Lesson 4
How Many Groups? (Part 1)
Let’s play with blocks and diagrams to think about division with fractions.
Problem 1
Consider the problem: A shopper buys cat food in bags of 3 lbs. Her cat eats \(\frac34\) lb each week. How many weeks does one bag last?

Draw a diagram to represent the situation and label your diagram so it can be followed by others. Answer the question.

Write a multiplication or division equation to represent the situation.

Multiply your answer in the first question (the number of weeks) by \(\frac34\). Did you get 3 as a result? If not, revise your previous work.
Problem 2
Use the diagram to answer the question: How many \(\frac13\)s are in \(1\frac23\)? The hexagon represents 1 whole. Explain or show your reasoning.
Problem 3
Which question can be represented by the equation \({?}\boldcdot \frac18=3\)?
How many 3s are in \(\frac18\)?
What is 3 groups of \(\frac18\)?
How many \(\frac 18\)s are in 3?
What is \(\frac 18\) of 3?
Problem 4
Write two division equations for each multiplication equation.
 \(15\boldcdot \frac25 = 6\)
 \(6 \boldcdot \frac43 = 8\)
 \(16\boldcdot \frac78 = 14\)
Problem 5
Noah and his friends are going to an amusement park. The total cost of admission for 8 students is $100, and all students share the cost equally. Noah brought $13 for his ticket. Did he bring enough money to get into the park? Explain your reasoning.
Problem 6
Write a division expression with a quotient that is:
 greater than \(8 \div 0.001\)
 less than \(8 \div 0.001\)
 between \(8 \div 0.001\) and \(8 \div \frac{1}{10}\)
Problem 7
Find each unknown number.
 12 is 150% of what number?
 5 is 50% of what number?
 10% of what number is 300?
 5% of what number is 72?
 20 is 80% of what number?