Sophia used 1/3 of an ounce of cheese to make 1/12 of a pound of pizza dough. How l many ounces of cheese are needed to make a pound of pizza dough?

Note: One pound is the same as #16# ounces

Let's make a ratio of these two statements:

#1/3 : 1/12#

This is saying that for every #1/3# of an #color(red)(o u n c e# we have #1/12# of a #color(blue)(pound)#. Uh-oh, those units don't match. Let's make them match before things get confusing

To go from #1/3# ounces to pounds, we need to divide by #16#. That gives us #1/48# #color(blue)(pounds)# instead of #1/3# ounces

So now our ratio is #1/48 : 1/12#

We are looking for how much cheese we need when we have a pound of pizza. So, we need to make #1/12# lbs of pizza into
#1# lb of pizza. We do this by multiplying by #12#.

BUT we need to do the same on the other side

So now we have #12 xx 1/48 : 1/12 xx 12#

or #12/48 : 1#

or #1/4 : 1#

We are almost done! This ratio says that for every #1/4# #color(blue)(pound# of cheese we have #1# #color(blue)(pound)# of pizza. However, our final answer is supposed to be in ounces.

So we convert again, multiplying #1/4# by #16#, which gives us #4# ounces.

So, if you have #1# pound of pizza, you must have used #4# ounces of cheese