Lesson 7

What Fraction of a Group?

Let’s think about dividing things into groups when we can’t even make one whole group.

Problem 1

A recipe calls for \(\frac12\) lb of flour for 1 batch. How many batches can be made with each of these amounts?

  1. 1 lb
  2. \(\frac34\) lb
  3. \(\frac14\) lb

Problem 2

Whiskers the cat weighs \(2\frac23\) kg. Piglio weighs \(4\) kg. For each question, write a multiplication equation and a division equation, decide whether the answer is greater than 1 or less than 1, and then find the answer.

  1. How many times as heavy as Piglio is Whiskers?
  2. How many times as heavy as Whiskers is Piglio?

Problem 3

Andre is walking from his home to a festival that is \(1\frac58\) kilometers away. He walks \(\frac13\) kilometer and then takes a quick rest. Which question can be represented by the equation \({?} \boldcdot 1\frac58 = \frac13\) in this situation?

A:

What fraction of the trip has Andre completed?

B:

What fraction of the trip is left?

C:

How many more kilometers does Andre have to walk to get to the festival?

D:

How many kilometers is it from home to the festival and back home?

Problem 4

Draw a tape diagram to represent the question: What fraction of \(2\frac12\) is \(\frac45\)?
Then find the answer.

Problem 5

How many groups of \(\frac34\) are in each of these quantities?

  1. \(\frac{11}{4}\)
  2. \(6\frac12\)
(From Unit 4, Lesson 6.)

Problem 6

Which question can be represented by the equation \(4\div \frac27 = {?}\)

A:

What is 4 groups of \(\frac 27\)?

B:

How many \(\frac27\)s are in 4?

C:

What is \(\frac 27\) of 4?

D:

How many 4s are in \(\frac27\)?

(From Unit 4, Lesson 4.)