Question

perform the indicated operation. if possible, reduce the answer to its lowest terms.
$left(-8dfrac{2}{3}
ight)div 2dfrac{1}{6}$
$left(-8dfrac{2}{3}
ight)div 2dfrac{1}{6}=square$
(simplify your answer. type an integer, fraction, or mixed number.)

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(-8\frac{2}{3}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(-8\frac{2}{3}\), we have \(a = -8\), \(b = 2\), \(c = 3\). Then \(-8\frac{2}{3}=-\frac{8\times3 + 2}{3}=-\frac{24 + 2}{3}=-\frac{26}{3}\).

Next, convert \(2\frac{1}{6}\) to an improper fraction. Here, \(a = 2\), \(b = 1\), \(c = 6\). So \(2\frac{1}{6}=\frac{2\times6+1}{6}=\frac{12 + 1}{6}=\frac{13}{6}\).

Step2: Divide the fractions

Dividing by a fraction is the same as multiplying by its reciprocal. So \(-\frac{26}{3}\div\frac{13}{6}=-\frac{26}{3}\times\frac{6}{13}\).

Step3: Simplify the multiplication

First, we can simplify the numbers before multiplying. The 26 and 13 have a common factor of 13, and 6 and 3 have a common factor of 3. So \(-\frac{26\div13}{3}\times\frac{6\div3}{13\div13}=-\frac{2}{1}\times\frac{2}{1}\). Wait, actually, let's do it step by step. \(-\frac{26}{3}\times\frac{6}{13}=-\frac{26\times6}{3\times13}\). Now, 26 and 13: \(26\div13 = 2\), and 6 and 3: \(6\div3=2\). So substituting back, we get \(-\frac{2\times2}{1\times1}=- 4\). Wait, let's check again. \(26\times6 = 156\), \(3\times13 = 39\), then \(\frac{156}{39}=4\), but with the negative sign, it's \(-4\).

Wait, let's re - do the multiplication: \(-\frac{26}{3}\times\frac{6}{13}\). The 26 and 13: 26 is 2×13, so we can cancel 13 from numerator and denominator. So we have \(-\frac{2\times13}{3}\times\frac{6}{13}\). The 13 in the numerator of the first fraction and the 13 in the denominator of the second fraction cancel out. Then we have \(-\frac{2}{3}\times6\). Now, 6 and 3: 6÷3 = 2, so \(-2\times2=-4\).

Answer:

\(-4\)