Exercises

1. Find the quotient (the answer to the division statement).
   1. \(5 \div \dfrac{1}{4} =\boxed{\phantom\square}\)
   2. \(\dfrac{5}{6} \div \dfrac{1}{6} =\boxed{\phantom\square}\)
   3. \(\dfrac{2}{3} \div \dfrac{2}{5} =\boxed{\phantom\square}\)
   4. \(\dfrac{3}{8} \div \dfrac{5}{6} =\boxed{\phantom\square}\)
   5. \(3\dfrac{2}{3} \div \dfrac{2}{5} =\boxed{\phantom\square}\)
   6. \(1 \dfrac{1}{2} \div 2 \dfrac{3}{4} =\boxed{\phantom\square}\)
2. A piano teacher has \(4\dfrac{1}{2}\) hours available to teach each night.  One lesson will last \(\dfrac{3}{4}\) of an hour.  How many lessons can the teacher schedule each night?
3. Vera would like to use her phone for the whole \(6\)-hour day at school.  When she arrives at school, she sees that her battery life is down to \(\dfrac{1}{2}\).  If the phone drains another \(\dfrac{1}{8}\) of a full battery every hour, will her phone last all day?
4. A company uses \(\dfrac{1}{4}\) of a barrel of chocolate chips to make each batch of their marshmallow chocolate chip granola bars.  In one day, the company uses \(3\dfrac{1}{2}\) barrels of chocolate chips to make granola bars.  How many batches of granola bars did the company make in the day?
5. You are dividing two proper fractions.  Justify whether it is possible that the resulting quotient is
   1. larger than 1?
   2. equal to 1?
   3. smaller than 1?
6. 1. Colin divided two proper fractions and got a quotient of \(\dfrac{3}{4}\).  What might the two fractions have been?  
   2. Colin divided two improper fractions and got a quotient of \(\dfrac{2}{3}\).  What might the two fractions have been?  
7. Consider the following list of fractions: \(\dfrac{3}{4}, ~\dfrac{7}{12},~\dfrac{3}{5},~\dfrac{5}{6},~\dfrac{1}{2},~\dfrac{1}{3}\).  
   1. Select two fractions from the list that when divided one from the other will produce the smallest possible quotient.
   2. Select two fractions from the list that when divided one from the other will produce the largest possible quotient.
   3. What do you notice about the two quotients that you found?
8. Consider the following pattern: \[1, \quad 1\div\dfrac{1}{2}, \quad 1\div\dfrac{1}{2}\div\dfrac{1}{3},\quad 1\div\dfrac{1}{2}\div\dfrac{1}{3}\div\dfrac{1}{4}, \ldots \]
   1. Explain how you know if the pattern is increasing or decreasing?
   2. Does the pattern ever give a value over \(500\)?  If it does, when does this happen?