Explain why multiplying a quantity by a conversion factor does not change the quantity's value

A conversion factor can be more accurately described as a UNIT. A unit is something equivalent to 1. When we multiply something by 1, it doesn't change it's value, although it might change how it looks.

Example:
1 foot = 12 inches

Dividing both sides by 12 inches gives us this unit,



So when we multiply a quantity by (1foot)/(12inches),
we're really just multiplying that quantity by 1,
which doesn't change its value.