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

Question

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Partial Products", "Multi-Digit Multiplication", "Place Value Multiplication" ], "current_concepts": [ "Partial Products", "Multi-Digit Multiplication", "Place Value Multiplication" ] } ## 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: $$ 12 + 300 + 20 + 500 = 832 $$ 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: - $12$ $ ightarrow$ $6$ ones $\times$ $2$ ones - $300$ $ ightarrow$ $6$ ones $\times$ $5$ tens - $20$ $ ightarrow$ $1$ ten $\times$ $2$ ones - $500$ $ ightarrow$ $1$ ten $\times$ $5$ tens - The final sum is $832$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Multi-Digit Multiplication" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the place values of the digits

Calculate the first partial product

Calculate the second partial product

Calculate the third partial product

Calculate the fourth partial product

Sum the partial products

Answer: