multiply in the indicated base.

\
\begin{array}{r}
535_6 \\
\times \quad 14_6 \\
\hline
\end{array}
\

\
\begin{array}{r}
535_6 \\
\times \quad 14_6 \\
\hline
\box_6
\end{array}
\

Question

multiply in the indicated base.

\
\begin{array}{r}
535_6 \\
\times \quad 14_6 \\
\hline
\end{array}
\

\
\begin{array}{r}
535_6 \\
\times \quad 14_6 \\
\hline
\box_6
\end{array}
\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Base Arithmetic" ], "new_concepts": [ "Base Multiplication" ], "current_concepts": [ "Base Conversion", "Base Arithmetic", "Base Multiplication" ] } ## Set up the multiplication in base 6 Using the **Base Arithmetic** knowledge point $$ \begin{aligned} &\text{Multiply } 535_6 \text{ by } 14_6. \end{aligned} $$ ## Multiply the top number by the units digit Using the **Base Arithmetic** knowledge point $$ \begin{aligned} &5_6 \times 4_6 = 20_{10} = 32_6 \implies \text{Write } 2, \text{ carry } 3\ &3_6 \times 4_6 + 3_6 = 15_{10} = 23_6 \implies \text{Write } 3, \text{ carry } 2\ &5_6 \times 4_6 + 2_6 = 22_{10} = 34_6 \implies \text{Write } 34\ &\text{First partial product: } 3432_6 \end{aligned} $$ ## Multiply the top number by the next digit Using the **Base Arithmetic** knowledge point $$ \begin{aligned} &535_6 \times 10_6 = 5350_6\ &\text{Second partial product: } 5350_6 \end{aligned} $$ ## Add the partial products in base 6 Using the **Base Arithmetic** knowledge point $$ \begin{aligned} &3432_6 + 5350_6\ &2 + 0 = 2_6\ &3 + 5 = 8_{10} = 12_6 \implies \text{Write } 2, \text{ carry } 1\ &4 + 3 + 1 = 8_{10} = 12_6 \implies \text{Write } 2, \text{ carry } 1\ &3 + 5 + 1 = 9_{10} = 13_6 \implies \text{Write } 13\ &\text{Sum: } 13222_6 \end{aligned} $$ Multiply in the indicated base. $$ \begin{array}{r} 535_6 \ \times\phantom{0} 14_6 \ \hline \end{array} $$ $13222$$_6$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Number Theory", "Base Arithmetic" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the multiplication in base 6

Multiply the top number by the units digit

Multiply the top number by the next digit

Add the partial products in base 6

Answer: