What is the difference between the symbols ÷ / in division?

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SUMMARY

The discussion clarifies the differences between division symbols, specifically the colon (:) and the division symbols (÷ and /). It establishes that in the expression 6:2(2+1), the colon represents a ratio, leading to the evaluation of 6:2 as 3, and then multiplying by (2+1) results in 9. The participants confirm that the colon behaves differently than the division symbols, which are interchangeable in mathematical operations. The interpretation of expressions involving these symbols can lead to confusion, as demonstrated by the example of Wolfram Alpha's output.

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the result of 6:2(2+1) is 9 or 1?
 
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chrisgk said:
the result of 6:2(2+1) is 9 or 1?

Hi chrisgk, welcome to MHB,

Divisions and multiplications have equal precedence and are evaluated from left to right.
So 6:2(2+1) = (6:2)(2+1) = 9.
 
question ...

Doen't colon ratio symbol, " : ", behave like a vinculum?

i.e. $a:b+c = \dfrac{a}{b+c}$ ?

reason I ask is Wolfram Alpha interprets 4:5+6 as 4/11
 
skeeter said:
question ...

Doen't colon ratio symbol, " : ", behave like a vinculum?

i.e. $a:b+c = \dfrac{a}{b+c}$ ?

reason I ask is Wolfram Alpha interprets 4:5+6 as 4/11

That's... unexpected...

Just saying:
View attachment 6669

It's kind of interesting to see that the OP's question is a perfect match for a meme on the internet...
 

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perfect match?

the result of 6:2(2+1) is 9 or 1?

looks to me the OP posted a colon, $\colon$ , not a division symbol, $\div$
 
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Who is the difference between the symbols ÷ / :
 
chrisgk said:
Who is the difference between the symbols ÷ / :

$\div$ and $/$ mean the same thing, the operation of division

$a \div b = a/b = \dfrac{a}{b}$

the colon symbol, $\colon$ , indicates a ratio ... a ratio is a comparison of two values achieved by division.
 

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