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.

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Operand names for generic operation

For binary arithmetic operations (addition, subtractions, multiplication, etc.) the form is an operator and two operands. Each arithmetic operator has its down names for the operands (this post). For example, with addition there augend and addend;…
A. Que
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How to solve the Profit and loss problem?

Problem: A shop keeper prices p toys at Rs. q per toy. If the cost of each toy is increased by Rs. r, then find how much more money will be earned by the shop owner after selling p toys?​ Effort : Let the Old cost price of each toy be Rs. $x$. Then…
MKS
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Investigate the reason for a number of undefined expressions in mathematics

Why are the following terms undefined in mathematics? $$ \dfrac{a}{0},0^0$$ such that $a$ is real number. if $n$ to be even number then $\sqrt[n]{x}$ is not negetive number. For example $\sqrt[2]{25}$ is $5$ but is not $-5$. If $a$ is a…
user1019364
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Why can multiplication be done in any order?

I have proof of $ab=ba$ and $abc=acb=bac=cab=cba=bca$ when the terms are all positive. But what about when they are not positive? What about when any number of terms multiplied together? I can't understand why we can rearrange the terms in any way…
S l
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Why is the remainder P when P000000 is divided by 13?

I was trying to solve this question, If the number $413283P759387$ is divisible by $13$,then what is the value of $P$? and stumbled upon this solution. $413283P759387 = 0$ mod $13$ $4132830000000 + P000000 + 759387 = 0$ mod $13$ $4132830000000 = 0$…
Gem
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Adding simultaneous rates

If I have 3 rates like units/second produced by 3 separate devices and I want to get the total rate, is it ok to add the 3 rates up? This seems basic and I'd say it's correct but I thought I'd ask. Thanks
cristian.petroaca
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Why is square root of 2 less than cube root of 3

Square root of 2=1.41421..... Cube root of 3=1.44224..... 4th root of 4=1.41421...... 5th root of 5=1.37972...... 6th root of 6=1.34800...... 7th root of 7=1.32046...... . . nth root of n=.......... Similarly thereafter nth root of n will converge…
user132079
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Arithmetic Remainder Problem

"What is the remainder when 582 is divided by 3?" I want to know how can I solve questions like the one displayed in the image above whether they have a remainder or not, quickly and without the use of a calculator, with paper drafts and without…
Michael Vainshtein
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estimate encoding bits for a sparse array bitmask using arithmetic encoding

I am trying to work out how to estimate the cost in bits for encoding a bitmask using arithmetic encoding. For example, I have an array of 4096 bits. Only 30 of which can be set at any given time, so the probability table looks like the…
DeveloperChris
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Really complicated sales situation

I'm trying to put the following situation into one simple formula: Imagine a store that sells a product for X dollars. They pay Y for it and profit Z (which may or may not be greater than Y). The store receives the payment A days after the…
JoeGeddsMe
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Quick multiplication

How can we explain this with equations ? Quick Multiplication of any two numbers whose last two digits add up to 10 and all other numbers are the same $32\times 38 = 3\times (3+1)|(2\times 8)\implies (3\times 4)|16\implies 12|16 \implies…
Sudheej
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Confused about order of operations to simplify $\frac15\div\frac15\div\frac15\div\frac15\div\frac15\div5\div5\div5$ (and others)

Here is the question that confused me: $$\text{What is the value of}\;\frac15\div\frac15\div\frac15\div\frac15\div\frac15\div5\div5\div5\;? \tag1$$ If the signs stay the same, is the operation done LTR or RTL? I always assumed that it would be LTR.…
Real Noob
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Find the smallest group of integers that has a certain mean

The two integers 1, 2 have the mean 1.5. It's actually the fewest number of integers that has this mean; 0, 1, 2, 3, also has the mean 1.5, but there are four integers now instead of two. How can I find a smallest group of numbers that has a certain…
minseong
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When do we need parenthesis to change order of operations?

A few questions about order of operations: $1$) In an expression such as $1+3+3^2$, it is legal to simplify to $4+3^2$, a violation of the grade school order of operations. In this case, are we adding an implicit set of parenthesis and then…
sakurashinken
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How to show that $5/(1+2^{2/3}) = 1+2\sqrt[3]{2}-2^{2/3}$?

I was trying to simplify the solution, $\frac{1}{5}(1+2\sqrt[3]{2}-2^{2/3})$, from a problem I done and saw that mathematica suggested $\frac{1}{1+2^{2/3}}$. I was wondering if anyone could show how to approach simplification of such expressions…
A quarky name
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