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?

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

  2. Write a multiplication or division equation to represent the situation.

  3. 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.

A diagram of two figures made of pattern blocks. The figure on the left is of one yellow hexagon and the figure on the right is of two blue rhombuses alinged along one vertical side.

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.

  1. \(15\boldcdot \frac25 = 6\)
  2. \(6 \boldcdot \frac43 = 8\)
  3. \(16\boldcdot \frac78 = 14\)

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.

(From Unit 4, Lesson 2.)

Problem 6

Write a division expression with a quotient that is:

  1. greater than \(8 \div 0.001\)
  2. less than \(8 \div 0.001\)
  3. between \(8 \div 0.001\) and \(8 \div \frac{1}{10}\)
(From Unit 4, Lesson 1.)

Problem 7

Find each unknown number.

  1. 12 is 150% of what number?
  2. 5 is 50% of what number?
  3. 10% of what number is 300?
  4. 5% of what number is 72?
  5. 20 is 80% of what number?
(From Unit 3, Lesson 14.)