Sure! Let's go through the multiplication of [tex]\(6 \times 9\)[/tex] step by step using the distributive property of multiplication over addition.
### Step-by-Step Solution:
1. Break down 9 into two parts:
[tex]\[
9 = 5 + 4
\][/tex]
Therefore, the expression becomes:
[tex]\[
6 \times 9 = 6 \times (5 + 4)
\][/tex]
2. Apply the distributive property:
The distributive property states that [tex]\(a \times (b + c) = (a \times b) + (a \times c)\)[/tex]. So we can rewrite the expression as:
[tex]\[
6 \times 9 = (6 \times 5) + (6 \times 4)
\][/tex]
3. Calculate each part separately:
[tex]\[
6 \times 5 = 30
\][/tex]
and
[tex]\[
6 \times 4 = 24
\][/tex]
4. Add the results together:
[tex]\[
30 + 24 = 54
\][/tex]
### Filling in the Blanks:
Now, let's insert these values into the given model:
[tex]\[
\begin{array}{l}
6 \times 9=6 \times(5+\mathbf{4}) \\
6 \times 9=(6 \times \mathbf{5})+(6 \times 4) \\
6 \times 9=\mathbf{30}+(6 \times 4) \\
6 \times 9=30+\mathbf{24} \\
6 \times 9=\mathbf{54}
\end{array}
\][/tex]
So, the detailed solution demonstrates that [tex]\(6 \times 9 = 54\)[/tex].
