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

In summary: Meghan is right about equivalent fractions, but the question specifically asks if they are the same amount. Equivalent fractions may represent the same value, but they are not necessarily the same amount. Therefore, Josh is correct.In summary, Josh and Meghan are discussing whether 2/3 and 4/6 are the same amount. Josh argues that they are, while Meghan acknowledges that they are equivalent fractions but could represent different amounts. Based on the given information, Josh is correct.
  • #1
mathdad
1,283
1
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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  • #2
Josh
 
  • #3
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.
 
  • #4
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
 
  • #5
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.
 
  • #6
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.
 
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  • #7
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.
 
  • #8
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
 
  • #9
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
 

1. What are equivalent fractions?

Equivalent fractions are fractions that represent the same value, even though they may look different. They have different numerators and denominators, but they are equal to each other.

2. How do you find equivalent fractions?

To find equivalent fractions, you can multiply or divide both the numerator and denominator by the same number. For example, to find an equivalent fraction to 1/2, you can multiply both the numerator and denominator by 2 to get 2/4.

3. Why are equivalent fractions useful?

Equivalent fractions are useful because they help us compare and order fractions. They also help us simplify fractions and make working with fractions easier.

4. Can all fractions be equivalent?

Yes, all fractions can be equivalent. As long as you multiply or divide both the numerator and denominator by the same number, the resulting fraction will be equivalent.

5. How can you use a visual model to understand equivalent fractions?

A visual model, such as a fraction bar or a pie chart, can help you understand equivalent fractions by showing you how different fractions represent the same amount. For example, 1/2 and 2/4 may look different on paper, but they both represent half of a whole when shown in a visual model.

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