# Need help with a fractions problem

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• 12-05-2017, 10:46 PM
palespring
Need help with a fractions problem
For the question

"Juanita made two sandwiches. She cut the sandwiches into 4 pieces each. She has 5 pieces left. What fraction of the sandwiches are left?"

Shouldn't the answer be 5/8? Yet in my math textbook it says the answer is 1 1⁄4. I've attached a scan of the textbook page.

It seems that both answers make sense, yet if that were true, then 5/8 would equal to 1 1⁄4 but that is obviously not the case, so I'm really confused. Could someone explain to me which answer is correct? Thanks in advance!

Attachment 8793
• 12-05-2017, 11:28 PM
tkhunny
Interesting. I think I could go either way, but the question is poorly worded.

1) What portion of "the sandwiches" remains? 5/8

2) What portion or EACH sandwhich remains? 1, 1/4

3) How many sandwiches remain? 1 + 1/4 = 5/4

Seriously, I'd complain about this one. Very unclear. It appears to want #3, but it seems to me that the words are asking for #1.
• 12-05-2017, 11:52 PM
JeffM
Quote:

Originally Posted by palespring
For the question

"Juanita made two sandwiches. She cut the sandwiches into 4 pieces each. She has 5 pieces left. What fraction of the sandwiches are left?"

Shouldn't the answer be 5/8? Yet in my math textbook it says the answer is 1 1⁄4. I've attached a scan of the textbook page.

It seems that both answers make sense, yet if that were true, then 5/8 would equal to 1 1⁄4 but that is obviously not the case, so I'm really confused. Could someone explain to me which answer is correct? Thanks in advance!

Attachment 8793

There are five quarters left. How much is five quarters of a sandwich? Clearly, 1 and 1 quarter of a sandwich.

I agree with tkhunny. The question is very badly worded. What is intended is to ask what fraction of a sandwich is left. Five quarter sandwiches do represent five eighths of eight original quarter sandwiches, but those eight quarters represented TWO sandwiches, not one.

[tex]\dfrac{5}{8} * 2 = \dfrac{5}{4} = 1 + \dfrac{1}{4}.[/tex]

But the use of the plural "sandwiches" completely destroys the intended meaning.
• 12-06-2017, 12:08 AM
Dr.Peterson
Quote:

Originally Posted by palespring
"Juanita made two sandwiches. She cut the sandwiches into 4 pieces each. She has 5 pieces left. What fraction of the sandwiches are left?"

I fully agree with tkhunny and JeffM. "The sandwiches" should mean "the total amount she started with", and 5/8 of that amount is what is left. There is also a grammatical error: the subject of this sentence is "what fraction", so the verb should be singular, "is left", not "are left".

One way to explain the issue is that when you talk about a fraction in any applied problem, you have to identify the "unit": what is being thought of as "the whole" or "1". This is indicated in English by "of": a fraction of the whole. In the question (both the form you quote and the later version, "What fraction of the sandwiches does Juanita have left?"), the unit seems to be "the sandwiches". The proper phrasing for the question they intended to ask (in which the unit is one sandwich) is, "What fraction of a sandwich", or just "How many sandwiches".

I think the authors were so focused on the answer (introducing the idea of a mixed number) that they forgot to write the question carefully. (Actually, it seems that they used the plural verb because they knew what their answer was going to be: more than one. But "the fraction of the sandwiches" that is left has to be less than one.)

I hope they make things clearer going forward, especially in problems you have to solve yourself. But good for you in recognizing the correct answer.
• 12-06-2017, 05:57 PM
palespring
Thanks for the reply everyone! I was also thinking that the question was wrongly worded but wasn't sure, and now I am.

Quote:

Originally Posted by Dr.Peterson
Actually, the only person who can really clarify doubts about the meaning of a question is the author of the question! If you are unsure of the meaning of a question posed by your teacher, ask your teacher. Don't ask some third party.

I'm actually an adult self-teaching out of a textbook so I don't have a teacher. Thanks for your input!
• 12-06-2017, 07:41 PM
Dr.Peterson
Quote:

Originally Posted by palespring
I'm actually an adult self-teaching out of a textbook so I don't have a teacher. Thanks for your input!

