grade 8 fraction word problem help please

[puco]

twice a week i go swimming and swim the same number of lengths of the pool each time.
as i swim, i count the lengths i've done so far, and make it into a fraction of the wohle number of lengths i know i'm going to swim.

For example, if i swam 10 lengths each time, as i finished the 5th length i'd think that's 5/10.
If i make that into a simpler fraction, I get 1/2. after 8 lengths it would be 8/10 or 4/5.

But I don't swim 10 lengths. how many do i swim??

here's the clue you need to work it out...

After the first length, the only numbers of lengths that can't be changed to a simpler fraction are prime numbers.

An example of such fraction would be 7/10.

I swim the highest number of lengths for which this is possible.

How many lengths do I swim each week??


----- i know that prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.. but i have problems working out word questions. please help me understand it. thank you!!

 

[Deleted member 4993]

twice a week i go swimming and swim the same number of lengths of the pool each time.
as i swim, i count the lengths i've done so far, and make it into a fraction of the wohle number of lengths i know i'm going to swim.

For example, if i swam 10 lengths each time, as i finished the 5th length i'd think that's 5/10.
If i make that into a simpler fraction, I get 1/2. after 8 lengths it would be 8/10 or 4/5.

But I don't swim 10 lengths. how many do i swim??

here's the clue you need to work it out...

After the first length, the only numbers of lengths that can't be changed to a simpler fraction are prime numbers.

An example of such fraction would be 7/10.

I swim the highest number of lengths for which this is possible.

How many lengths do I swim each week??


----- i know that prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.. but i have problems working out word questions. please help me understand it. thank you!!

Are you supposed to find the minimum number possible?

 

[puco]

twice a week i go swimming and swim the same number of lengths of the pool each time.
as i swim, i count the lengths i've done so far, and make it into a fraction of the wohle number of lengths i know i'm going to swim.

For example, if i swam 10 lengths each time, as i finished the 5th length i'd think that's 5/10.
If i make that into a simpler fraction, I get 1/2. after 8 lengths it would be 8/10 or 4/5.

But I don't swim 10 lengths. how many do i swim??

here's the clue you need to work it out...

After the first length, the only numbers of lengths that can't be changed to a simpler fraction are prime numbers.

An example of such fraction would be 7/10.

I swim the highest number of lengths for which this is possible.

How many lengths do I swim each week??


----- i know that prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.. but i have problems working out word questions. please help me understand it. thank you!!

Are you supposed to find the minimum number possible?

i'm not sure... this was the sheet she gave us.. i think that the length = denominator..
and that the final answer would be 2 times the length. since this person swims 2 times a week.
if i'm wrong please tell me.. it's due tomorrow.

the topic says reasoning and proving.

i don;t know if i'm supposed to find out the minimum number possible.

 

[DrMike]

twice a week i go swimming and swim the same number of lengths of the pool each time.
as i swim, i count the lengths i've done so far, and make it into a fraction of the wohle number of lengths i know i'm going to swim.

For example, if i swam 10 lengths each time, as i finished the 5th length i'd think that's 5/10.
If i make that into a simpler fraction, I get 1/2. after 8 lengths it would be 8/10 or 4/5.

But I don't swim 10 lengths. how many do i swim??

here's the clue you need to work it out...

After the first length, the only numbers of lengths that can't be changed to a simpler fraction are prime numbers.

An example of such fraction would be 7/10.

I swim the highest number of lengths for which this is possible.

How many lengths do I swim each week??


----- i know that prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.. but i have problems working out word questions. please help me understand it. thank you!!

i think that the length = denominator..

You're right about this

and that the final answer would be 2 times the length. since this person swims 2 times a week.

And about this.

i don;t know if i'm supposed to find out the minimum number possible.

But not this. The second last line says :

I swim the highest number of lengths for which this is possible.

Your denominator has this property :

It has a common factor with every composite number less than it.

You might start thinking about this : if the denominator is D, then... can you simplify (D-1)/D ? (D-2)/D ? (D-3)/D ? Answering these questions will tell you a lot about D, I think...

 

[DrMike]

You might start thinking about this : if the denominator is D, then... can you simplify (D-1)/D ? (D-2)/D ? (D-3)/D ? Answering these questions will tell you a lot about D, I think...

Hmm, nope. It's better to think...

If D is yay big, what composite numbers are less than it? What factors must D have? And therefore how big must it be?

And see where that leads you.

If you can't solve the question, but you can find some partial answers, be sure to submit those partial answers to the teacher.