Or search by topic
Every day I go to the swimming pool and swim the same number of lengths. I like to count the number of lengths I've done as I go as a fraction of the total number of lengths I'm going to do that day.
If I swam ten lengths a day...
I don't swim ten lengths a day. In fact, the total number of lengths I swim each day is rather special...
Let's call the total number of lengths I swim $n$.
After the first length, for every length I swim, the total so far (let's call it $t$) is either a prime number, or the fraction $\frac{t}{n}$ will simplify (or both).
It is, in fact, the largest number for which this is true.
Can you work out how many lengths I swim each day?
Two brothers were left some money, amounting to an exact number of pounds, to divide between them. DEE undertook the division. "But your heap is larger than mine!" cried DUM...
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 � 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers?
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.