Question

question 3 (1 point)
evaluate the expression. give your answer in simplest form.
\\(\frac{1}{4} * \frac{2}{5} = ?\\)

• 2/20
• 3/20
• 1/10
• 1/3

question 4 (1 point)
evaluate the expression. give your answer in simplest form.
\\(\frac{10}{21} * \frac{7}{15} = ?\\)

• 14/63
• 70/315

Explanation:

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<reasoning>

Multiply the numerators and denominators for Question 3

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

Simplify the resulting fraction for Question 3

\[
\frac{2}{20} = \frac{2 \div 2}{20 \div 2} = \frac{1}{10}
\]

Multiply and simplify by cross-canceling for Question 4

\[
\frac{10}{21} \times \frac{7}{15} = \frac{10}{15} \times \frac{7}{21} = \frac{2}{3} \times \frac{1}{3} = \frac{2 \times 1}{3 \times 3} = \frac{2}{9}
\]
</reasoning>

<answer>

Question 3

<mcq-option>2/20</mcq-option>
<mcq-option>3/20</mcq-option>
<mcq-correct>1/10</mcq-correct>
<mcq-option>1/3</mcq-option>

Question 4

Note: The correct simplified answer is \(\frac{2}{9}\).
</answer>

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

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 2,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
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"concepts_used": [],
"new_concepts": [
"Fraction Multiplication",
"Fraction Simplification"
],
"current_concepts": [
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"Fraction Simplification"
]
}
</pre_analysis>

<reasoning>

Multiply the numerators and denominators for Question 3

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

Simplify the resulting fraction for Question 3

\[
\frac{2}{20} = \frac{2 \div 2}{20 \div 2} = \frac{1}{10}
\]

Multiply and simplify by cross-canceling for Question 4

\[
\frac{10}{21} \times \frac{7}{15} = \frac{10}{15} \times \frac{7}{21} = \frac{2}{3} \times \frac{1}{3} = \frac{2 \times 1}{3 \times 3} = \frac{2}{9}
\]
</reasoning>

<answer>

Question 3

<mcq-option>2/20</mcq-option>
<mcq-option>3/20</mcq-option>
<mcq-correct>1/10</mcq-correct>
<mcq-option>1/3</mcq-option>

Question 4

Note: The correct simplified answer is \(\frac{2}{9}\).
</answer>

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