So I’ve noticed there are a lot of mathematical symbols for the same purpose.
For example:
Two times two can be written as (2×2),(2•2) and (2*2)
Two to the power of two can be written as (2^2) (2²)
And finally two divided by two can be written as (2:2) (2 and 2 as fraction) and (2/2)
So when do you use the different symbols
In: 0
Whenever you want. If you want to use 2×2, use 2×2. If you want to use 2•2. Etc. It’s just a matter of preference, ease, or limitation of whatever median you’re using. For example, if the text box doesn’t support superscripts, you would basically *have* to use 2^2 to represent powers.
The only exception would be the ones you have identified as “division.” I would say it is not strictly correct to say that the ratios and fractions are equivalent to division.
If I tell you the ratio of cats to dogs in my house is 4:3, yes, you can use division to find the exact number of cats per individual dog (or vice versa) but I’m not telling you I have 1.333… cats and 1 dog. I’m telling you something specific about the relationship between cats and dogs in my house.
The same comes with the fraction symbol. While you can convert it into a decimal using division, the fraction line itself isn’t the same as the division operator. Again, you are saying something above and beyond division about some thing being put into equal parts and how many of those parts you had.
This extra, contextual information would lead you to use one over the other.
On paper, you use whatever is convenient and clear to communicate the idea. As you get into higher levels of mathematics different representations make more or less sense. For example, if you have “x” as a variable in an equation you would never want to write it as “xx2” because its technically ambiguous whether you mean 2x or 2x^2.
Another scenario worth considering is typing things into a computer program to solve. In that scenario, for multiplication you always use “*” and for exponents you always use “^ “
Most of the time, it is simply preference. It won’t change anything if you use x or * for multiplication.
The only slight exception is when dealing with fractions, decimals, and percents. While they’re all just 3 different ways of representing the same exact concept, some are better for certain cricumstances. So, while it technically would be correct to say, “Do you want 1:1 of my sandwich?”, it makes WAY more sense to say “Do you want half of my sandwich?” You’re still correct, one just makes way more sense.
As you said they serve the same purpose, it doesn’t matter which one you use.
Sometimes symbols can have multiple meanings. You wouldn’t use x to denote multiplication if there was a risk of it being mistaken for a “variable”.
Unless you’re working with vectors where scalar (dot) and vector (cross) multiplication are different, or you’re programming where you obviously need to stick to a specific convention.
Depends on the keyboard i’m using. Generally whatever feels good to me in the moment is fine, so long as its consistent within the document.
5:10 or 5/10 can get the point across, but using both in the same document invites confusion. Ultimately the point of written communication is so that the reader can understand the writers intent. Doesnt matter if its Hunter S. Thompson or Archimedes, as long as the intent is clear, it doesnt matter how you get there.
If there is a chance of confusion, use the one that will cause less confusion without putting out an enormous amount of effort.
I don’t use x for multiplication anymore because I will often use x as a variable. Also, when I use x as a variable in a handwritten equation, I use cursive x in order to make it more obvious that I don’t mean multiply. I don’t use the dot (2•2) when I type because I don’t have a quick and easy way to do that on my keyboard. Likewise, I don’t do (2²) because I don’t have a handy way to type that. Instead, I write it as (2^2).
2•2 is a hard symbol to type since it doesn’t appear on most keyboards, and depending on the software/website it might not support superscript such as 2².
Besides those circumstances, use whatever you want.
It doesn’t matter, but some ways can be confusing. (2×2) and (2•2) are mostly only used for numbers, rather than equations, because we often use “x” or “•” for other purposes. 2:2 is rarely used in formal mathematics, 2/2 is common when writing math in the text of a sentence, and
2
—
2
is used in math on its own line in the text.
Mostly doesn’t matter, but I’d only use * for multiplication as • can mean a dot product and × can mean cross product.
In arithmetic you use 2 × 2
– this is the main symbol for multiplication
In algebra you use 2 • 2
– because × can be confused with the variable x
In programming you use 2 * 2
– to decrease confusion with x and to avoid special characters like •
The superscript 2 to the power 2 is the main way exponents are meant to be written (as you have it in the post. I’m on mobile right now so I can’t type it in)
2² uses the small superscript 2 character, so it’s used when superscripts are not supported by the program you’re using. (Such as the mobile Reddit app)
In programming you use 2^2
– because that doesn’t use special characters
– though more commonly you use Math.pow(2,2)
In arithmetic you use 2 ÷ 2
– this is the main symbol for division
– it’s meant to resemble a fraction, horizontal bar, and the two dots are each a number
In algebra you use 2 over 2 (as a fraction)
– it’s easier to work with the numbers by grouping them on the top and bottom of a fraction, this also avoids the clutter of × and ÷ symbols
In programming you use 2/2
– because it avoids special characters
– this is meant to resemble a fraction, 2 over 2
In statistics you use ratios like 2:2
– this has a mathematically different meaning than a fraction. It’s saying that the left thing happened twice, compared to the right thing, which happened twice.
In division, the top thing is compared to the total at the bottom.
– ratios and fractions are sometimes interchanged but for good reason, usually you would NOT use 2:2 to represent 2 ÷ 2 because they mean different things
Ex… you might say 3/6 sides of a die are odd. And the ratio of even to odd sides is 3:3
3:6 is the ratio of even to all sides of a die (which is a weird way to say the same thing, so generally it’s not used as much)
So I’ve noticed there are a lot of mathematical symbols for the same purpose.
