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Answer :
To divide the mixed numbers [tex]\(-3 \frac{1}{6}\)[/tex] and [tex]\(11 \frac{2}{5}\)[/tex], the first step is to convert these mixed numbers into improper fractions. Here's how you do it:
1. Convert [tex]\(-3 \frac{1}{6}\)[/tex] to an improper fraction:
The whole number part is [tex]\(-3\)[/tex], and the fraction part is [tex]\(\frac{1}{6}\)[/tex].
[tex]\[
\text{Improper Fraction} = -\left((3 \times 6) + 1\right) / 6 = -19/6
\][/tex]
2. Convert [tex]\(11 \frac{2}{5}\)[/tex] to an improper fraction:
The whole number part is [tex]\(11\)[/tex], and the fraction part is [tex]\(\frac{2}{5}\)[/tex].
[tex]\[
\text{Improper Fraction} = \left((11 \times 5) + 2\right) / 5 = 57/5
\][/tex]
Now, the mixed numbers have been converted to the fractions [tex]\(-19/6\)[/tex] and [tex]\(57/5\)[/tex]. So the correct choice is:
D. Convert the mixed numbers to fractions. The fractions are [tex]\(-19/6, 57/5\)[/tex].
1. Convert [tex]\(-3 \frac{1}{6}\)[/tex] to an improper fraction:
The whole number part is [tex]\(-3\)[/tex], and the fraction part is [tex]\(\frac{1}{6}\)[/tex].
[tex]\[
\text{Improper Fraction} = -\left((3 \times 6) + 1\right) / 6 = -19/6
\][/tex]
2. Convert [tex]\(11 \frac{2}{5}\)[/tex] to an improper fraction:
The whole number part is [tex]\(11\)[/tex], and the fraction part is [tex]\(\frac{2}{5}\)[/tex].
[tex]\[
\text{Improper Fraction} = \left((11 \times 5) + 2\right) / 5 = 57/5
\][/tex]
Now, the mixed numbers have been converted to the fractions [tex]\(-19/6\)[/tex] and [tex]\(57/5\)[/tex]. So the correct choice is:
D. Convert the mixed numbers to fractions. The fractions are [tex]\(-19/6, 57/5\)[/tex].
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