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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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"Faster" version of powers.

I know that essentially, multiplication is just a faster version of addition, as $5 \times 3$ is just $5 + 5 + 5$. I also know that powers are a faster version of multiplication as $5^3$ is $5 \times 5 \times 5$. I am wondering if there is a faster…
Bob Joe
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Determining the value of the nth term in this triangle

So I have this issue here with a certain sequence or rather group of sequences. The number triangle is as follows, $7$ $4$ $8$ $2$ $5$ $9$ $1$ $3$ $6$ $10$ I've realized that the bottom row is triangle numbers, with $(x(x+1))/2$ The first column is…
Sajjad Abbas
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get 2 numbers and return the second number with the sign of the first number

I know it's more about programming, but I can use arithmetic operators only so I think it fits the math community.
Code Newbie
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Positive and negative square roots

If the number $13$ is squared it gives $169$. Then if we take the square root of $169$; $\sqrt{169}$ it gives $13$ and $-13$. Why is this so if we know that $13$ was positive and it was multiplied by itself and produced $169$.
Samama Fahim
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Consider set of integers between 1 000 and 9 999 inclusive. How many integers in this set: are divisible by 2? divisible by 3? divisible by 2 & 3?

Consider the set of integers between $1000$ and $9 999$ inclusive. How many integers in this set: (i) are divisible by $2$? (ii) are divisible by $3$? (iii) are divisible by $2$ and $3$? What I've tried so far: (i) $\frac{9999-1000}{2} =…
user780357
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How to find the 48th multiple of 7 that contains a 7 in its decimal representation

So I'm doing an online puzzle and at a specific point there's a hint to find the 48th multiple of 7 that contains a 7 in its decimal representation How do I go into calculating something like that? Any help would be appreciated!
Da Mike
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Is there a way to add positives and negatives with the same algorithm where the |negative number| is greater?

I recently asked this question on adding positives and negatives using the same algorithm. The accept answer works amazingly, until I tried where the absolute value of the negative number is larger. When I used the same steps, I got this: 7 6 7 …
Ank i zle
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Converting 16-bit integer to 8-bit integer?

I found a question that asks for a method to copy a 16-bit sign and magnitude integer to an 8-bit sign and magnitude integer. Is that even possible? Could someone please explain how to do this?
Sorin Cioban
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Shortest path to sum with given operations

(Apologies since this was likely asked before, but I cannot find it. ) Is there a way to find the shortest path from some value V to some destination value D using only addition of values from a given set of numbers S? For example, starting value V…
Michael Seltenreich
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Intuition behind multiplication of decimals that are greater than 0.1

How can I visualize the multiplication of 2 decimals that both are greater than 0.1? For example, 0.2×0.25. I understand that 0.1×0.1 is to: step 1. divide a size into 10 parts 2. divide 1 of those parts into another 10 parts 3. retrieve 1 part…
Claire
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Solve $\frac{1}{(x - 2)(x-3)} + \frac{1}{(x -1)(x -2)} = \frac{2}{3}$, $x$ is not equal to $1$, $2$, $3$.

Solve the following equation: $$\frac{1}{(x - 2)(x-3)} + \frac{1}{(x -1)(x -2)} = \frac{2}{3},$$ where $x \ne 1,2,3$ Taking $(x - 2)$ as a common factor I got the quadratic equation $x^2 - 4x = 0$ and got values $x = 0$ and $x = 4$ as solutions. But…
Shivangi Asthana
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Contribution percentage of terms in a sum

I have two different terms contributing to a sum. One is positive and one is negative(-0.077 and 0.067) How do I note the contribution of these terms in percentage? 0.067/(-0.01) -> -670% doesn't make any sense. Edit: I know that logically 0.067 is…
Atilla Filiz
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Summing Fractions

I realize that this is basic arithmetic, but I really can't see how these terms combine... here goes: $4[(.5)^4\cdot (.6)^3]+4[(.5)^4\cdot(.6)^3\cdot(.4)]=4[(.3)^3\cdot (.7)]$ I do understand where the $(.3)^3$ comes from, that is…
PortMadeleineCrumpet
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arithmetic power, root definition

By definition, $x^1$=$x$ and $\sqrt[1]{x}$ = $x$ My own personal understanding of this rule is just rote memory, so if you were to ask me to explain why I wouldn't know what to say. For example does $9^1 = 9\cdot1$ ? Intuitively I would say yes…
dps1212
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Multiplication in a 3x3 grid

If I place all the numbers from 1 to 9 in a 3x3 grid and I add the products of each row and column, then what is the minimal sum? For example, the sum is 450 in the picture below.
Display maths
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