I was wondering about your context -- you could have been a child, a parent, a teacher, or a future teacher. Sometimes it can be helpful to know that.

I hope we haven't beaten the subject to death. It is worth knowing that textbooks aren't perfect, so sometimes when you disagree, you may be right. Especially as an adult, you can think of authors as fellow-humans, but still learn from them. And as I said, others like us, though "third parties", can be helpful in recognizing errors so you can move on, even though we can only guess what the author was thinking. (Or maybe it was an editor.)
• 12-06-2017, 10:58 PM
palespring
Quote:

Originally Posted by Dr.Peterson
It is worth knowing that textbooks aren't perfect, so sometimes when you disagree, you may be right. Especially as an adult, you can think of authors as fellow-humans, but still learn from them. And as I said, others like us, though "third parties", can be helpful in recognizing errors so you can move on, even though we can only guess what the author was thinking. (Or maybe it was an editor.)

Yep, agreed. I've encountered a few errors in this textbook before so I've learned not to have blind faith in the book's accuracy. And this forum has been very helpful in clarifying and validating my concerns so again I appreciate everyone's input.
• 12-07-2017, 07:50 AM
V Meenakshi
Mixed number and Improper fractions
Improper fractions are when numerator is greater than denominator.........eg:5/4,9/7

Mixed number is a number consisting of a whole number and a proper fraction. eg: 1 1/4, 2 3/4

In your case Juanita has cut each sandwich to 4, if 5 pieces are left, then the mixed number is 1 and 1/4 sandwich is left or 5/4 sandwich is left ............it is not 5/8 left.

If Juanita cut each sandwich to 8 pieces each, and 10 pieces are left, then the mixed number or sandwich left is 1 and 2/8 or as improper fraction 10/8 .
If Juanita had cut each sandwich to 5 pieces each, and 8 pieces are left, then the sandwich left in terms of mixed number is 1 and 3/8 and as improper fraction it is 8/5.
If Juanita had cut each sandwich to 3 pieces each and 5 pieces are left, then the sandwich left in terms of mixed numbers is 1 and 2 /3 and improper fraction is 5/3.

Eg below:This is 1 and 3/4 as a mixed number. It can be written as 7/4 as a improper fraction so 1 and 3/4 pizzas are left or 7/4 pizzas are left....................its not 7/8.

https://www.mathsisfun.com/images/fractions/pie-1-1.jpghttps://www.mathsisfun.com/images/fractions/pie-3-4.jpg
• 12-07-2017, 06:34 PM
Dr.Peterson
Quote:

Originally Posted by V Meenakshi
In your case Juanita has cut each sandwich to 4, if 5 pieces are left, then the mixed number is 1 and 1/4 sandwich is left or 5/4 sandwich is left ............it is not 5/8 left.
...
Eg below:This is 1 and 3/4 as a mixed number. It can be written as 7/4 as a improper fraction so 1 and 3/4 pizzas are left or 7/4 pizzas are left....................its not 7/8.

https://www.mathsisfun.com/images/fractions/pie-1-1.jpghttps://www.mathsisfun.com/images/fractions/pie-3-4.jpg

You seem to be missing the point of the question and discussion.

We agree that there are 1 1/4 sandwiches left; if the question had been phrased as you put it, "What [mixed] number of sandwiches are left?", we would have no problem.

But it was not asked that way. It was "What fraction of the sandwiches are left?". That is at best ambiguous.

Your example is 7/4 = 1 3/4 pizzas; but if they started with 2 pizzas, it would be 7/8 of the initial amount. Those are two different descriptions of the same quantity, using different "units" or "wholes": one whole pizza, vs. the whole original amount. Both are correct; but they answer different questions.

I don't think anyone in the conversation fails to understand what mixed numbers are. It is the English that is at issue.
• 12-07-2017, 07:22 PM
stapel
Quote:

Originally Posted by palespring
"Juanita made two sandwiches. She cut the sandwiches into 4 pieces each. She has 5 pieces left. What fraction of the sandwiches are left?"