary methods. Thanks a lot!
EQJ
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Prove that $2002^{2001}$ and $2002^{2001}+2^{2001}$ have the same number of digits.

I have an arithmetic exercise as follows: Prove that $2002^{2001}$ and $2002^{2001}+2^{2001}$ have a same number of digits. It seems easy but I don't know how to do. I can do it if $2002$ is replaced by $2000$. Any hints are appreciated. Thanks a…
mapping
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Quotition versus partition

This new Wikipedia article may look different by the time the reader of this question sees it. For now, it says $6\div 2$ can be construed in either of two ways: "How many parts of size $2$ must be added to get $6$?" (Quotition division) "What is…
Michael Hardy
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How do "proofs" work in mathematics, down to the basic level?

I came across this basic example of a problem: Prove by mathematical induction that 1 + 2 + 4 + 8 + 6 What am I supposed to prove, the sum? I don't quite get it, so I decided to dig in to encyclopedia references for help: In mathematics, a proof…
Not Fine With Maths
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When I state $(a\cdot b) \cdot c = (a \cdot c) \cdot b$ , what properties am I using?

When I state $(a\cdot b) \cdot c = (a \cdot c) \cdot b$ , am I using only the commutative property or both the commutative and associative property?
Bentley4
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How to manually calculate cube roots

I have always used a calculator for determining roots But I think it would be useful to know how to do this on paper. Are there different procedures for calculating square roots than for cubic roots or does it all use the same principles? So my…
Antonio
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How do I transform the left side into the right side of this equation?

How does one transform the left side into the right side? $$ (a^2+b^2)(c^2+d^2) = (ac-bd)^2 + (ad+bc)^2 $$
Dan Webster
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Adding and Removing Non-Compounded Percentages does not produce the same result?

If I take the value 100 and I want to and 10% tax to it and then a 7% tax to it, I am doing the following: $$\begin{align*} 100 \times \left(1 + \frac{10}{100}\right) &= 110\\ 100 \times \left(1 + \frac{7}{100}\right) &= 107\\ 100 + 10 + 7 &=…
Xaisoft
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How is rearranging $56\times 100\div 8$ into $56\div 8\times 100$ allowed by the commutative property?

So according to the commutative property for multiplication: $a \times b = b \times a$ However this does not hold for division $a \div b \neq b \div a$ Why is it that in the following case: $56 \times 100 \div 8 = 56 \div 8\times 100$ It seems…
Sphygmomanometer
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