Fractions

The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.

Which dilutions can you make using only 10ml pipettes?

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

Can you tangle yourself up and reach any fraction?

Relate these algebraic expressions to geometrical diagrams.

Can you use the given image to say something about the sum of an infinite series?

When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?

We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.