Lesson 6

Using Diagrams to Find the Number of Groups

Let’s draw tape diagrams to think about division with fractions.

Problem 1

We can think of \(3\div \frac14\) as the question “How many groups of \(\frac14\) are in 3?” Draw a tape diagram to represent this question. Then find the answer.

Problem 2

Describe how to draw a tape diagram to represent and answer \(3 \div \frac35 = {?}\) for a friend who was absent.

Problem 3

How many groups of \(\frac12\) day are in 1 week?

  1. Write a multiplication equation or a division equation to represent the question.

  2. Draw a tape diagram to show the relationship between the quantities and to answer the question. Use graph paper, if needed.

Problem 4

Diego said that the answer to the question “How many groups of \(\frac56\) are in 1?” is \(\frac 65\) or \(1\frac15\). Do you agree with him? Explain or show your reasoning.

Problem 5

Select all the equations that can represent the question: “How many groups of \(\frac45\) are in 1?”

A:

\({?} \boldcdot 1=\frac45\)

B:

\(1 \boldcdot \frac45 = {?}\)

C:

\(\frac45 \div 1 = {?}\)

D:

\({?} \boldcdot \frac45 =1\)

E:

\(1\div \frac45 = {?}\)

(From Unit 4, Lesson 5.)

Problem 6

Calculate each percentage mentally.

  1. What is 10% of 70?
  2. What is 10% of 110?
  3. What is 25% of 160?
  4. What is 25% of 48?
  5. What is 50% of 90?
  6. What is 50% of 350?
  7. What is 75% of 300?
  8. What is 75% of 48?
(From Unit 3, Lesson 14.)