Fraction Differences - Urgent Help!!

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February 22nd 2008, 10:05 AM
Sanfordl11

Fraction Differences - Urgent Help!!

I'm doing coursework for Maths which needs to be handed in Monday (25th February 2008). It is....

Ruth was investigating fraction differences.

She wrote down this sequence of fractions:

1 1 1 1 1 1
1 2 3 4 5 6

.....

Then she worked out the differences between the consecutive fractions:

1 1 1 1 1
2 6 12 20 30

.....

Then she worked out the differences between the fractions in her second series:

1 1
3 12

Investigate further.

Please can you help ASAP! Thanks
February 22nd 2008, 10:14 AM
galactus

Keep going until you get to the 'peak' of your triangle made up from the differences.

Look for patterns.
February 22nd 2008, 10:18 AM
angel.white

Quote:

Originally Posted by Sanfordl11

I'm doing coursework for Maths which needs to be handed in Monday (25th February 2008). It is....

Ruth was investigating fraction differences.

She wrote down this sequence of fractions:

1 1 1 1 1 1
1 2 3 4 5 6

.....

Then she worked out the differences between the consecutive fractions:

1 1 1 1 1
2 6 12 20 30

.....

Then she worked out the differences between the fractions in her second series:

1 1
3 12

Investigate further.

Please can you help ASAP! Thanks

What does "investigate further" mean? They want you to continue the series from 1/3 and 1/12? Or they want you to find the differences between these consecutive fractions? Something else?
February 22nd 2008, 10:43 AM
Sanfordl11

Help!! Ok......

It means, I think find the nth term of each sequence if u were to carry on and to set it out in a coursework/essay style - please hellp!! thnks for replies newaii and find differecnes
February 22nd 2008, 02:10 PM
angel.white

Quote:

Originally Posted by Sanfordl11

It means, I think find the nth term of each sequence if u were to carry on and to set it out in a coursework/essay style - please hellp!! thnks for replies newaii and find differecnes

Well, difference is another term for subtraction.

So what they did was this:
$\frac 11 \frac 12 \frac 13$

Then they wanted to find the difference so they did this:

the first term will be the difference between 1/1 and 1/2 so:
$\frac 11 - \frac 12 ~~~~= ~~~~\frac 22*\frac 11 - \frac 12 ~~~~= ~~~~\frac 22 - \frac 12 ~~~~=~~~~ \frac{2-1}2 ~~~~=~~~~ \frac 12$

And that is how they got the first term. Then they went onto the second term, the difference between 1/2 and 1/3
$\frac 12 - \frac 13 ~~~~=~~~~ \frac 33*12 - \frac 22 * \frac13 ~~~~=~~~~\frac 36-\frac 26 ~~~~=~~~~ \frac{3-2}6~~~~=~~~~\frac 16$

and that is how they got the second term. They proceeded to do this through $\frac 15 -\frac 16 = \frac 1{30}$

Then they went on to find the differences between the differences. Since the first two, which we found, were 1/2 and 1/6, they did:
$\frac 12-\frac 16 ~~~~=~~~~\frac 33*\frac 12-\frac 16~~~~=~~~~\frac 36 - \frac 16~~~~=~~~~ \frac{3-1}6~~~~=~~~~\frac 26 ~~~~=~~~~ \frac 22*\frac 13 ~~~~=~~~~ \frac 13$

Then they did the next one, and got 1/6 - 1/12 = 1/12

So, it's not clear to me what you're supposed to do, but if you understand what you are supposed to do, then you can follow this technique to figure out the proper answers.