Mathematics Stack Exchange
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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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Sum of 12 numbers

Which formula can be used to calculate the sum: $$\sum\limits_{i=1}^{12} \left(1 + \frac{i^2 -i}{2}\right)~~?$$ Is there any formula that can be applied instead of manually adding the 12 numbers?
acigard
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Multiplication of large numbers, e.g. $97\times 96$: why does this work?

I've seen various versions of the above image floating around social media on how to multiply large numbers in your head. I know it doesn't work for all numbers, but why does it work for some numbers and what is the rule for knowing whether it will…
米凯乐
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Sn the sum of the first n odd numbers

i need help to solve a question that say : Sn the sum of the first n odd numbers 1 - Formalize this sum: (Give mathematical expression)? 2 - Calculate this sum? how to solve that ? :/
Adel
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Equation simplification

Sorry if the question is pretty trivial but can anyone tell me what rule or law was used to go from $$e_2=C_4^{-1}x_1+C_{10}^{-1}x_2-R_{7}I_3^{-1}x_4-R_{7}R_2^{-1}e_2$$ $$to$$…
CptPackage
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What is the correct value of 2^5^4^3?

My calculator and google calculated it differently, why? To avoid confusion, where should I put the parenthesis. This can be write in at least 16 ways with parenthesis, but which one gives the correct value?
Talha ŞAHİN
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Percentage, Voting, Arithmatic

800 people were supposed to vote on a resolution, but 1/3rd of the people who had decided to vote for the motion were abducted. However, the opponents of the motion, through some means managed to increase their strength by 100%. The motion…
Soumee
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integer S transform

I found the following integer transform, where all variables $x_0,x _1$ and $x_2$ are integers: $ y_0=x_1+floor(\frac{1}{4}(x_0+2x_1+x_2))\\ y_1=x_2-x_1\\ y_2=x_0-x_1 $ The inverse transform is following: $ x_0=s+y_2\\ x_1=s\\ x_2=s+y_1\\ $ where…
Ion Caciula
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Process for reducing calculations to their simplest form

I have the following formula which I suspect I may be able to reduce further but I haven't found a way yet. Is there is method I can follow to ensure that I have reached the simplest form possible? $$\sqrt{1 - \frac{2 - \sqrt{2}}{4}}$$ Generally…
Tim
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Sum a sequence of numbers based on their order

I'm not great with math so please bear with me. I have two sequences of numbers: $$ 4,3,2,1\\ 1,2,3,4 $$ I aggregate them using addition: $$ 4+3+2+1 = 10\\ 1+2+3+4 = 10 $$ I aggregate them using multiplication: $$ 4*3*2*1 = 24\\ 1*2*3*4 = 24 $$ They…
sebjwallace
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Difference between price ratio and spread cumulative return.

Assume I have a $100%$ long position in Apple vs $100%$ short position in Microsoft. I want to calculate the cumulative return to date. In my mind the following approaches should arrive at the same outcome but they do not (and I have a view why…
Definiteweird
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How is $\frac{4\times 3+5\times 6}{18\times -22} = 3$?

I was preparing for civil services tests and recently came across this question in a book. Its answer is option C as given in that book. I have tried to solved it by following DMAS rule and also not following DMAS rule, but I could not get it equal…
Umair Ayub
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Time, Speed and Distance. Moderate Level Question.

Ravi, who lives in the countryside, caught a train for home earlier than usual day. His wife normally drives to the station to meet him. But that day he set out on foot from the station(as he had reached the station earlier than usual) to…
Soumee
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Time, Speed and Distance. Arithmetic question (Moderate Level)

Ajay and Kajol start towards each other at the same time from Barabanki and Fatehpur for their destinations Fatehpur and Barabanki respectively which are 300 km apart. They meet each other 120 km away from Barabanki. Shahrukh starts from…
Soumee
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Time, Speed and Distance: Arithmetic

The Speed of a Car during the second hour of its Journey is thrice that in the first hour. Also, its third hour's speed is the average speed of the first two hours. Had the car travelled at the second hour speed during all the first three…
Soumee
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percentage and consumption arithmetic

Due to an increment of 50% in the price of egg a person is able to buy 4 eggs less for Rs. 24. Find the initial cost of per dozen egg? I am getting the answer as 24. However, the answer given in the book is 36. Please help regarding this.
Soumee
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