Certainly! Let's use the partial products strategy to solve the multiplication problem [tex]\( 125 \times 7 \)[/tex].
### Step-by-Step Breakdown
1. Multiply each digit of the second number by the first number:
- The second number is [tex]\( 7 \)[/tex], which is a single-digit number. Let's break this down simply:
[tex]\[
125 \times 7
\][/tex]
2. Calculate Partial Product for Units Place:
- Multiply [tex]\( 125 \)[/tex] by [tex]\( 7 \)[/tex]:
[tex]\[
125 \times 7 = 875
\][/tex]
3. List the partial products:
- The product [tex]\( 875 \)[/tex] wholly comes from multiplying the first number by the single-digit second number.
4. Arrange in the format with place values:
- When multiplying a three-digit number by a single-digit number, you only get a one-step multiplication shown as follows:
[tex]\[
\begin{array}{r}
125 \\
\times \quad 7 \\
\hline
875 \\
\hline
\end{array}
\][/tex]
- Notice that there are no multi-place partial products like tens or hundreds from decomposing the second number further because it was a single digit, not requiring additional layers.
Given the provided question format:
[tex]\[
\begin{array}{r}
125 \\
\times \quad 7 \\
\hline 35 \\
? \\
+\quad 700 \\
\hline
\end{array}
\][/tex]
### Explanation
1. The first row product [tex]\( 35 \)[/tex] matches with [tex]\( 125 \times 7 = 875 \)[/tex]'s less significant digit (units).
2. The tens-digit partial result and hundreds align directly in total.
Thus, the missing number (symbolized by a question mark) should be such that adding the partial outcomes conforms to the final multiplication result of [tex]\( 875 \)[/tex]:
Given the answer's implication directly aligns:
[tex]\[
875_{\ total}
\][/tex]
Finalizing, the missing number in the problem should reflect direct [tex]\( 0 \)[/tex] as the immediate result assertion, simplifying:
Thus, the values link [tex]\( \, + = 875 \)[/tex],
From descending evaluation confirming:
Thus, this breakdown finalizes with missing unmatched intermediate value [tex]\( 0 \)[/tex].
So the missing part of partial products should be:
[tex]\[ \boxed{0} \][/tex]
matching solution from reviewed \( 1-step\ Checked. }
