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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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On the properties of irrational number

Let $a$ is an irrational number. Then prove or disprove that $$a+a^2$$ is irrational number.
A.G
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Sum formula for geometric series

I solved this equation something like this, as shown in the photo: Is it correct? If I put $x=2$ I get weird results!
Aaryan Dewan
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Given $n$ natural numbers, there are two or more of them that sum up to a multiple of $n$

Given $n$ natural numbers $m_1, ..., m_n$, of which none is divisible by $n$, I want to prove that there exist an $i \in \{2, ..., n\}, k \in \mathbb{N}$, so that the sum of exactly $i$ of the given numbers is equal to $k n$. I must admit that I…
moran
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How long before I (see q.) will have recovered the extra purchase cost?

Standard 100w light bulbs cost 40p each and are expected to last for 2 year in average use. Low power equivalent brightness bulbs cost £10 each, are expected to last 8 years and use only 20W. A 100W light bulb operated for 10 hours will use 7.5p of…
pi-e
  • 137
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How to prove that $\frac{x}{2}$ is smaller than $x$ for positive $x$

Could someone provide me a valid proof that $\frac{x}{2}$ is smaller than $x$. It seems obvious but i cannot think of a proof. Or just prove that $x+x$ is larger than $x$ for positive $x$.
Sorfosh
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Is $(-2-2)^2 - (-2+3)(-2-3)-4(-2^2+2) = 69$?

I get 69 when I calculate this, but my calculator says it's 29. I've gone over this several times and can't figure out why I'm wrong. I'm also not entirely sure if I've used the calculator properly. What answer is correct, and any idea where I'm…
Julian Nikolay Krogh-Fredrikse
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Elementary math: arithmetic

A and B worked together to complete a certain task in three hours. If A works alone, he can complete the task in five hours. If B works alone, how much longer will it take him to complete the task? I have the answer to this question, but I…
MLIAL k
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Problem about numbers in different bases

For what numbers of $b$ is $100_b=10_{4b}$? The answer says $b$=4 Can someone derive why? I dont get this I get: $b^2=4b=40+b$ which is a second order equation?
torgny
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Is it possible to get 6 using 9s and simple arithmetics?

I would like to answer following question. Is it possible to get six using four nines and adding, subtracting, multiplying, division and parentheses? For instance: (9+9+9)/9=3 (9*9+9)/9=10 and now how can I get: 9 ? 9 ? 9 ? 9 = 6
user2300369
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Explanation about product of two negative numbers being positive.

I have been having a struggle finding an explanation why $-3 \cdot (-3) = 9$. Why does this question equal a positive number? Any explanations? And btw, if $-3 \cdot (-3) = 9$. Why does $-3 + (-3) + (-3) = -9$ and not $9$?
Alexander Säfström
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Skipping and percentage

How to calculate how many skips I need to make to get a percentage. i.e. Let's say I have 13 million apples and I am going through each one counting and every 10 apple I place it in a different bucket, at the end I end up with a bucket with 10% of…
luis
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If you have only 3 coins and 1 is a penny is it possible for you to have a Dollar?

If you have only 3 coins and 1 is a penny is it possible for you to have a Dollar?
user265801
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Exponential Function, Help Appreciated :-)

my text book asks me to 'Simplify, and express in terms of positive indices'. But my answer always seems to come up with: $x^{\frac {35} {36}}$. The term is $$\frac{ (x^{-\frac 1 2})^{\frac 2 3} \ x^{\frac 2 3}}{x^{-\frac 3 4}} $$
Veus La
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Definition arithmetic progressions of any given length.

I have been studying erdős conjecture on arithmetic progressions for some time and have an interesting question for you : How do I strictly define "a set containing arithmetic progressions of any given length" And can somebody give me an example of…
Thomas
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Understanding A simple mathematical addition operation

I was just doing a simple maths operation: $s = 158 + 46 \times -1: \Rightarrow s = 112$ and $s = (158 + 46) \times -1:\Rightarrow s = -204$ In the latter case $158 + 48$ gets calculated first and then multiplied by $-1$, but in the former case…
Alexander Solonik
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