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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.

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Three consecutive terms of an arithmetic sequence have a sum of 36 and a product of 1428. Find three terms.

Now I already know the answer to that you have to do this first $3x=36$ And then the rest you are just subbing in, but why do you have to divide 36 by 3. I am confused.
Exodus
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How many 6-digit numbers are divisible by 7?

How many $6$ digit numbers are divisible by $7$ ? How do I calculate it ? I know the obvious solution using arithmetic progression .I am looking for how to solve this linear modular equation:- $1000000a+100000b+10000c+1000d+100e+10f+g= 0$($mod 7$)…
Ananya Agarwal
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Is there a number which is a perfect square, cube, fourth power and so on?

as the title asks, is there an integer which is a perfect square, cube, fourth power, fifth power, etc until, well, it's a tenth power per say? Are there integers that are squares, cubes, and so on until it is a... Say, 100th power? I was wondering…
BittersweetNostalgia
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Significant figure question

The size of an rectangular sheet of paper is found by measuring as accurately as possible, $8.45$ inches by $11.03$ inches. What is the area, to the same accuracy, in square inches? Answer is $93.20$, not $93.2$ I thought since $8.45$ only had $3$…
user122415
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Numbers ending with 0

$2n$ ends with $0$ if $n$ ends with $0$. So how can we know if 2n ended with 0 in the first place?
user67527
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551 used items, it takes 6 used to create one new... how many new items can you make?

I had this question recently in an online exam that really confused me (it's not hard). A business decided to recycle all their old paper cups and produce new ones from the recycled cardboard. For every new cup it would require $6$ used cups. They…
David Barker
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Mathematical tricks to check the result of a multiplication

I wondered myself about some tricks allowing quick checks to know whether the result of an operation can be true or is surely false. I found several for square roots on Internet, and so I looked for multiplication, but trying to found them by…
MetaZenithian
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Why is the number of threes in a number related to the number divided into three equal parts?

Like here's the video: https://www.khanacademy.org/math/arithmetic-home/multiply-divide/division-intro/v/division-1?modal=1 Explanation 1 is at 4:08 Explanation 2 is at 5:31 How are the two related?
bumblehumble
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Can iterated arithmetical operators break closure over $\mathbb C$?

Multiplication is iterated addition; exponentiation is iterated multiplication, tetration is iterated exponentiation, call all of those as different grades of iterated arithmetical operators. Is there a known $n$-iterated arithmetical operator such…
Zuhair
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Find it hard to do long division $\frac{10000}{0.08}$

Sorry if this is very basic! But I can't seem to do something like $\frac{10000}{0.08}$, without a calculator. How would one go about solving this without a calculator?
natalie99
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Arithmetic Progression Time and Work Problem

A group of men working at the same rate can finish a job in $45$ hours. However, the men report to work, one at a time, at equal intervals over a period of time. Once on the job, each man stays until the job is finished. If the first man works…
RaphX
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Geometric Progression - find ith and r

Hi great if you could please help me solve this: Given: $$a_0=12$$ $$a_5=24$$ $$a_{10} =48$$ thus ratio $$a_0:a_5 = 2$$ $n =$ number of terms in scale $= 5 (a_0, a_1, a_2, a_3, a_4) $ $a_0 =$ first term $= 12$ What is the equation to find $i$-th…
Jean-Lou Désiré
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linear equations

A shopkeeper buys a number of books for Rs.1200. If he had bought 5 less books for the same amount, each book would have cost him Rs.20 more. How many books did he buy? I have this question found in my brother's tenth class book and unable to…
gpuguy
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Perform addition that disregards carries

In long addition the overflow is carried across columns like so $$ \begin{array}{cccc} & \tiny{1} & \tiny{1} & \\ & 3 & 5 & 8 \\ + & 2 & 9 & 6 \\ \hline \\ & 6 & 5 & 4 \\ \end{array} $$ I'm doing some crypto work at the moment and I need to…
jjs
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casting out nines: division

the division in the casting out nines is not clear to me. In the given example he got a 8 and a 4, and later he got an 8 and a 3. Shouldn't it be an 8 and a 4 (or 3) in both?
The Student
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