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Sagot :
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].
### 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].
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