Ratios

[Butter]

Maria shares some seashells with Jeff.
Maria says, “Two for you, three for me, two for you, three
for me …”
Tonya watches.
At the end, she says, “So Jeff got
2/3
of the shells.”
Do you agree with Tonya? Give reasons for your answer.

My question:
Is the fraction 2/3 the same to the ratio 2:3?
If it is, than my answer the question is that Tonya is correct. Is my answer correct?

 

[stapel]

Maria shares some seashells with Jeff.
Maria says, “Two for you, three for me, two for you, three
for me …”
Tonya watches.
At the end, she says, “So Jeff got 2/3
of the shells.”
Do you agree with Tonya? Give reasons for your answer.

Hint: Try using actual numbers. For instance, if Maria stops after three times of "two for you, three for me", how many does Maria have? How many does Jeff have? How many have been given out in total? Does Jeff have "two-thirds" of this total?

My question:
Is the fraction 2/3 the same to the ratio 2:3?

That will depend upon what is the "whatever" that you're taking the two-thirds of, and also what the "ratio of two to three" is of (two of what, to three of what). One must define one's terms.

 

[HallsofIvy]

After the first "two for you, three for me", Jeff has two shells, Maria has three for a total of 5 shells. is 2 two-thirds of 5?

 

[JeffM]

After the first "two for you, three for me", Jeff has two shells, Maria has three for a total of 5 shells. is 2 two-thirds of 5?

How come I end up with the short end of the stick all the time?