Solve: 2/3 Divided by 5 - Step-by-Step Division

To solve this problem of dividing a fraction by a whole number, we will follow these steps:

• Step 1: Convert the division problem into a multiplication by the reciprocal.
• Step 2: Multiply the fraction by the reciprocal of the whole number.
• Step 3: Simplify the resulting fraction, if possible.

Let's work through these steps in detail:

Step 1: Convert the division into a multiplication by the reciprocal.
The given problem is $\frac{2}{3} : 5$. In arithmetic, division by a whole number can be converted into multiplication by its reciprocal. The reciprocal of the whole number 5 is $\frac{1}{5}$. Therefore, the expression becomes:

$\frac{2}{3} \times \frac{1}{5}$.

Step 2: Multiply the fraction by the reciprocal.
We now multiply the numerators and the denominators:

$\frac{2}{3} \times \frac{1}{5} = \frac{2 \times 1}{3 \times 5} = \frac{2}{15}$.

Step 3: Simplify the resulting fraction.
We check if the fraction $\frac{2}{15}$ can be simplified further. Since 2 and 15 have no common divisors besides 1, the fraction is already in its simplest form.

Therefore, the solution to the division problem $\frac{2}{3} : 5$ is $\frac{2}{15}$.

Upon examining the provided answer choices, we confirm that our solution, $\frac{2}{15}$, matches choice number 4.