Question

question 9 of 23 - multiple choice

\\(6/8 \times 13-14/15 = ?\\)

a \\(9-9/20\\)

b \\(9-1/2\\)

c \\(10-9/20\\)

d \\(10-1/2\\)

Explanation:

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<reasoning>

Convert the mixed number to an improper fraction

Using the Fraction Arithmetic knowledge point
\[
13\frac{14}{15} = \frac{13 \times 15 + 14}{15} = \frac{195 + 14}{15} = \frac{209}{15}
\]

Simplify the multiplying fraction

Using the Fraction Arithmetic knowledge point
\[
\frac{6}{8} = \frac{3}{4}
\]

Multiply the fractions

Using the Fraction Arithmetic knowledge point
\[
\frac{3}{4} \times \frac{209}{15} = \frac{3 \times 209}{4 \times 15} = \frac{1 \times 209}{4 \times 5} = \frac{209}{20}
\]

Convert back to a mixed number

Using the Fraction Arithmetic knowledge point
\[
\frac{209}{20} = 10\frac{9}{20}
\]

Analyze the common misconception for Option B

Using the Fraction Arithmetic knowledge point
\[

$$\begin{aligned} &\text{Incorrect method: } \frac{6}{8} \times 13 + \frac{6}{8} \times \frac{14}{15}\\ &\text{If a student rounds } 13\frac{14}{15} \approx 14 \text{ first:}\\ &\frac{6}{8} \times 14 = \frac{3}{4} \times 14 = \frac{42}{4} = 10\frac{1}{2}\\ &\text{If a student rounds } 13\frac{14}{15} \approx 13 \text{ or makes a calculation error:}\\ &\frac{6}{8} \times 13 = \frac{3}{4} \times 13 = \frac{39}{4} = 9\frac{3}{4} \approx 9\frac{1}{2} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>A \(9\text{-}9/20\)</mcq-option>
<mcq-option>B \(9\text{-}1/2\)</mcq-option>
<mcq-correct>C \(10\text{-}9/20\)</mcq-correct>
<mcq-option>D \(10\text{-}1/2\)</mcq-option>
</answer>

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"Mathematics",
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]
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</post_analysis>

Answer:

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</pre_analysis>

<reasoning>

Convert the mixed number to an improper fraction

Using the Fraction Arithmetic knowledge point
\[
13\frac{14}{15} = \frac{13 \times 15 + 14}{15} = \frac{195 + 14}{15} = \frac{209}{15}
\]

Simplify the multiplying fraction

Using the Fraction Arithmetic knowledge point
\[
\frac{6}{8} = \frac{3}{4}
\]

Multiply the fractions

Using the Fraction Arithmetic knowledge point
\[
\frac{3}{4} \times \frac{209}{15} = \frac{3 \times 209}{4 \times 15} = \frac{1 \times 209}{4 \times 5} = \frac{209}{20}
\]

Convert back to a mixed number

Using the Fraction Arithmetic knowledge point
\[
\frac{209}{20} = 10\frac{9}{20}
\]

Analyze the common misconception for Option B

Using the Fraction Arithmetic knowledge point
\[

$$\begin{aligned} &\text{Incorrect method: } \frac{6}{8} \times 13 + \frac{6}{8} \times \frac{14}{15}\\ &\text{If a student rounds } 13\frac{14}{15} \approx 14 \text{ first:}\\ &\frac{6}{8} \times 14 = \frac{3}{4} \times 14 = \frac{42}{4} = 10\frac{1}{2}\\ &\text{If a student rounds } 13\frac{14}{15} \approx 13 \text{ or makes a calculation error:}\\ &\frac{6}{8} \times 13 = \frac{3}{4} \times 13 = \frac{39}{4} = 9\frac{3}{4} \approx 9\frac{1}{2} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>A \(9\text{-}9/20\)</mcq-option>
<mcq-option>B \(9\text{-}1/2\)</mcq-option>
<mcq-correct>C \(10\text{-}9/20\)</mcq-correct>
<mcq-option>D \(10\text{-}1/2\)</mcq-option>
</answer>

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