To solve the multiplication [tex]\( 102 \times 4 \)[/tex] using the distributive property, we can break it down as follows:
First, we split 102 into two parts: 100 and 2. This allows us to use the distributive property to simplify the multiplication:
[tex]\[ 102 \times 4 = (100 + 2) \times 4. \][/tex]
Using the distributive property, we can separate this into two smaller multiplications:
[tex]\[ (100 + 2) \times 4 = (100 \times 4) + (2 \times 4). \][/tex]
Now, we perform the individual multiplications:
[tex]\[
100 \times 4 = 400
\][/tex]
[tex]\[
2 \times 4 = 8
\][/tex]
When we add these two products together, we get the total:
[tex]\[
100 \times 4 + 2 \times 4 = 400 + 8 = 408
\][/tex]
Thus, the complete solution is:
[tex]\[ 102 \times 4 = (100 \times 4) + (2 \times 4) = 400 + 8 = 408. \][/tex]
So, the value that goes into the blank square is 2:
[tex]\[ 102 \times 4 = (100 \times 4) + (2 \times 4). \][/tex]
