Find Product Using Distributive Property - Math Worksheets ... - Free Printable

Problem Analysis:

The task requires us to use the distributive property of multiplication to derive the next five facts of 8. The distributive property states that:

\[
a \times (b + c) = (a \times b) + (a \times c)
\]

We are given the first five facts of 8:
- \( 8 \times 1 = 8 \)
- \( 8 \times 2 = 16 \)
- \( 8 \times 3 = 24 \)
- \( 8 \times 4 = 32 \)
- \( 8 \times 5 = 40 \)

We need to find the next five facts:
- \( 8 \times 6 \)
- \( 8 \times 7 \)
- \( 8 \times 8 \)
- \( 8 \times 9 \)
- \( 8 \times 10 \)

The hint suggests using the fact \( 8 \times 5 = 40 \) and adding the other fact of 8 to it. This means we can break down each multiplication problem into a sum of known facts.

Solution Approach:

For each multiplication fact, we will express it as a sum of two known facts using the distributive property. For example:
- To find \( 8 \times 6 \), we can write \( 6 \) as \( 5 + 1 \):
\[
8 \times 6 = 8 \times (5 + 1) = (8 \times 5) + (8 \times 1)
\]
- Similarly, for \( 8 \times 7 \), we can write \( 7 \) as \( 5 + 2 \):
\[
8 \times 7 = 8 \times (5 + 2) = (8 \times 5) + (8 \times 2)
\]

We will apply this method to all the required facts.

---

Step-by-Step Solution:

#### 1. \( 8 \times 6 \)
- Express \( 6 \) as \( 5 + 1 \):
\[
8 \times 6 = 8 \times (5 + 1) = (8 \times 5) + (8 \times 1)
\]
- Substitute the known values:
\[
8 \times 6 = 40 + 8 = 48
\]

#### 2. \( 8 \times 7 \)
- Express \( 7 \) as \( 5 + 2 \):
\[
8 \times 7 = 8 \times (5 + 2) = (8 \times 5) + (8 \times 2)
\]
- Substitute the known values:
\[
8 \times 7 = 40 + 16 = 56
\]

#### 3. \( 8 \times 8 \)
- Express \( 8 \) as \( 5 + 3 \):
\[
8 \times 8 = 8 \times (5 + 3) = (8 \times 5) + (8 \times 3)
\]
- Substitute the known values:
\[
8 \times 8 = 40 + 24 = 64
\]

#### 4. \( 8 \times 9 \)
- Express \( 9 \) as \( 5 + 4 \):
\[
8 \times 9 = 8 \times (5 + 4) = (8 \times 5) + (8 \times 4)
\]
- Substitute the known values:
\[
8 \times 9 = 40 + 32 = 72
\]

#### 5. \( 8 \times 10 \)
- Express \( 10 \) as \( 5 + 5 \):
\[
8 \times 10 = 8 \times (5 + 5) = (8 \times 5) + (8 \times 5)
\]
- Substitute the known values:
\[
8 \times 10 = 40 + 40 = 80
\]

---

Final Answers:

\[
\begin{aligned}
&8 \times 6 = 40 + 8 = 48 \\
&8 \times 7 = 40 + 16 = 56 \\
&8 \times 8 = 40 + 24 = 64 \\
&8 \times 9 = 40 + 32 = 72 \\
&8 \times 10 = 40 + 40 = 80 \\
\end{aligned}
\]

Boxed Final Answer:

\[
\boxed{
\begin{aligned}
&8 \times 6 = 40 + 8 = 48 \\
&8 \times 7 = 40 + 16 = 56 \\
&8 \times 8 = 40 + 24 = 64 \\
&8 \times 9 = 40 + 32 = 72 \\
&8 \times 10 = 40 + 40 = 80 \\
\end{aligned}
}
\]