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.

A tape diagram. 

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.

Four pattern blocks: One large yellow hexagon, one blue rhombus, one red trapezoid, and one green triangle.

Problem 3

Use a standard inch ruler to answer each question. Then, write a multiplication equation and a division equation that answer the question.

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

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

  3. How many \(\frac{5}{16}\)s are in \(1\frac78\)?

Image of a ruler. Top, inches. Scale 0 to 8, by 1's. Bottom, centimeters. Scale 0 to 20, by 1's. 

Problem 4

Use the tape diagram to answer the question: How many \(\frac25\)s are in \(1\frac12\)? Show your reasoning.

A tape diagram of two equal parts on a square grid. Each part is composed of 5 squares. A brace from the beginning of the diagram to the middle of the eighth square is labeled "one and one half."

Problem 5

Write a multiplication equation and a division equation to represent each sentence or diagram.

  1. There are 12 fourths in 3.

  2. A tape diagram of 4 equal parts with each part labeled one half. Above the diagram is a brace, labeled 2, that contains all 4 parts.
  3. How many \(\frac 23\)s are in 6?

  4. Fraction bar diagram. 5 equal parts. Each part labeled "the fraction 2 over 5." Total labeled "2."

(From Unit 4, Lesson 4.)

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.

(From Unit 3, Lesson 5.)

Problem 7

A recipe uses 5 cups of flour for every 2 cups of sugar.

  1. How much sugar is used for 1 cup of flour?

  2. How much flour is used for 1 cup of sugar?

  3. How much flour is used with 7 cups of sugar?

  4. How much sugar is used with 6 cups of flour?
(From Unit 3, Lesson 6.)