Question

evaluate the expression. give your answer in simplest form.

\\(1/4 + 2/5 = ?\\)

• \\(3/20\\)
• \\(13/20\\)
• \\(3/5\\)
• \\(3/4\\)

question 2 (1 point)
evaluate the expression. give your answer in simplest form.

\\(6/7 - 3/5 = ?\\)

• \\(9/35\\)
• \\(1/2\\)
• \\(3/7\\)
• \\(3/2\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 2,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Fraction Addition",
"Fraction Subtraction",
"Common Denominator"
],
"current_concepts": [
"Fraction Addition",
"Fraction Subtraction",
"Common Denominator"
]
}
</pre_analysis>

<reasoning>

Find a common denominator and add the fractions

\[
\frac{1}{4} + \frac{2}{5} = \frac{1 \times 5}{4 \times 5} + \frac{2 \times 4}{5 \times 4} = \frac{5}{20} + \frac{8}{20} = \frac{13}{20}
\]

Find a common denominator and subtract the fractions

\[
\frac{6}{7} - \frac{3}{5} = \frac{6 \times 5}{7 \times 5} - \frac{3 \times 7}{5 \times 7} = \frac{30}{35} - \frac{21}{35} = \frac{9}{35}
\]
</reasoning>

<answer>

Question 1

<mcq-option>(A) 3/20</mcq-option>
<mcq-correct>(B) 13/20</mcq-correct>
<mcq-option>(C) 3/5</mcq-option>
<mcq-option>(D) 3/4</mcq-option>

Question 2

<mcq-correct>(A) 9/35</mcq-correct>
<mcq-option>(B) 1/2</mcq-option>
<mcq-option>(C) 3/7</mcq-option>
<mcq-option>(D) 3/2</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Fraction Arithmetic"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 2,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Fraction Addition",
"Fraction Subtraction",
"Common Denominator"
],
"current_concepts": [
"Fraction Addition",
"Fraction Subtraction",
"Common Denominator"
]
}
</pre_analysis>

<reasoning>

Find a common denominator and add the fractions

\[
\frac{1}{4} + \frac{2}{5} = \frac{1 \times 5}{4 \times 5} + \frac{2 \times 4}{5 \times 4} = \frac{5}{20} + \frac{8}{20} = \frac{13}{20}
\]

Find a common denominator and subtract the fractions

\[
\frac{6}{7} - \frac{3}{5} = \frac{6 \times 5}{7 \times 5} - \frac{3 \times 7}{5 \times 7} = \frac{30}{35} - \frac{21}{35} = \frac{9}{35}
\]
</reasoning>

<answer>

Question 1

<mcq-option>(A) 3/20</mcq-option>
<mcq-correct>(B) 13/20</mcq-correct>
<mcq-option>(C) 3/5</mcq-option>
<mcq-option>(D) 3/4</mcq-option>

Question 2

<mcq-correct>(A) 9/35</mcq-correct>
<mcq-option>(B) 1/2</mcq-option>
<mcq-option>(C) 3/7</mcq-option>
<mcq-option>(D) 3/2</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Fraction Arithmetic"
]
}
</post_analysis>