Fractions, Decimals, Percentages and Ratio - November 2004, Stage 4&5

Problems

Peaches Today, Peaches Tomorrow....

Stage: 3 and 4 Challenge Level:

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Circuit Training

Stage: 4 Challenge Level:

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .

What a Joke

Stage: 4 Challenge Level:

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?

And So on - and on -and On

Stage: 5 Challenge Level:

Can you find the value of this function involving algebraic fractions for x=2000?

Complex Partial Fractions

Stage: 5 Challenge Level:

To break down an algebraic fraction into partial fractions in which all the denominators are linear and all the numerators are constants you sometimes need complex numbers.

Can it Be

Stage: 5 Challenge Level:

When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?

FA Cup

Stage: 5 Challenge Level:

In four years 2001 to 2004 Arsenal have been drawn against Chelsea in the FA cup and have beaten Chelsea every time. What was the probability of this? Lots of fractions in the calculations!