Answer :
To find the value of
[tex]$$\frac{4}{15} \div \frac{2}{3},$$[/tex]
we first rewrite the division as a multiplication by the reciprocal of the second fraction:
[tex]$$
\frac{4}{15} \div \frac{2}{3} = \frac{4}{15} \times \frac{3}{2}.
$$[/tex]
Next, we multiply the numerators and the denominators:
[tex]$$
\text{Numerator: } 4 \times 3 = 12,
$$[/tex]
[tex]$$
\text{Denominator: } 15 \times 2 = 30.
$$[/tex]
This gives us the fraction:
[tex]$$
\frac{12}{30}.
$$[/tex]
We then simplify the fraction by finding the greatest common divisor (GCD) of 12 and 30, which is 6. Dividing both the numerator and the denominator by 6, we get:
[tex]$$
\frac{12 \div 6}{30 \div 6} = \frac{2}{5}.
$$[/tex]
Thus, the value of
[tex]$$\frac{4}{15} \div \frac{2}{3}$$[/tex]
is
[tex]$$\boxed{\frac{2}{5}}.$$[/tex]
[tex]$$\frac{4}{15} \div \frac{2}{3},$$[/tex]
we first rewrite the division as a multiplication by the reciprocal of the second fraction:
[tex]$$
\frac{4}{15} \div \frac{2}{3} = \frac{4}{15} \times \frac{3}{2}.
$$[/tex]
Next, we multiply the numerators and the denominators:
[tex]$$
\text{Numerator: } 4 \times 3 = 12,
$$[/tex]
[tex]$$
\text{Denominator: } 15 \times 2 = 30.
$$[/tex]
This gives us the fraction:
[tex]$$
\frac{12}{30}.
$$[/tex]
We then simplify the fraction by finding the greatest common divisor (GCD) of 12 and 30, which is 6. Dividing both the numerator and the denominator by 6, we get:
[tex]$$
\frac{12 \div 6}{30 \div 6} = \frac{2}{5}.
$$[/tex]
Thus, the value of
[tex]$$\frac{4}{15} \div \frac{2}{3}$$[/tex]
is
[tex]$$\boxed{\frac{2}{5}}.$$[/tex]