For example:
Two times two can be written as (2×2),(2•2) and (2*2)
Two to the power of two can be written as (2^2) (2²)
And finally two divided by two can be written as (2:2) (2 and 2 as fraction) and (2/2)
So when do you use the different symbols
In: 0
Whenever you want. If you want to use 2×2, use 2×2. If you want to use 2•2. Etc. It’s just a matter of preference, ease, or limitation of whatever median you’re using. For example, if the text box doesn’t support superscripts, you would basically *have* to use 2^2 to represent powers.
The only exception would be the ones you have identified as “division.” I would say it is not strictly correct to say that the ratios and fractions are equivalent to division.
If I tell you the ratio of cats to dogs in my house is 4:3, yes, you can use division to find the exact number of cats per individual dog (or vice versa) but I’m not telling you I have 1.333… cats and 1 dog. I’m telling you something specific about the relationship between cats and dogs in my house.
The same comes with the fraction symbol. While you can convert it into a decimal using division, the fraction line itself isn’t the same as the division operator. Again, you are saying something above and beyond division about some thing being put into equal parts and how many of those parts you had.
This extra, contextual information would lead you to use one over the other.
On paper, you use whatever is convenient and clear to communicate the idea. As you get into higher levels of mathematics different representations make more or less sense. For example, if you have “x” as a variable in an equation you would never want to write it as “xx2” because its technically ambiguous whether you mean 2x or 2x^2.
Another scenario worth considering is typing things into a computer program to solve. In that scenario, for multiplication you always use “*” and for exponents you always use “^ “
Most of the time, it is simply preference. It won’t change anything if you use x or * for multiplication.
The only slight exception is when dealing with fractions, decimals, and percents. While they’re all just 3 different ways of representing the same exact concept, some are better for certain cricumstances. So, while it technically would be correct to say, “Do you want 1:1 of my sandwich?”, it makes WAY more sense to say “Do you want half of my sandwich?” You’re still correct, one just makes way more sense.
As you said they serve the same purpose, it doesn’t matter which one you use.
Sometimes symbols can have multiple meanings. You wouldn’t use x to denote multiplication if there was a risk of it being mistaken for a “variable”.
Unless you’re working with vectors where scalar (dot) and vector (cross) multiplication are different, or you’re programming where you obviously need to stick to a specific convention.
Depends on the keyboard i’m using. Generally whatever feels good to me in the moment is fine, so long as its consistent within the document.
5:10 or 5/10 can get the point across, but using both in the same document invites confusion. Ultimately the point of written communication is so that the reader can understand the writers intent. Doesnt matter if its Hunter S. Thompson or Archimedes, as long as the intent is clear, it doesnt matter how you get there.
If there is a chance of confusion, use the one that will cause less confusion without putting out an enormous amount of effort.
I don’t use x for multiplication anymore because I will often use x as a variable. Also, when I use x as a variable in a handwritten equation, I use cursive x in order to make it more obvious that I don’t mean multiply. I don’t use the dot (2•2) when I type because I don’t have a quick and easy way to do that on my keyboard. Likewise, I don’t do (2²) because I don’t have a handy way to type that. Instead, I write it as (2^2).
2•2 is a hard symbol to type since it doesn’t appear on most keyboards, and depending on the software/website it might not support superscript such as 2².
Besides those circumstances, use whatever you want.
It doesn’t matter, but some ways can be confusing. (2×2) and (2•2) are mostly only used for numbers, rather than equations, because we often use “x” or “•” for other purposes. 2:2 is rarely used in formal mathematics, 2/2 is common when writing math in the text of a sentence, and
2
—
2
is used in math on its own line in the text.
Mostly doesn’t matter, but I’d only use * for multiplication as • can mean a dot product and × can mean cross product.
In arithmetic you use 2 × 2
– this is the main symbol for multiplication
In algebra you use 2 • 2
– because × can be confused with the variable x
In programming you use 2 * 2
– to decrease confusion with x and to avoid special characters like •
The superscript 2 to the power 2 is the main way exponents are meant to be written (as you have it in the post. I’m on mobile right now so I can’t type it in)
2² uses the small superscript 2 character, so it’s used when superscripts are not supported by the program you’re using. (Such as the mobile Reddit app)
In programming you use 2^2
– because that doesn’t use special characters
– though more commonly you use Math.pow(2,2)
In arithmetic you use 2 ÷ 2
– this is the main symbol for division
– it’s meant to resemble a fraction, horizontal bar, and the two dots are each a number
In algebra you use 2 over 2 (as a fraction)
– it’s easier to work with the numbers by grouping them on the top and bottom of a fraction, this also avoids the clutter of × and ÷ symbols
In programming you use 2/2
– because it avoids special characters
– this is meant to resemble a fraction, 2 over 2
In statistics you use ratios like 2:2
– this has a mathematically different meaning than a fraction. It’s saying that the left thing happened twice, compared to the right thing, which happened twice.
In division, the top thing is compared to the total at the bottom.
– ratios and fractions are sometimes interchanged but for good reason, usually you would NOT use 2:2 to represent 2 ÷ 2 because they mean different things
Ex… you might say 3/6 sides of a die are odd. And the ratio of even to odd sides is 3:3
3:6 is the ratio of even to all sides of a die (which is a weird way to say the same thing, so generally it’s not used as much)
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