Why is it when you multiply two proper fractions your product is less than either factor?

Remember the denominator shows how many equal parts the item is divided into, so because you are multiplying the number of parts (you are increasing the number of cuts) the denominator will get bigger ...which in turn means the pieces will be smaller. Just remember the higher a denominator is the smaller it will be in size...multiplying a fraction means you are multiplying the number of cuts and sections that is why the size gets smaller.