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What is the value of [tex]\frac{4}{15} \div \frac{2}{3}[/tex]?

A. [tex]\frac{8}{45}[/tex]
B. [tex]\frac{14}{15}[/tex]
C. [tex]\frac{2}{5}[/tex]

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]

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