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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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How to find $2^{2^{2^{2^0}}}$?

What is the result of $2^{2^{2^{2^0}}}$?
user377675
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Question on half yearly compound interest system.

$X$ borrowed Rs.$150000$ from $Y$ at the rate of $21$ percent per year. At the end of $15$ months, how much compound interest should $X$ pay compounded half yearly? My Attempt. I solved it using the formula ; $$C.I=P[(1+\frac {R}{200})^{2T}…
pi-π
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How to perform the following division?

How to perform the following division? 74628/25/12? which division is to be performed first?First or second and why?
Anwesa Roy
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Proof of Equality

Possible Duplicate: What is 48÷2(9+3)? I was having a heated debate with my colleague and we can't agree on the answer to this question: Does 6÷2(2+1) equal 9 or does it equal 1?
Nosrettap
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Is there an invariant for mapping $(p,q) \mapsto (\frac{p}{1-(1-p)q}, \frac{qp}{1-(1-p)q})$?

Suppose starting with $0
athos
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a, b, c, d are positive integers $\frac{a}{b} < \frac{c}{d}$. What is bigger $\frac{a + c}{b + d}$ or $\frac{c}{d}$

The answer is $\frac{c}{d}$ is bigger. Why? What is the intuition behind? How to prove it? *I took this question from GRE preparation, the resource just says plug in numbers and no intuition or proof or proper explanation. Thanks
YohanRoth
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$a > b > k > 0$ what is bigger: $\frac{a}{b}$ or $\frac{a+k}{b+k}$

The right answer is: : $\frac{a}{b}$ is bigger. But.. I don't understand the intuition behind. Why is it the case? How can I prove it? Thanks
YohanRoth
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Calculate total revenue

I need help on this question. Thanks in advance! my calculation is like this: Percentage difference: 31-27=4 4% = £50,000 100% = £1.25mil Need to find total revenue: Profit = Revenue - Cost Not too sure about this part.
Alvin
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0.999... = 1? What is the secret?

If x = 0.999... (a) -> 10x=9.999... -> 10x-x=(9.999...)-(0.999...) -> 9x = 9 -> x = 9/9 = 1 (b) x = 0.999 (a) = 1 (b) ? So... what is the right explanation for this occur? I know that exists a tiny error somewhere... I think that the subtraction…
Marco
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Question on Compound Interest:

A man borrowed a certain sum of money and paid it back in $2$ years in two equal installments. If the rate of compound interest was $4$% p.a. and he paid back $Rs. 676$ annually, what sum did he borrow? My Approach: Here, First…
pi-π
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Profit and Loss question......

A fruitseller by means of a false balance cheats $20$% in buying and also cheats the buyer to the same extent in selling. Find the gain percent on his outlay. My Approach: He cheats $20$% on purchasing means; He pays only Rs. $100$ which worth Rs.…
pi-π
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How many identical digits end the product?

I'm trying to figure out the pattern: There is 10 , 20, 30 whose product gives three 0s (6000) Then there are the following that would result in 10: 2 x 5 = 10 4 x 15 = 60 6 x 25 = 150 So, initially I thought there are 6 zeros by merely counting the…
Gopinath Rajee
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Evaluating without a calculator

Given that $31 \times 417 = 12927$ , without using a calculator , evaluate $31 \times 0.417 + 12927/4170 $ I'm stuck at how to solve this ... First I deal with $12927/4170$ From the given equation , $ 310 \times 4170 = 129270 $ Therefore .. …
user307640
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A deck of cards.

Player A dealt some cards to player B and himself from a full pack of playing cards and laid the rest aside. A then said to B "If you give me a certain number of your cards, I will have four times as many cards as you will have. If I give you the…
piepi
  • 189
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Summation arithmetic distributing the summation sign

Assuming that $\bar{x} = \frac{\sum_{i = 1}^n x_i}{n}$, I have the following expression that I'm trying to simplify: $\sum_{i = 1}^n (x_i - \bar{x})^2 + n\bar{x}^2$ $ = \sum_{i = 1}^n (x_i^2 - 2\bar{x}x_i + \bar{x}^2) + n\bar{x}^2$ $ = \sum_{i =…
Adrian
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