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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Binary arithmetic with two's complement

By intuition I can see that the 2's complement will be the negative of a number but I want a more rigorous proof to convince myself that no arithmetic will ever fail. EDIT More clarification: Consider the domain [0,8) decimal | 2's comp | integer …
Raja
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Averaging Whole Numbers

Average survey results I'm curious which way is correct when rounding whole numbers. My issue is that the customer wants decimal places included in the average when the User only ever will select whole numbers in a range from 1-5. In my head it…
Avien
  • 133
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Proving $mn=nm$ for all $n,m\in \mathbb N$

How can I prove that $mn=nm ,\forall m,n \in \mathbb N$, by using just the following axioms? $(\forall n \in \mathbb N)(n\cdot 0=0)$ $(\forall m,n \in \mathbb N)(m(n+1)=mn+m)$, The axioms and properties of addition.
Walter r
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Another Approach to Long division

I need your help with a lifelong problem I have always had. There are two things in life I hate most, 1) weddings and 2) Long division. For the life of me I hate division. I am horrible at it. I can multiple large numbers in my head but I can’t…
jessica
  • 1,002
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Inverse of percentage?

What is the best way to cacluate the inverse of a percentage? For example: 100 * .85 = 85 85 * x = 100 x = 100 / 85 x = 1.17647 Also, 279 * .85 = 237.15 237.15 * x = 279 x = 279 / 237.15 x = 1.17647 For any percentile y (i.e. .85), how do I…
Kirk Woll
  • 133
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Find the coefficient of $w^{3}x^{5}z^{2}$ in the expansion of $(w+x+y+z)^{10}$

I need to find the coefficient of $w^{3}x^{5}z^{2}$ in the expansion of $(w+x+y+z)^{10}$. How can I do this? The solution is probably connected somehow to ordinary generating functions. I found something similar: coefficient of $x^{17}$ in…
khernik
  • 1,369
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A clock synchronisation problem

I need the precise time between two time stamps from a remote computer and to eliminate any difference due to the transmission time of signals to and from my computer. I have an NTP program running to do this and think that all I need to do is…
user36093
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For integers $a < b < c$, is there a general way to sort $a^{1/a}, b^{1/b}, c^{1/c}$?

I'm working through the Math GRE Practice Book and I was struck by problem #6, which asks to sort $\{ 2^{1/2}, 3^{1/3}, 6^{1/6} \}$ in ascending order. I solved it like this: $$ 2^{1/2} \quad \gtrless \quad 3^{1/3} \quad \gtrless \quad 6^{1/6} $$ $$…
Robert D. French
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Division by subtraction - dividing the remainder by subtraction?

We can divide a number by subtraction and stop at the remainder as shown here - How to divide using addition or subtraction. But how do we continue to divide the remainder by subtraction ? I looked on google and could not find such answers. They…
math mongol
  • 31
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How does a student complete >> more than two problems per week in this problem?

A website currently has a bank of 770 questions with two new questions added every three days. A student has already completed 300 of the questions and plans on completing one question per day moving forward. In how many days will the student have…
user1086853
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2 answers

Basic math ahead

I am a bit ashamed for asking such a simple question, but we really need the answer. We develop a program to calculate... something for our clients (I would be hard pressed to explain it in english, but in french : calculer les cotisations des…
thomasb
  • 155
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How much is 93 more than 47?

This was a question that i came across in my 7 year old daughters book. My wife and i have argued at length whether the two numbers should be added and subtracted. I think the statement is ambiguous and both 140 and 46 can be the correct…
Kumar Bibek
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If $10^{20} +20^{10}$ is divided by 4 then what would be its remainder?

If $$10^{20} +20^{10}$$ is divided with 4 then what would be its remainder?
DebojyotiMukh
  • 915
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property of equality

The property of equality says: "The equals sign in an equation is like a scale: both sides, left and right, must be the same in order for the scale to stay in balance and the equation to be true." So for example in the following equation, I want to…
JohnMerlino
  • 621
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Estimating $(\frac{37}{38})^{36}$

I'm working through a bank of probability questions from 1965, so pre-calculator era (I think?). The solution to one of the questions confidently states that $\left(\frac{37}{38}\right)^{36}\approx 0.383$. Is this obvious/is there a trick here?
Oxonon
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