Lesson 2-2: Decimal × Decimal

Master multiplying decimals by decimals using area models and decimal place value rules!

Learning Scenario: Table Design

Scenario: You're designing a rectangular table for your room. The table needs to be 1.2 meters long and 0.8 meters wide. What is the area of the table?

What We Need to Find:

• Area of the rectangular table
• Length: 1.2 meters
• Width: 0.8 meters
• We need: 1.2 × 0.8 = ?

Tools We'll Use:

• Area models
• Place value rules
• Error correction
• Real-world verification

Method 1: Area Model

Visual Understanding

To find 1.2 × 0.8, we can use an area model. Think of a 1.2m × 0.8m rectangle:

1.2m × 0.8m rectangle

12 × 8 = 96 small squares

Step 1: Break Down the Numbers

1.2 = 1 + 0.2 and 0.8 = 0.8

Step 2: Use Distributive Property

1.2 × 0.8 = (1 + 0.2) × 0.8

Calculating the Area

Let's calculate using the distributive property:

1.2 × 0.8 = (1 + 0.2) × 0.8

Distributive property

= 1 × 0.8 + 0.2 × 0.8

Multiply each part

= 0.8 + 0.16 = 0.96

Add the results

Answer: The table has an area of 0.96 square meters!

Method 2: Algorithm with Place Value

The Standard Algorithm

We can also use the standard multiplication algorithm:

1.2

× 0.8

96 (12 × 8)

Count decimal places: 1 + 1 = 2

0.96

Step 1: Multiply as Whole Numbers

First, multiply 12 × 8 = 96

Step 2: Count Decimal Places

1.2 has 1 decimal place, 0.8 has 1 decimal place, so result has 2 decimal places: 0.96

Common Error and Correction

Common Mistake

Many students make this error when multiplying decimals:

❌ 0.2 × 0.3 = 0.6 (WRONG!)

This is a common mistake!

Why It's Wrong:

The answer is too big. 0.2 × 0.3 should be smaller than both numbers.

Correct Method:

0.2 × 0.3 = 0.06 (2 × 3 = 6, with 2 decimal places)

Model Verification

Let's verify the correct answer using a visual model:

0.2 × 0.3 = 6/100 = 0.06

6 out of 100 squares = 0.06

Correct Answer: 0.2 × 0.3 = 0.06

Practice Problems

Problem 1: Glass Area

A piece of glass is 2.5 meters long and 1.1 meters wide. What is the area? If glass costs $8.50 per square meter, what is the total cost?

Area: 2.5 × 1.1 = 2.75 m²

Cost: 2.75 × 8.5 = 23.375 ≈ $23.38

Answer: Area = 2.75 m², Cost ≈ $23.38

More Practice

Calculate: 0.4 × 0.7

0.4 × 0.7 = 0.28

Calculate: 1.5 × 0.6

1.5 × 0.6 = 0.9

Key Takeaways

Algorithm Steps

•Multiply as if they were whole numbers
•Count total decimal places in both numbers
•Place decimal point in the answer
•Use area models for understanding

Remember

•When multiplying decimals, the answer is usually smaller
•Use visual models to check your work
•Estimate first to see if your answer makes sense
•Practice with real-world area problems

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