# Lesson 7What Fraction of a Group?

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

### Learning Targets:

• I can tell when a question is asking for the number of groups and that number is less than 1.
• I can use diagrams and multiplication and division equations to represent and answer “what fraction of a group?” questions.

## 7.1Estimating a Fraction of a Number

1. Estimate the following quantities:

1. What is of 7?
2. What is of ?
3. What is of ?
1. Write a multiplication expression for each question.

## 7.2Fractions of Ropes

The segments in the applet represent 4 different lengths of rope. Compare one rope to another, moving the rope by dragging the open circle at one endpoint. You can use the yellow pins to mark off lengths.

1. Compare the lengths of rope B, C, and D to the length of rope A and complete each statement. Then, use the measurements shown on the grid to write a multiplication equation and a division equation for each statement.
1. Rope B is _______ times as long as rope A.

Multiplication equation: _________________
Division equation: _________________

2. Rope C is _______ times as long as rope A.

Multiplication equation: _________________
Division equation: _________________

3. Rope D is _______ times as long as rope A.

Multiplication equation: _________________
Division equation: _________________

2. Each equation can be used to answer a question about rope C and D. What could each question be?

1. and

2. and

## 7.3Fractional Batches of Ice Cream

One batch of an ice cream recipe uses 9 cups of milk. A chef makes different amounts of ice cream on different days. Here are the amounts of milk she used:

• Monday: 12 cups
• Tuesday: cups
• Thursday: 6 cups
• Friday: cups
1. How many batches of ice cream did she make on each of the following days? Write a division equation and draw a tape diagram for the question about each day. Then answer the question.

1. Monday
2. Tuesday
2. What fraction of a batch of ice cream did she make on each of the following days? Write a division equation and draw a tape diagram for the question about each day. Then answer the question.

1. Thursday
2. Friday
3. Write a division equation, and draw a tape diagram for each question. Then answer the question.

1. What fraction of 9 is 3?
2. What fraction of 5 is ?

## Lesson 7 Summary

It is natural to think about groups when we have more than one group, but we can also have a fraction of a group.

To find the amount in a fraction of a group, we can multiply the fraction by the amount in the whole group. If a bag of rice weighs 5 kg,  of a bag would weigh ( kg.

Sometimes we need to find what fraction of a group an amount is. Suppose a full bag of flour weighs 6 kg. A chef used 3 kg of flour. What fraction of a full bag was used? In other words, what fraction of 6 kg is 3 kg?

This question can be represented by a multiplication equation and a division equation, as well as by a diagram.

We can see from the diagram that 3 is of 6, and we can check this answer by multiplying: .

In any situation where we want to know what fraction one number is of another number, we can write a division equation to help us find the answer.

For example, “What fraction of 3 is ?” can be expressed as , which can also be written as .

The answer to “What is ?” is also the answer to the original question.

The diagram shows that 3 wholes contain 12 fourths, and contains 9 fourths, so the answer to this question is , which is equivalent to

We can use diagrams to help us solve other division problems that require finding a fraction of a group. For example, here is a diagram to help us answer the question: “What fraction of  is ?,” which can be written as .

We can see that the quotient is , which is equivalent to . To check this, let’s multiply.  , and is, indeed, equal to .

## Lesson 7 Practice Problems

1. A recipe calls for lb of flour for 1 batch. How many batches can be made with each of the following amounts?

1. 1 lb
2. lb
3. lb
2. Whiskers the cat weighs kg. Piglio weighs kg. For each question, write a multiplication and a division equation, decide whether the answer is greater or less than 1, and then answer the question.

1. How many times as heavy as Piglio is Whiskers?
2. How many times as heavy as Whiskers is Piglio?
3. Andre is walking from home to a festival that is kilometers away. He takes a quick rest after walking kilometers. In this situation, which question can be represented by the equation: ?

1. What fraction of the trip has Andre completed?
2. How many more kilometers does he have to walk to get to the festival?
3. What fraction of the trip is left?
4. How many kilometers is it from home to the festival and back home?
4. Draw a tape diagram to represent and answer the question: What fraction of is ?

5. How many groups of are in each of the following quantities?

6. Which question can be represented by the equation

1. What is 4 groups of ?
2. How many s are in 4?
3. What is of 4?
4. How many 4s are in ?