<<Disclaimer: Verify this information before applying it to your situation.>>

Here are some of the recommendations of responses I received about cutting
bread recipes by 1/3 to be used in a smaller bread machine. I tried to
include ideas from all the posts.  Thank you all for your help.

One of the member in our group would mix the full recipe in the bread
machine.   After it was mixed, she would remove 1/3 of the dough & make half
a dozen rolls or a pizza crust...Might be easier than doing the math.

There's a couple ways to work around the egg issue, if the eggs are
supposed to be beaten before adding, you could simply crack the full amount
(say two) and measure in a measuring cup/spoon and then just use one-third
of the full amount after beating. Once you have done it once write it down.
Another way might be to use small eggs in place of large and then just use
the same amount as in the full recipe. (I always assume large eggs unless
the recipe specifically states otherwise.) Also whenever you need a
fraction of something else it is multiplication that you will be doing. So
1/3 of 1/2 would be 1/6th. Multiply 1/3 X 1/2. Remember when you multiply
with fractions you get a smaller number whereas when you divide you will
get a larger number. One way to remember this is to think in terms of a pie
and cutting it into slices. For example, if you have half a pie and you
have three people to eat it then you would want to cut the pie into 1/3
slices, right. So you will end up with 3 slices but each of those slices
represents 1/6th of the whole, because if you cut two halves of the pie
into 1/3 slices you would get six slices. I hope this helps.

             1    1     1
             - x  -  =  -
             2    3     6

But since I don't have a 1/3 or a 1/6 of a teaspoon, what I would do is use
your 1/2 teaspoon and eyeball filling it to a 1/3 of its capacity.   It
should be close enough.   Of course, if you are trying to reduce something by
1/3 you need to put 2/3 of the measurement in ... so again try to eyeball
filling the bowl of the 1/2 teaspoon to 2/3 of its capacity.

As for eggs, I use Deb-El Just Whites, a dried egg white
product.   It's much easier to use a smaller quantity than
normal if I want.   If you want to use the whole egg, though,
you may find it easier to use small or medium eggs instead
of large ones.   Just look at them, decide which ones are
2/3 the size of the large ones (the size usually called for),
buy those, and use the same number of eggs as originally
called for.

You would use 1/6 of a tsp. Since there is not a spoon this size, I would
measure 1/4 a tsp. and remove about a third of it. It shouldn't make too much
difference if it is not exact, it's such a small amount.

As far as the eggs, I would use the whole one or two if that's what it called
for. You could also put them in a cup and lightly beat them, then measure out
of the amount.