To find the quotient of [tex]\(\frac{2}{3} \div 5\)[/tex], we need to follow these steps:
1. Understand that dividing by 5 is the same as multiplying by the reciprocal of 5. The reciprocal of 5 is [tex]\(\frac{1}{5}\)[/tex].
2. Set up the multiplication with the reciprocal:
[tex]\[
\frac{2}{3} \div 5 = \frac{2}{3} \times \frac{1}{5}
\][/tex]
3. Multiply the fractions. To multiply fractions, you multiply the numerators (the numbers on top) and the denominators (the numbers on bottom):
[tex]\[
\frac{2}{3} \times \frac{1}{5} = \frac{2 \times 1}{3 \times 5} = \frac{2}{15}
\][/tex]
This implies that the quotient of [tex]\(\frac{2}{3} \div 5\)[/tex] is [tex]\(\frac{2}{15}\)[/tex].
Converting this fraction into a decimal, we calculate:
[tex]\[
\frac{2}{15} \approx 0.13333333333333333
\][/tex]
Thus, the quotient of [tex]\(\frac{2}{3} \div 5\)[/tex] is approximately [tex]\(0.1333\)[/tex] (repeating).