Certainly! We'll use the partial products strategy to find the missing number in the given multiplication problem.
The problem is:
[tex]\[
\begin{array}{r}
573 \\
\times \quad 6 \\
\hline ? \\
420 \\
+3,000 \\
\hline
\end{array}
\][/tex]
with a total sum of 3,438.
1. Step 1: Break down the number 573 into its place values:
- Hundreds place: 500
- Tens place: 70
- Ones place: 3
2. Step 2: Multiply each place value by 6:
- Ones place: [tex]\(3 \times 6 = 18\)[/tex]
- Tens place: [tex]\(70 \times 6 = 420\)[/tex]
- Hundreds place: [tex]\(500 \times 6 = 3,000\)[/tex]
3. Step 3: Add the partial products together:
- Partial product for the ones place: [tex]\(18\)[/tex]
- Partial product for the tens place: [tex]\(420\)[/tex]
- Partial product for the hundreds place: [tex]\(3,000\)[/tex]
4. Step 4: Sum the partial products:
- [tex]\(18 + 420 + 3,000 = 3,438\)[/tex]
Therefore, the missing number (the partial product for the ones place):
[tex]\[
\boxed{18}
\][/tex]
