Fractions word problem
- Thread starter momtocam
- Start date
- Joined
- Apr 12, 2005
- Messages
- 11,339
One for free. After this, you simply must demonstrate some ability to get started. Otherwise, you will not be of much help to your children or to yourself.
Rule #1 - Name Stuff!
Question #1 - Name what?
Answer #1 - What does it want? Name that.
"How many books total in her collection?"
That's what it wants. Name it.
B = Total number of books in the collection.
Now just translate.
"1/3 are nonfiction"
B*(1/3) are nonfiction
"1/6 are 'natural'"
B*(1/6) are 'natural'
"12 are mystery"
12
Unfortunately, we do not have the rest of the problem statement. There should be some sort of clue about the entire population of books and the relationship of the various types.
Example:
Mary has only three kinds of books and no book belongs to any two types.
This means there are no funny fiction books or any other variety. The three types mentioned are all the types there are.
This means there are no nonfiction books that are also mysteries. There are no mysteries that are 'natural' and etc.
It is very important to have this information or the problem cannot be solved. It could appear in more technical jargon, "The three types are mutually exclusive and comprise the total population."
Assuming we know that "Mary has only three kinds of books and no book belongs to any two types.", we have:
B*(1/3) + B*(1/6) + 12 = B
That's where I'll leave it for now. You tell me why I wrote that. Go back up and read the definitions and translations and see if you can get a sense of it.
Rule #1 - Name Stuff!
Question #1 - Name what?
Answer #1 - What does it want? Name that.
"How many books total in her collection?"
That's what it wants. Name it.
B = Total number of books in the collection.
Now just translate.
"1/3 are nonfiction"
B*(1/3) are nonfiction
"1/6 are 'natural'"
B*(1/6) are 'natural'
"12 are mystery"
12
Unfortunately, we do not have the rest of the problem statement. There should be some sort of clue about the entire population of books and the relationship of the various types.
Example:
Mary has only three kinds of books and no book belongs to any two types.
This means there are no funny fiction books or any other variety. The three types mentioned are all the types there are.
This means there are no nonfiction books that are also mysteries. There are no mysteries that are 'natural' and etc.
It is very important to have this information or the problem cannot be solved. It could appear in more technical jargon, "The three types are mutually exclusive and comprise the total population."
Assuming we know that "Mary has only three kinds of books and no book belongs to any two types.", we have:
B*(1/3) + B*(1/6) + 12 = B
That's where I'll leave it for now. You tell me why I wrote that. Go back up and read the definitions and translations and see if you can get a sense of it.
12 + 9 - 21. This is the answer I came up with. Will find out tomorrow if it is right. And no, there is no association between non fiction and the other type books. I did the formula counting up 6 blocks and 3 blocks to show the fraction in diagram.
You sure did analyze the phrase though, and I don't see how a 4th grader can grasp that let alone me.
Thanks for you help
You sure did analyze the phrase though, and I don't see how a 4th grader can grasp that let alone me.
Thanks for you help
- Joined
- Apr 12, 2005
- Messages
- 11,339
I had a suspicion we were dealing with other than a high school student. It would have helped if you would have included that information.
The most useful information usually is a description of what unit you are on and any sort of new methodology or worksheet the young student brings home.
Indeed, sorry to give your 4th Grader the algebra version. Generally, the problem should be sufficiently tractable that experimentation would solve the problem. This seems to have been your approach and it should be sufficient.
Just for the record: B*(1/3) + B*(1/6) + 12 = B leads to B = 24, so you should get 8 nonfiction, 4 "natural", and 12 mysteries.
The most useful information usually is a description of what unit you are on and any sort of new methodology or worksheet the young student brings home.
Indeed, sorry to give your 4th Grader the algebra version. Generally, the problem should be sufficiently tractable that experimentation would solve the problem. This seems to have been your approach and it should be sufficient.
Just for the record: B*(1/3) + B*(1/6) + 12 = B leads to B = 24, so you should get 8 nonfiction, 4 "natural", and 12 mysteries.
- Joined
- Feb 4, 2004
- Messages
- 16,582
The whole collection is 1. If 1/3 are non-fiction and 1/6 are nature books, then what fraction remain to be mystery books? (Hint: Subtract from 1.)momtocam said:
If this fraction corresponds to twelve books, then how many books are in the whole collection?
Eliz.
well considering we're dealing with fractions, I did not come up with your answer of :
Just for the record: B*(1/3) + B*(1/6) + 12 = B leads to B = 24, so you should get 8 nonfiction, 4 "natural", and 12 mysteries
I took 1/3 of 12 = 4
I took 1/6 of 12= 2
2 + 4 + 12= 18 (total books that Mary has)
I am confused, please forgive me, but I barely passed modern math in 9th grade, and graduated from 12th grade in 1980. I am still not good at math, as you can see.
My son did something completely different, but I suppose the teacher will give him her answer tomorrow.
Please excuse my short giving in math.
Just for the record: B*(1/3) + B*(1/6) + 12 = B leads to B = 24, so you should get 8 nonfiction, 4 "natural", and 12 mysteries
I took 1/3 of 12 = 4
I took 1/6 of 12= 2
2 + 4 + 12= 18 (total books that Mary has)
I am confused, please forgive me, but I barely passed modern math in 9th grade, and graduated from 12th grade in 1980. I am still not good at math, as you can see.
My son did something completely different, but I suppose the teacher will give him her answer tomorrow.
Please excuse my short giving in math.
- Joined
- Feb 4, 2004
- Messages
- 16,582
stapel said:
Okay, but you really should know fractions. I mean, they come up all the time "in real life", after all! :wink:momtocam said:
Take 1. Subtract 1/3 from this. What fraction do you get? (Hint: 1 = 3/3. 3 - 1 = 2.)
Take the resulting 2/3. Subtract 1/6 from this. What fraction do you get? (Hint: 2/3 = 4/6. 4 - 1 = 3. 3/6 = 1/2.)
If half of the books are accounted for, what fraction remains to comprise the twelve other books? (Hint: The other half is 1/2.)
If twelve books is this fraction of the total, how many books are there, in total? (Hint: If twelve is half, then twice that many will be two halves, or the whole.)
Hope that helps!
Eliz.