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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Keep it Simple

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 $\frac{1}{16}$?

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Age 11 to 14

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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 $\frac{1}{16}$?

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 ï¿½ 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.