Lesson 5
How Many Groups? (Part 2)
Let’s use blocks and diagrams to understand more about division with fractions.
Problem 1
Use the tape diagram to find the value of \(\frac12\div\frac13\). Show your reasoning.
Problem 2
What is the value of \(\frac12\div\frac13\)? Use pattern blocks to represent and find this value. The yellow hexagon represents 1 whole. Explain or show your reasoning.
Problem 3
Use a standard inch ruler to answer each question. Then, write a multiplication equation and a division equation that answer the question.

How many \(\frac12\)s are in 7?

How many \(\frac38\)s are in 6?

How many \(\frac{5}{16}\)s are in \(1\frac78\)?
Problem 4
Use the tape diagram to answer the question: How many \(\frac25\)s are in \(1\frac12\)? Show your reasoning.
Problem 5
Write a multiplication equation and a division equation to represent each sentence or diagram.

There are 12 fourths in 3.

How many \(\frac 23\)s are in 6?
Problem 6
At a farmer’s market, two vendors sell fresh milk. One vendor sells 2 liters for $3.80, and another vendor sells 1.5 liters for $2.70. Which is the better deal? Explain your reasoning.
Problem 7
A recipe uses 5 cups of flour for every 2 cups of sugar.

How much sugar is used for 1 cup of flour?

How much flour is used for 1 cup of sugar?

How much flour is used with 7 cups of sugar?
 How much sugar is used with 6 cups of flour?