Connecting and Applying Fraction Division

Lesson 2 of 2

In this lesson:

• Use multiplication to verify fraction division
• Write story problems for both division types
• Tell the two types apart every time

Goals for Connecting and Applying Division

By the end of this lesson, you should be able to:

1. Verify any fraction division answer using multiplication
2. Create story contexts for both division types
3. Distinguish between the two types and choose the right approach

Same Numbers, Very Different Answers

Compare these two problems using and 4:

• — a tiny piece
• — a large count

Same numbers. Opposite results. Order matters!

Comparing Both Division Types Side by Side

Two different questions. Two different models. Two different answers.

Fact Families Connect Division and Multiplication

Every division equation has a matching multiplication equation:

• Whole numbers: 12 ÷ 4 = 3 because 3 × 4 = 12
• Type A: because
• Type B: because

Verify With Multiplication: Type A Example

Problem:

Think: What number times 2 equals ?

So .

Verify With Multiplication: Type B Example

Problem:

Think: What number times equals 6?

So .

Which Type Is This Problem?

• Ask: What is being divided? (, a fraction)
• Ask: What are we dividing by? (3, a whole number)
• Type A: Unit fraction shared among groups

Answer:

Mixed Practice: Classify and Solve

For each problem, decide: Type A or Type B? Then solve.

Classify first, then compute and check.

Answers for Mixed Classification Practice

1. Type A:

2. Type B:

3. Type A:

4. Type B:

Writing Stories for Division Expressions

Now let's learn to create word problems for each type.

• Good stories have a real-world context
• The dividend is what you start with
• The divisor is what you divide by

Type A Stories: Sharing a Fraction

Template: "You have of something. You share it equally among groups. How much does each group get?"

Type A Story Example Solved

Expression:

Story: "You have gallon of paint. You pour it equally into 3 cups. How much is in each cup?"

Check:

Type B Stories: Counting Pieces in Wholes

Template: "You have units. Each piece is of a unit. How many pieces can you make?"

Type B Story Example Solved

Expression:

Story: "You have 3 pounds of trail mix. Each bag gets pound. How many bags can you fill?"

Check:

Your Turn: Write a Story

Write a story for:

Hints:

• This is Type A — sharing a fraction
• You start with of something
• You share it among 2 groups
• Answer:

Write your story, then share with a partner.

Word Problems: Runner and Baker Scenarios

Problem 1: A runner has mile left, split into 4 equal sprints. How long is each?

Problem 2: A baker has 3 cups of sugar. Each batch uses cup. How many batches?

Pause and solve before the next slide.

Answers: Runner and Baker Scenarios Solved

Problem 1: Type A — mile

• Check:

Problem 2: Type B — batches

• Check:

Word Problems: Granola Bar and Garden

Problem 3: You have of a granola bar, split into 2 equal snacks. How much is each?

Problem 4: A garden is 6 meters long. You plant every meter. How many flowers?

Pause and solve before the next slide.

Answers: Granola Bar and Garden Solved

Problem 3: Type A — bar

• Check:

Problem 4: Type B — flowers

• Check:

Summary of Fraction Division Strategies

✓ Verify every answer: quotient × divisor = dividend
✓ Type A: share a fraction → smaller result
✓ Type B: count pieces → larger result

Always identify the dividend and divisor first