#### You may also like ### Tweedle Dum and Tweedle Dee

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... ### 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 ï¿½ 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.

# Keep it Simple

##### Age 11 to 14Challenge Level

Try working systematically through all the possibilities.

$\frac{1}{8} = \frac{1}{9} + ?$

$\frac{1}{8} = \frac{1}{10} + ?$

$\frac{1}{8} = \frac{1}{11} + ?$

$\frac{1}{8} = \frac{1}{12} + ?$

$\frac{1}{8} = \frac{1}{13} + ?$

$\frac{1}{8} = \frac{1}{14} + ?$

$\frac{1}{8} = \frac{1}{15} + ?$

$\frac{1}{8} = \frac{1}{16} + ?$ (but this won't count)

Why is $\frac{1}{9}$ the first one you can use?
Why don't you need to go further than $\frac{1}{16}$?