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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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R Posner, Economic Analysis of the Law (8th edn, Aspen, 2011) 151

Paul Davies. JC Smith's The Law of Contract (2018 2 ed). p. 6. On a slightly different tack, but in a similar vein, Judge Richard Posner has written:17 Suppose I sign a contract to deliver 100,000 custom-ground widgets at \$.10 apiece to A, for…
user53259
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How to solve quadratic equation in base 13?

I have to use only operations in the base 13 to solve this equation, but I don't know how to do it. I came up with the idea to convert everything in the base 10, but I need to do it in a base 13. A equation is: $$x^2 - 176_{13}\times x + 8089_{13} =…
Mia09
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Tap filling Tank .. Time taken?

A tap can fill a tank in 16 hours whereas another tap can empty the tank it in 8 hours. If in a three fourth filled tank both the taps are opened, then how long will it take to empty the tank in this scenario? I know that time to…
techno
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A fruit dealer fixes selling price of watermelon juice in such a way that he ends up earning a profit of 30% after paying tax which is 13%

A fruit dealer fixes selling price of watermelon juice in such a way that he ends up earning a profit of 30% after paying tax which is 13% of the cost price. A shopkeeper buys watermelon juice from dealer and marks up the price by 15% and then…
Sachin
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Fraction of non integers?

By definition of a fraction, can the numerator or the denominator be a non integer ? For example, can we call the expression $\frac{\pi}{2}$ a fraction ? The popular answer is no, but since the calculus of fractions is valid even with non integers,…
Sephi
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Chopping arithmetic on terms such as $\pi^2$, $\pi^3$ or $e^3$

I have a problem where I have to use 3-digit chopping with numbers such as $\pi^2$, $\pi^3$, $e^3$, etc. If I wanted to 3-digit chop $\pi^2$, do I square the true value of $\pi$ and then chop, or do I chop $\pi$ first to 3.14 then square it?
badjr
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Is this a valid non formal proof for fundamental theorem of arithmetic?

Any composite number can be expressed as a unique product of prime factors. My attempt was: Let $b \in \mathbb{Z}$ and is a composite number. One of the ways to find the divisors of a number is to divide it by an integer $a$, such that…
ESCM
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Men, Work and Time

10 men can do a piece of work in X days and 20 women can do the same work in X-5 days. 30 men can do the same work in Y days and 80 women can do that work in Y-5 days. Find X and Y I wish to understand the solution of this question. I know the…
ShiS
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converting infix to postfix

24 * (5 + 6) - 2 I am trying to find the post fix for this I got this so far 24 5 * 6 2 + - is this correct or wrong I am quite struggling with these
Adil Ali
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Convert Repeating Decimals to Fraction

If there is a number $x = 0.333333333$ where 3 is repeated infinitely how to convert it to fraction ? It is said that $-> 0.(3) = \frac{3}{10} - 1$ and $0.33 = \frac{33}{100} - 1$, But I can't understand Why ? I searched for similar Questions like…
Khaled Mohamed
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How to check if the set can be divided into two equal parts?

We are given a multi-set of numbers which consist of "$x$" 1's, "$y$" 2's and "$z$" 3's. Given x,y and z , how to figure how out if this set can be divided into 2 equal parts(where sum of both the sets is equal to each other)…
user707538
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How to distribute points to players based on their effort?

Assume that a HOME team and an AWAY team play each other in a game. The HOME team defeats the AWAY team, so the HOME team gains 30 points and the AWAY team loses 30 points. Each team has two players. The winning team distributes the points that it…
JV-
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Solve for distance when given 2 speeds and a difference between the 2 in time

I was given a question in math class which asked this question: Raj went Xkm in 90kmh to go to his work. One day he went 120kmh and shaved 16 minutes off of his regular time. What is X? I was very confused and just wanted to see how this would be…
Vraj P
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Show that $2 ^ n - 1$ divides $3 ^ n -1$ if and only if $n = 1$

My idea was: If $n$ is even, $\gcd (3ⁿ-1; 2ⁿ-1) = \gcd (6ⁿ-3ⁿ + 3ⁿ-1; 2ⁿ-1) = \gcd (6ⁿ-1; 3ⁿ-1) = 2ⁿ-1 $ So $3ⁿ-1 = 2ⁿ-1$ So $3ⁿ = 2ⁿ$, what does $n = 0$ (nonsense pq gets 0/0) $3ⁿ-1 \equiv 0 \mod 2ⁿ-1$, so $3ⁿ \equiv 1 \mod 2ⁿ-1$, i.e. $3 \equiv…
Lambert macuse
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Integer $N$, in base $b$, is $6789$. If $N$ is a multiple of $b-1$, and $b<16$, then what is the successor of $b$?

An integer $N$, expressed in base $b$, is $6789$. If $N$ is a multiple of $b-1$, and $b$ is less than $16$, then what is the successor of $b$? I couldn't develop anything more than $$N_b = \left(\;n\cdot (b-1)\;\right)_b = 6789_b$$ (with…
Lambert macuse
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