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```
[tex]$
6 \div \frac{2}{3}=6 \times \frac{3}{2}=\frac{6}{1} \times \frac{3}{2}=\frac{18}{2}=9
$[/tex]

The quotient of [tex]$\frac{2}{3} \div 6$[/tex] can be found by multiplying [tex]$\frac{2}{3}$[/tex] by the reciprocal of 6.

[tex]$
\frac{2}{3} \div 6=\frac{2}{3} \times \frac{1}{6}=\frac{2}{18}=\frac{1}{9}
$[/tex]

1. To divide [tex]$\frac{2}{3} \div 5$[/tex], first shade the diagram to represent the dividend.
2. Divide the diagram into 5 equal parts.

\begin{tabular}{|l|l|l|l|l|}
\hline[tex]$\times$[/tex] & & & \\
\hline & & & \\
\hline
\end{tabular}

Circle the shaded parts of one row to find the quotient.

[tex]$\frac{2}{3} \div 5=$[/tex] [tex]$\qquad$[/tex]
```

Sagot :

GinnyAnsweridn
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).
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