Multiply Two Tenths less than 1: Vertical Multiplication - Math ... - Free Printable

Problem Description:

The task is to multiply two decimal numbers (tenths) that are less than 1. The goal is to find the product of each pair of numbers provided.

Given Pairs:

1. \( 0.9 \times 0.4 \)
2. \( 0.4 \times 0.3 \)
3. \( 0.7 \times 0.1 \)
4. \( 0.8 \times 0.2 \)
5. \( 0.5 \times 0.8 \)
6. \( 0.1 \times 0.5 \)

Solution Approach:

To solve these multiplications, follow these steps:
1. Ignore the decimal points initially: Multiply the numbers as if they were whole numbers.
2. Count the total number of decimal places: In each pair, count the total number of digits after the decimal points.
3. Place the decimal point in the product: After multiplying, place the decimal point in the product so that the total number of decimal places matches the sum from step 2.

Step-by-Step Calculations:

#### 1. \( 0.9 \times 0.4 \)
- Ignore decimals: \( 9 \times 4 = 36 \)
- Total decimal places: \( 1 + 1 = 2 \)
- Place the decimal: \( 0.36 \)
- Result: \( 0.9 \times 0.4 = 0.36 \)

#### 2. \( 0.4 \times 0.3 \)
- Ignore decimals: \( 4 \times 3 = 12 \)
- Total decimal places: \( 1 + 1 = 2 \)
- Place the decimal: \( 0.12 \)
- Result: \( 0.4 \times 0.3 = 0.12 \)

#### 3. \( 0.7 \times 0.1 \)
- Ignore decimals: \( 7 \times 1 = 7 \)
- Total decimal places: \( 1 + 1 = 2 \)
- Place the decimal: \( 0.07 \)
- Result: \( 0.7 \times 0.1 = 0.07 \)

#### 4. \( 0.8 \times 0.2 \)
- Ignore decimals: \( 8 \times 2 = 16 \)
- Total decimal places: \( 1 + 1 = 2 \)
- Place the decimal: \( 0.16 \)
- Result: \( 0.8 \times 0.2 = 0.16 \)

#### 5. \( 0.5 \times 0.8 \)
- Ignore decimals: \( 5 \times 8 = 40 \)
- Total decimal places: \( 1 + 1 = 2 \)
- Place the decimal: \( 0.40 \) (which simplifies to \( 0.4 \))
- Result: \( 0.5 \times 0.8 = 0.4 \)

#### 6. \( 0.1 \times 0.5 \)
- Ignore decimals: \( 1 \times 5 = 5 \)
- Total decimal places: \( 1 + 1 = 2 \)
- Place the decimal: \( 0.05 \)
- Result: \( 0.1 \times 0.5 = 0.05 \)

Final Answers:

\[
\begin{aligned}
1. & \quad 0.9 \times 0.4 = 0.36 \\
2. & \quad 0.4 \times 0.3 = 0.12 \\
3. & \quad 0.7 \times 0.1 = 0.07 \\
4. & \quad 0.8 \times 0.2 = 0.16 \\
5. & \quad 0.5 \times 0.8 = 0.4 \\
6. & \quad 0.1 \times 0.5 = 0.05 \\
\end{aligned}
\]

Boxed Final Answer:

\[
\boxed{0.36, 0.12, 0.07, 0.16, 0.4, 0.05}
\]