Is 2/3 Always the Same as 4/6?

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    Equivalent Fractions
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Discussion Overview

The discussion revolves around the equivalence of the fractions 2/3 and 4/6, particularly in the context of a fourth-grade math question. Participants explore whether these fractions represent the same quantity or if they could differ based on the context in which they are applied.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Meta-discussion

Main Points Raised

  • Josh asserts that 2/3 is always the same as 4/6.
  • Meghan claims that while 2/3 and 4/6 are equivalent fractions, they could represent different amounts.
  • Some participants, including Dan, suggest that the interpretation of the question is ambiguous, noting that 2/3 of one pie could differ from 4/6 of another pie.
  • One participant expresses confusion about the teaching methods used in schools, questioning the relevance of equivalent fractions in this context.
  • Another participant argues that while the numbers 2/3 and 4/6 are not literally the same, they are equivalent in terms of quantity, but suggests that Meghan's statement is partially incorrect.
  • Some participants express frustration with modern teaching methods and their implications for students' understanding of basic arithmetic.
  • A participant acknowledges their lack of understanding of math but sides with Josh's view.

Areas of Agreement / Disagreement

Participants do not reach a consensus; multiple competing views remain regarding the interpretation of the fractions and the implications of the question posed.

Contextual Notes

The discussion highlights limitations in the clarity of the question and the assumptions about the objects being referenced, which may affect interpretations of the fractions.

mathdad
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Josh says that 2/3 is always the same as 4/6. Meghan says that 2/3 and 4/6 are equivalent fractions, but they could be different amounts. Which student is correct?

I say Josh.
 
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Josh
 
I was told by my nephew that most of his classmates said that Meghan is correct but how can this be? This is a fourth grade common core math question. Honestly, I do not get it.
 
RTCNTC said:
Josh says that 2/3 is always the same as 4/6. Meghan says that 2/3 and 4/6 are equivalent fractions, but they could be different amounts. Which student is correct?

I say Josh.
I'm taking Meghan to be correct. Josh can have 2 slices out of 3 in a single pie, but Meghan could have 4/6 (4 slices out of 6) of two pies.

That's the only thing I can think of.

-Dan
 
What are on Earth are they teaching kids? What does this have to do with equivalent fractions? Why can't they teach fractions the old fashioned way? No wonder students are so behind in terms of reading, writing, and basic arithmetic.
 
topsquark said:
I'm taking Meghan to be correct. Josh can have 2 slices out of 3 in a single pie, but Meghan could have 4/6 (4 slices out of 6) of two pies.

That's the only thing I can think of.

-Dan

It really depends if you assume the question is referring to the same object, otherwise we can argue that one pie could be larger than the other. If we can assume they are different sizes, then what stops us from assuming they have to even be the same object? 2/3 of a pizza vs. 4/6 of a pie. I just think this is an ambiguously-worded question. The answer depends on interpretation, so it's a bad question in my book.
 
Last edited:
It's an interesting question, since it triggers some thought. And yes, the answer is a bit open to interpretation.

Since 2/3 is a different pair of numbers than 4/6 they are not literally the same. It"s more correct to say they are equivalent, which is the first part of what Meghan says.
In real life we might assign different meanings to them, as topsquark explained. However, the amounts are the same. That makes the 2nd part of Meghan's statement false. And therefore her statement as a whole is false.
My interpretation: they are both wrong.

Either way, if it's a question in an graded exam, I consider it a bad question, since it's open to interpretation.
 
It's the Math they are teaching today. For example, 3 x 5 is not the same as 5 x 3. The first is 3 groups of 5 and the second is 5 groups of 3.

This is what they are teaching US 3rd graders, folks. God help us all.

-Dan
 
topsquark said:
It's the Math they are teaching today. For example, 3 x 5 is not the same as 5 x 3. The first is 3 groups of 5 and the second is 5 groups of 3.

This is what they are teaching US 3rd graders, folks. God help us all.

-Dan

Now that I think about it, I seem to recall that I've learned the term 'equivalent fractions' as well. That may have been around 3rd grade (non-US).
 
  • #10
I don't understand math at all, but Josh is correct
 

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