Keep it Simple printable sheet
For example
$\frac{1}{2} = \frac{1}{3} + \frac{1}{6}$
Charlie thought he'd spotted a rule and made up some more examples.
$\frac{1}{2} = \frac{1}{10} + \frac{1}{20}$
$\frac{1}{3} = \frac{1}{4} + \frac{1}{12}$
$\frac{1}{3} = \frac{1}{7} + \frac{1}{21}$
$\frac{1}{4} = \frac{1}{5} + \frac{1}{20}$
Can you describe Charlie's rule?
Are all his examples correct?
What do you notice about the sums that are correct?
Find some other correct examples..
How would you explain to Charlie how to generate lots of correct examples?
She found:
$\frac{1}{6} = \frac{1}{7} + \frac{1}{42}$
$\frac{1}{6} = \frac{1}{8} + \frac{1}{24}$
$\frac{1}{6} = \frac{1}{9} + \frac{1}{18}$
$\frac{1}{6} = \frac{1}{10} + \frac{1}{15}$
$\frac{1}{6} = \frac{1}{12} + \frac{1}{12}$ (BUT she realised this one didn't count because they were not different.)
$\frac{1}{8} = \frac{1}{9} + ?$
$\frac{1}{8} = \frac{1}{10} + ?$
$\frac{1}{8} = \frac{1}{11} + ?$
..........
Can all unit fractions be made in more than one way like this?
Choose different unit fractions of your own to test out your theories.