Peaches Today, Peaches Tomorrow...
The monkey will always keep a whole number of peaches.
For part (ii), you could use a tree diagram: at each stage, branch off the fractions it would be possible to try next so that all possibilities are checked.
For Part (iii), why not try a starting value and see what happens? Then decide whether you need to start with a bigger or smaller starting value next time.
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Sum Equals Product
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?
Special Sums and Products
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.