Hi my name is Katie Mutz and my level of question is elementry. I am a student.

When you multiply two positive fractions less than 1, how does the answer compare to the size of the fraction? Why? Thanks Katie

One way to see what happens is to use money. If a unit is $1.00 then ¹/₂x¹/₁₀ is  ¹/₂ of ¹/₁₀ of a dollar. One tenth of a dollar is ten cents so  ¹/₂ of ¹/₁₀ of a dollar is five cents. Thus  ¹/₂ x ¹/₁₀ is smaller than both ¹/₂ and ¹/₁₀.

Even without the money analogy you can see that  ¹/₂x¹/₁₀ is smaller than one-tenth since it is only part of one-tenth. In fact it is only one-half of one-tenth. It is also smaller than one-half since it is only one-tenth of one-half.