6. (Givena fraction, produce another fraction)

a. Find a way to further partition a third of a unit segment so that you can make 1/2 of the unit segment. Before you start, write an equation that symbolizes what you plan to do.

If I want to break thirds up to make a half then I'll just use (1/2)(1/3)=1/6 length pieces. this works because 3(1/2)(1/3)=(3/3)(1/2). So cut each 1/3 in half.

b. Find a way to further partition a seventh of a unit segment so that you can make exactly 1/5 of the unit segment. Before you start, write an equation that symbolizes what you plan to do.

As in (a) I'll use (1/5)(1/7) since 7(1/5)(1/7)=1/5. That is, I break the 1/7 segment into pieces of length 1/35...there are 5 pieces since 5/35=1/7.

c.