Lesson 5

How Many Groups? (Part 2)

Problem 1

Use the tape diagram to find the value of \(\frac12\div\frac13\). Show your reasoning.

A tape diagram. 

Solution

For access, consult one of our IM Certified Partners.

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.

Solution

For access, consult one of our IM Certified Partners.

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. 

Solution

For access, consult one of our IM Certified Partners.

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."

Solution

For access, consult one of our IM Certified Partners.

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."

Solution

For access, consult one of our IM Certified Partners.

(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.

Solution

For access, consult one of our IM Certified Partners.

(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?

Solution

For access, consult one of our IM Certified Partners.

(From Unit 3, Lesson 6.)