Certainly! To solve the problem using the partial product method, we'll break down the multiplication of 219 by 3 step by step. Here's how we can do it:
1. Break down the number 219:
- 219 can be written as [tex]\(200 + 10 + 9\)[/tex].
2. Multiply each component by 3:
- First, multiply 200 by 3.
- Then, multiply 10 by 3.
- Finally, multiply 9 by 3.
3. Calculate each partial product:
- [tex]\(200 \times 3 = 600\)[/tex]
- [tex]\(10 \times 3 = 30\)[/tex]
- [tex]\(9 \times 3 = 27\)[/tex]
4. Add the partial products together:
- Combine the results of the multiplications:
[tex]\[
600 + 30 + 27 = 657
\][/tex]
5. Identify the missing number:
-Given the partial products:
[tex]\[
\begin{array}{r}
219 \\
\times \quad 3 \\
\hline 27 \\
+\quad 30 \\
\hline
\end{array}
\][/tex]
- The only missing component is from [tex]\(200 \times 3\)[/tex].
So the value of the missing number is 600.
