subtract the given numbers in the indicated base.

\
\begin{array}{r}
2251_{7} \\
-\quad 334_{7} \\
\hline
\end{array}
\

the difference is $1213_{7}$.

Question

subtract the given numbers in the indicated base.

\
\begin{array}{r}
2251_{7} \\
-\quad 334_{7} \\
\hline
\end{array}
\

the difference is $1213_{7}$.

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 Conversion" ], "new_concepts": [ "Base Arithmetic", "Base Subtraction" ], "current_concepts": [ "Base Conversion", "Base Arithmetic", "Base Subtraction" ] } ## Align the numbers vertically Using the *Base Conversion* knowledge point $$ \begin{array}{r@{\quad}l} 2251_7 & \text{(Minuend)} \ - \phantom{2}334_7 & \text{(Subtrahend)} \ \hline \end{array} $$ ## Subtract the units column Using the *Base Conversion* knowledge point $$ \begin{aligned} &\text{Units column: } 1_7 - 4_7 \ &\text{Borrow } 1 \text{ from the next column (value } 7_{10}\text{):} \ &1_7 + 7_{10} = 8_{10} \ &8_{10} - 4_{10} = 4_{10} = 4_7 \end{aligned} $$ ## Subtract the sevens column Using the *Base Conversion* knowledge point $$ \begin{aligned} &\text{Sevens column: } (5 - 1)_7 - 3_7 = 4_7 - 3_7 \ &4_7 - 3_7 = 1_7 \end{aligned} $$ ## Subtract the forty-nines column Using the *Base Conversion* knowledge point $$ \begin{aligned} &\text{Forty-nines column: } 2_7 - 3_7 \ &\text{Borrow } 1 \text{ from the next column (value } 7_{10}\text{):} \ &2_7 + 7_{10} = 9_{10} \ &9_{10} - 3_{10} = 6_{10} = 6_7 \end{aligned} $$ ## Subtract the final column Using the *Base Conversion* knowledge point $$ \begin{aligned} &\text{Three-hundred-forty-threes column: } (2 - 1)_7 - 0_7 \ &1_7 - 0_7 = 1_7 \ &\text{Result: } 1614_7 \end{aligned} $$ Subtract the given numbers in the indicated base. $$ \begin{array}{r@{\quad}l} 2251_7 \ - \phantom{2}334_7 \ \hline \end{array} $$ The difference is $1614_7$. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Number Theory", "Base Arithmetic" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Align the numbers vertically

Subtract the units column

Subtract the sevens column

Subtract the forty-nines column

Subtract the final column

Answer: