- #1
chrisgk
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the result of 6:2(2+1) is 9 or 1?
What is the difference between the symbols ÷ / in division?
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Discussion Overview
The discussion revolves around the differences between the symbols used for division, specifically the colon (:), the division sign (÷), and the slash (/). Participants explore the implications of these symbols in mathematical expressions and their interpretations in various contexts.
Discussion Character
- Conceptual clarification
- Debate/contested
- Mathematical reasoning
Main Points Raised
- Some participants assert that divisions and multiplications have equal precedence and should be evaluated from left to right, leading to the interpretation of 6:2(2+1) as 9.
- Others question whether the colon symbol behaves like a vinculum, suggesting that expressions like $a:b+c$ could be interpreted as $\dfrac{a}{b+c}$.
- There is a mention of Wolfram Alpha's interpretation of ratios, with one participant noting that it interprets 4:5+6 as 4/11, which raises questions about the consistency of these symbols.
- Some participants clarify that the division sign (÷) and the slash (/) represent the same operation, while the colon (:) indicates a ratio, which is a comparison of two values achieved by division.
Areas of Agreement / Disagreement
Participants express differing views on the precedence of the colon symbol compared to other division symbols, and there is no consensus on how to interpret the expression 6:2(2+1). The discussion remains unresolved with multiple competing interpretations.
Contextual Notes
There are limitations regarding the assumptions about symbol precedence and the definitions of the symbols in different mathematical contexts, which have not been fully resolved in the discussion.
- #2
I like Serena
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chrisgk said:
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.
- #3
skeeter
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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
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
- #4
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skeeter said:
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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- #5
skeeter
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perfect match?
looks to me the OP posted a colon, $\colon$ , not a division symbol, $\div$
looks to me the OP posted a colon, $\colon$ , not a division symbol, $\div$
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- #6
chrisgk
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Who is the difference between the symbols ÷ / :
- #7
skeeter
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chrisgk said:
$\div$ 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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