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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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How to convert a hexadecimal number to an octal number?

How can I convert a hexadecimal number, for example 0x1A03 to its octal value? I know that one way is to convert it to decimal and then convert it to octal 0x1A03 = 6659 = 0o15003 Is there a simple way to do it without the middle step (conversion…
Lazer
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Are "sum" and "product" defined when there is only one number?

I solved a math problem on an online judge site recently. The question specified that the answer should be for an input number N, the smallest non-negative number Q so that the product of the digits of Q exactly equal N. The answer for inputs 1…
Bogatyr
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How to divide using addition or subtraction

We can multiply $a$ and $n$ by adding $a$ a total of $n$ times. $$ n \times a = a + a + a + \cdots +a$$ Can we define division similarly using only addition or subtraction?
Monkey D. Luffy
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What is the value of $142,857 \times 7^2$?

What is the value of $142,857 \times 7^2$? Obviously you could solve this with a calculator and be done. But is there a more clever way to calculate this?
John Ryan
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How to Compare two multiplications without multiplying?

How to check if two multiplications are equal to each other or greater or lesser without actually multiplying them? For example, compare (254)(847) and (383)(536) EDIT: While trying to find a rule i got one (5)(11) < (6)(10) or (x)(y) < (x+1)(y-1)…
LifeH2O
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Find $P + Q + R$

I was doing questions from previous year's exam paper and I'm stuck on this question. Suppose $P, Q, R$ are positive integers such that $$PQR + PQ + QR + RP + P + Q + R = 1000$$ Find $P + Q + R$. It seems easy but I am not getting the point from…
aMighty
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Is it possible to calculate the arithmetic mean from the geometric mean?

An estimation method would be acceptable, doesn't need to be exact (but obviously that would be preferable). I have a dataset of geometric means, need to calculate the arithmetic mean.
node1377
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Calculate the product of these $98$ rational numbers

$$\left( 1 + \frac{1}{2} \right) \left( 1 + \frac{1}{3} \right) \left( 1 + \frac{1}{4} \right) ... \left( 1 + \frac{1}{99} \right) $$ Of course I could do it factor for factor but there has got to be a more efficient way. Does anyone know it?
user155980
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Why doesn't $255 \times 255 \times 255 = 16777215$

Ok, I obviously understand basic multiplication and understand why those don't equal. But in web colors, there is FFFFFF hexadecimal different colors (or rather $16,777,215$ in base $10$). This amount of colors can also be described by using three…
tysonsmiths
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$\frac{a}{b} = \frac{c}{d} $ if $ad = cb$, how to intuitively understand this?

This works if you multiply both sides with $bd$ and cancel stuff out... But how does it work? When I look at it, I would never guess something like that is valid without resorting to the established arithmetic rules. Maybe this is a nonsense…
Curiosity
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Distances and speeds

Alice and Bob started to walk towards each other’s home and then back to theirs, with steady speeds. Alice passed by a bus station at 25 m away from her home, while at the same time Bob was passing by an abandoned old car. Afterwards, they met at…
Nhung Huyen
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What is the sum of the $81$ products in the $9 \times 9$ multiplication grid?

What is an easy way to solve this problem? I believe that the value in each box is the product of $x$ and $y$. Suppose the 9 × 9 multiplication grid, shown here, were filled in completely. What would be the sum of the 81 products?
learning
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How many times can you halve a number?

Is there an formula stating the number of times you would have to halve a number to reduce it to some value less than or equal to $1$? For example, for $6$ it takes three halvings: $6/2=3$, $\ 3/2=1.5$, $\ 1.5/2=0.75$. Also, is there a…
Char
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When is $\sqrt{a^2}=\pm a$ and when is $\sqrt{a^2}=a$?

When we derive some formula and have to do huge algebraic expansions that deal with raising powers we use exponent rules mindlessly and we never write down the $\pm$ symbol. Why is this right? My reasoning is that we write $\pm$ when were looking…
DLV
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Expression with last digits different

Given the expression: $$1234567893 \times 1234567894 - 1234567895 \times1234567892$$ Is it correct to say that the answer is $ (3 \times 4) - (5 \times 2) $? If so, why?
Aspiring Mathlete
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