Let's solve the multiplication [tex]\(38 \times 29\)[/tex] step-by-step by breaking it down into smaller, more manageable parts using the distributive property.
We'll proceed by using the place values of the number 29, which can be decomposed as [tex]\(20 + 9\)[/tex].
1. First, we multiply [tex]\(38\)[/tex] by the tens place of [tex]\(29\)[/tex]:
[tex]\[
38 \times 20 = 760
\][/tex]
So, [tex]\(38 \times 20\)[/tex] gives us a partial product of [tex]\(760\)[/tex].
2. Next, we multiply [tex]\(38\)[/tex] by the units place of [tex]\(29\)[/tex]:
[tex]\[
38 \times 9 = 342
\][/tex]
This gives us another partial product of [tex]\(342\)[/tex].
3. Now, we sum both partial products to get the final product:
[tex]\[
760 + 342 = 1102
\][/tex]
So, the detailed solution is:
[tex]\[
38 \times 29 = (38 \times 20) + (38 \times 9) = 760 + 342 = 1102
\][/tex]
Therefore, the product of [tex]\(38 \times 29\)[/tex] is [tex]\(1102\)[/tex].
