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 is meant by "decimal adjustment" in this problem?

I know how to do addition in different bases, and I know how to convert between bases, but I have never heard of "adjustments" between bases while adding. I would solve this by simply getting a hexadecimal result and then converting it. But the…
Cameron Ball
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Help with $\sum (x_i- \bar{x})(y_i - \bar{y}) = \sum x_i(y_i - \bar{y})$

I can not understand how to get from one side to the other. $$\sum [(x_i- \bar{x})(y_i - \bar{y})] = \sum[x_i(y_i - \bar{y})]$$
Travis
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Interval arithmetic - faster version

As per the below question picked from self training exercise: Q4: In passing, Ben also cryptically comments, "By testing the signs of the endpoints of the intervals, it is possible to break mul_interval into nine cases, only one of which requires…
overexchange
  • 209
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Theory behind multiplying decimals

When multiplying two decimal numbers, you first ignore the decimals, find the product, then count the number of decimal places that need to be in the answer by taking the sum of the original decimal places. Why exactly does this work?
qetnr
  • 33
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Arbitrarily long arithmetic progressions?

I found a theorem that states that if $A\subset \mathbb{Z}$ such that the upper Banach density is non-zero, then $A$ contains arbitrarily long arithmetic progressions, this is called Szemerédi's Theorem. The converse however is not true. In fact T.…
Mathematician 42
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order of operation

For the following expressions,why we can get the right answer even we do addition /subtraction first ? $3+4\times 11-5 = (3+4)\times(11-5) = 42$ $6+4\times7-4$ $5+2\times13-10$ $4+7\times16-6$ $3-2\times1+5$
monk
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Prove the uniqueness of subtraction

I have to prove this proposition: Given $m,n \in\mathbb Z$, there exists one and only one $x \in\mathbb Z$ such that $m + x = n$. So, just to be sure: I am given an equation and asked to first prove the existence of solution x and then its…
Johnathan
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Relation between tolerance and correct decimal places

If I want to find an answer that is correct to say 10 decimal places, do I use a tolerance of $10^{-10}$ or $10^{-11}$ for example? In other words, is the tolerance to be used equal 10^ (- number of correct decimal places) ?
dramzy
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How to simplify this arithmetic expression

I'm trying to simplify: $\left[(\frac{3}{4}\right)^{7}\cdot$ $\left(\frac{3}{4}\right)^{-4}]^{2}$ $\cdot4^5$ The only advance that I have done is $\left[(\frac{3}{4}\right)^{14}\cdot$ $\left(\frac{3}{4}\right)^{-8}]$ $\cdot4^5$ and then…
Learner
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How to determine significant figures involving radicals and exponents

How do you determine the significant figures for solving equations with radicals and exponents? For example, how do you evaluate $x = \sqrt{4.56^2 +1.23^2}$?
user188811
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How many divisors of N ended by 5

I must know how to find how many divisor of N ended by 5 ? In my exercise, I have $\ N=63'000 = 2^3*3^2*5^3*7 $ and I can found the number of divisors of N using $\ (3+1)*(2+1)*(3+1)*(1+1)=96$ Among these 96 divisors, how many ended by 5 ? How can…
Cyrill Gremaud
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How to calculate (predict) how much I will be paid in 30 days if I know how much I was paid in the first 9?

I'm a very simple man living his life. I don't know much math. This is a real world scenario of me trying to apply math and trying to find how much approximately I will be paid this month. I know some math terms and basic theorems but I don't know…
bodacydo
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How to solve a subtraction equation that results in a negative number?

So we're home-schooling our 6-yr old and she's doing basic addition/subtraction/multiplication/division.. and I wrote a subtraction problem backwards by accident the other day, and I can't figure out how to show her how to solve it. Any help would…
Sam Axe
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Why does dividing by zero give us no answer whatsoever?

I've heard about this and I know that division can be used in one way like this: For example, if I want to do $30$ divided by $3$, how many times can I subtract $3$ from $30$ to get to $0$? Well, I can do it this way:…
Mathster
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How do I solve an equation with three terms, with the unknown inside a square root, inside a third root, in two of them?

The equation is $$\\ \sqrt[3]{\sqrt{a}+b}+\sqrt[3]{-\sqrt{a}+b}=k.$$ How do I find$\ a$?
Vincenzo Oliva
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