Question

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complete the steps to find the product of \\(52 \times 16\\).

\\
\

$$\begin{array}{r} 52 \\\\ \\times \\quad 16 \\\\ \\hline \\end{array}$$

\\

\\(\
ightarrow\\) ____ ones \\(\times\\) ____ ones
\\(\
ightarrow\\) ____ ones \\(\times\\) ____ tens
\\(\
ightarrow\\) ____ ten \\(\times\\) ____ ones
\\(\
ightarrow\\) ____ ten \\(\times\\) ____ tens

Explanation:

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<reasoning>

Identify the place values of the digits

To find the partial products of \(52 \times 16\), we first break down each number by place value:

• For \(52\): \(5\) is in the tens place (\(50\)) and \(2\) is in the ones place (\(2\)).
• For \(16\): \(1\) is in the tens place (\(10\)) and \(6\) is in the ones place (\(6\)).

Calculate the first partial product

The first step asks for:
\[
\text{ones} \times \text{ones}
\]
Using the ones digit from \(16\) and the ones digit from \(52\):
\[
6 \text{ ones} \times 2 \text{ ones} = 6 \times 2 = 12
\]

Calculate the second partial product

The second step asks for:
\[
\text{ones} \times \text{tens}
\]
Using the ones digit from \(16\) and the tens digit from \(52\):
\[
6 \text{ ones} \times 5 \text{ tens} = 6 \times 50 = 300
\]

Calculate the third partial product

The third step asks for:
\[
\text{ten} \times \text{ones}
\]
Using the tens digit from \(16\) and the ones digit from \(52\):
\[
1 \text{ ten} \times 2 \text{ ones} = 10 \times 2 = 20
\]

Calculate the fourth partial product

The fourth step asks for:
\[
\text{ten} \times \text{tens}
\]
Using the tens digit from \(16\) and the tens digit from \(52\):
\[
1 \text{ ten} \times 5 \text{ tens} = 10 \times 50 = 500
\]

Sum the partial products

To find the final product, we add all four partial products together:
\[
12 + 300 + 20 + 500 = 832
\]
</reasoning>

<answer>
Complete the steps to find the product of \(52 \times 16\).

\[

$$\begin{array}{r@{\quad}l} 52 \\ \times\ 16 \\ \hline \mathbf{12} & ightarrow \quad \mathbf{6} \text{ ones} \times \mathbf{2} \text{ ones} \\ \mathbf{300} & ightarrow \quad \mathbf{6} \text{ ones} \times \mathbf{5} \text{ tens} \\ \mathbf{20} & ightarrow \quad \mathbf{1} \text{ ten} \times \mathbf{2} \text{ ones} \\ +\quad \mathbf{500} & ightarrow \quad \mathbf{1} \text{ ten} \times \mathbf{5} \text{ tens} \\ \hline \mathbf{832} \end{array}$$

\]

The completed steps are:

• <blank>\(12\)</blank> \(

ightarrow\) <blank>\(6\)</blank> ones \(\times\) <blank>\(2\)</blank> ones

• <blank>\(300\)</blank> \(

ightarrow\) <blank>\(6\)</blank> ones \(\times\) <blank>\(5\)</blank> tens

• <blank>\(20\)</blank> \(

ightarrow\) <blank>\(1\)</blank> ten \(\times\) <blank>\(2\)</blank> ones

• <blank>\(500\)</blank> \(

ightarrow\) <blank>\(1\)</blank> ten \(\times\) <blank>\(5\)</blank> tens

• The final sum is <blank>\(832\)</blank>

</answer>

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"Mathematics",
"Algebra",
"Multi-Digit Multiplication"
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</post_analysis>

Answer:

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<reasoning>

Identify the place values of the digits

To find the partial products of \(52 \times 16\), we first break down each number by place value:

• For \(52\): \(5\) is in the tens place (\(50\)) and \(2\) is in the ones place (\(2\)).
• For \(16\): \(1\) is in the tens place (\(10\)) and \(6\) is in the ones place (\(6\)).

Calculate the first partial product

The first step asks for:
\[
\text{ones} \times \text{ones}
\]
Using the ones digit from \(16\) and the ones digit from \(52\):
\[
6 \text{ ones} \times 2 \text{ ones} = 6 \times 2 = 12
\]

Calculate the second partial product

The second step asks for:
\[
\text{ones} \times \text{tens}
\]
Using the ones digit from \(16\) and the tens digit from \(52\):
\[
6 \text{ ones} \times 5 \text{ tens} = 6 \times 50 = 300
\]

Calculate the third partial product

The third step asks for:
\[
\text{ten} \times \text{ones}
\]
Using the tens digit from \(16\) and the ones digit from \(52\):
\[
1 \text{ ten} \times 2 \text{ ones} = 10 \times 2 = 20
\]

Calculate the fourth partial product

The fourth step asks for:
\[
\text{ten} \times \text{tens}
\]
Using the tens digit from \(16\) and the tens digit from \(52\):
\[
1 \text{ ten} \times 5 \text{ tens} = 10 \times 50 = 500
\]

Sum the partial products

To find the final product, we add all four partial products together:
\[
12 + 300 + 20 + 500 = 832
\]
</reasoning>

<answer>
Complete the steps to find the product of \(52 \times 16\).

\[

$$\begin{array}{r@{\quad}l} 52 \\ \times\ 16 \\ \hline \mathbf{12} & ightarrow \quad \mathbf{6} \text{ ones} \times \mathbf{2} \text{ ones} \\ \mathbf{300} & ightarrow \quad \mathbf{6} \text{ ones} \times \mathbf{5} \text{ tens} \\ \mathbf{20} & ightarrow \quad \mathbf{1} \text{ ten} \times \mathbf{2} \text{ ones} \\ +\quad \mathbf{500} & ightarrow \quad \mathbf{1} \text{ ten} \times \mathbf{5} \text{ tens} \\ \hline \mathbf{832} \end{array}$$

\]

The completed steps are:

• <blank>\(12\)</blank> \(

ightarrow\) <blank>\(6\)</blank> ones \(\times\) <blank>\(2\)</blank> ones

• <blank>\(300\)</blank> \(

ightarrow\) <blank>\(6\)</blank> ones \(\times\) <blank>\(5\)</blank> tens

• <blank>\(20\)</blank> \(

ightarrow\) <blank>\(1\)</blank> ten \(\times\) <blank>\(2\)</blank> ones

• <blank>\(500\)</blank> \(

ightarrow\) <blank>\(1\)</blank> ten \(\times\) <blank>\(5\)</blank> tens

• The final sum is <blank>\(832\)</blank>

</answer>

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"Mathematics",
"Algebra",
"Multi-Digit Multiplication"
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