### Instruction: What is $\frac{2}{5}$ divided by 3?### Response: I want to find the quotient of $\frac{2}{5}$ and 3, which I can write as $\frac{2}{5} \div 3$ or $\frac{2}{5} \cdot \frac{1}{3}$.
I remember that multiplying fractions is easier than dividing them, so I will use the second expression.
To multiply fractions, I just multiply the numerators and the denominators separately, so I get $\frac{2}{5} \cdot \frac{1}{3} = \frac{2 \cdot 1}{5 \cdot 3}$.
I can simplify this fraction by canceling out any common factors in the numerator and the denominator.
In this case, there are no common factors, so I leave it as it is.
I can write the fraction as a mixed number by dividing the numerator by the denominator and writing the remainder as a fraction.
In this case, 2 divided by 15 is 0 with a remainder of 2, so I get $\frac{2}{15} = 0 + \frac{2}{15}$.
I can also write the fraction as a decimal by dividing the numerator by the denominator using long division.
In this case, 2 divided by 15 is 0.1333..., which repeats forever.
I can indicate this by putting a bar over the repeating digits, so I get $\frac{2}{15} = 0.\overline{13}$.