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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the relationship of subtraction and division

I think addition, multiplication and exponents comes naturally in a mental way. Let's say I have the number 133 in the decimal base 10 system. We know that 1 is in the hundred's place. We know that 3 is in the ten's place. And 3 is in the one's…
JohnMerlino
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Calculate Gross amount when only percent is known

Consider Rs.1000 as my Gross salary and suppose 20% is PF. so the simple thing is my NET amount is Rs.800. But when I know only my NET amount i.e. Rs.800 and I know that my 20% PF is already removed. So How can I know my Gross Amount?? please help…
DShah
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How to determine if a binary addition/subtraction has an overflow

From what I understand from my lecture notes, overflow occurs when: $C_{in} \neq C_{out}$ Change in sign For $C_{in} \neq C_{out}$: suppose $111+111=1110=110$. In this case $C_{in}=0, C_{out}=1$, but consider a carry in then: $111+111+1=1111=111$…
Jiew Meng
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Actual process for fractions to decimals?

Alright. I want to get a fraction into decimal. Without a calculator. $\frac{15}{7} = 2.14285714$ Basically, what are the steps for manually getting that decimal result?
Saturn
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How do I divide integers in a negative base?

What algorithm can I use to divide numbers in a negative base? To divide numbers in positive bases, I am accustomed to using short division: 1 1 0 4 9 3 2 r18 23 |2 5 4 1 3 4 5 4 2 1 11 21 7 6 That is, 23 goes into…
Peter Olson
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Negate an integer in a negative base

What is a simple algorithm you can feasibly do by hand to negate an integer in a negative base, such as negadecimal? In positive bases, you can simply append a negative sign if it is not there, and remove it if it is: Negate 123456 -> -123456 Negate…
Peter Olson
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What algorithm can I use to add negadecimal numbers?

I am trying to figure out how to add negadecimal numbers by hand. I can add normal decimal numbers using an algorithm I learned in kindergarten: start with the least significant digits, add them, carry, move left, repeat. Carry: 1111 1 First: …
Peter Olson
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Calculate $2^{1500}$

Is there a way of approximating $2^{1500}$ using pen and paper? I just took $2^{1500}$ as an example but it can be $2^{150000}$ or $12^{95}$. I am just looking for pen and paper method. By approximate, I mean a solution like $3.5*10^{21}$ or…
Eames Cobb
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How to sort numbers from 1 to 20 into 6 piles where sum in each pile is the same?

How to sort numbers from 1 to 20 into 6 piles where sum in each pile is the same? This question, my son got in school and I can't figure out what is the correct approach to solve this.
Nafas
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The operation before addition

I asked a question about operations and one comment puzzled me. Given a binary operation $\ast$ on integers at least $2$, define $\ast'$ by $$m\ast' n = \overbrace{m\ast m\ast \cdots \ast m}^{n\text{ times}}.$$ Example : if $*$ is $+$ , $*'$ is…
Pyrofoux
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How to prove that $2+2 = 2*2 = 2^2 \cdots= 4$

One day, I noticed that $2+2 = 2*2 = 4$. Later, I learned that $2+2 = 2*2 = 2^2 = 4$ Multiplication is an abstraction of a lot of additions , exponential is an abstraction of a lot of multiplications... I'm sure there is always an abstraction of…
Pyrofoux
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long division algorithm

Lets say we are running the long division algorithm (this long division algorithm) on two integers $A,B$ and we want to compute $\frac{B}{A}$. Why are we guaranteed to never have to place a digit greater than or equal to $10$ at the top of the…
user796511
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Linear Arithmetic - why calling it linear?

This might sound like a stupid question, but I could not figure out, why Linear Arithmetic is called linear. Linear Arithmetic often comes in play when talking about SMT Solving. For example, in this PDF linear arithmetic is defined as formulas…
John Threepwood
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Square and reverse reading of an integer

For all $n=\overline{a_k a_{k-1}\ldots a_1 a_0} := \sum_{i=0}^k a_i 10^i\in \mathbb{N}$, where $a_i \in \{0,...,9\}$ and $a_k \neq 0$, we define $f(n)=\overline{a_0 a_1 \ldots a_{k-1} a_k}= \sum_{i=0}^k a_{k-i}10^i$. Is it true that, for all…
francis-jamet
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Problem related to a clock

I faced the following problem: At what time after 4 o'clock, the hour and the minute hand will lie opposite to each other? $\quad$ 4-50'-31" $\quad$ 4-52'-51" $\quad$ 4-53'-23" $\quad$ 4-54'-33" Can someone point me in the right direction?
user53386
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