Solve: (3/5 ÷ 5/6) + 1/5 - Mixed Fraction Operations

Solve the following exercise:

$\frac{3}{5}:\frac{5}{6}+\frac{1}{5}=\text{?}$

To solve the problem, we'll follow the outlined steps:

• Step 1: Calculate the division $\frac{3}{5} : \frac{5}{6}$.
• Step 2: Add $\frac{1}{5}$ to the result from Step 1.
• Step 3: Simplify the resulting fraction.

Now, let's work through each step:

Step 1: To divide $\frac{3}{5}$ by $\frac{5}{6}$, we multiply by the reciprocal of $\frac{5}{6}$. This gives us:

$\frac{3}{5} \times \frac{6}{5} = \frac{3 \times 6}{5 \times 5} = \frac{18}{25}$

Step 2: Now, add $\frac{1}{5}$ to $\frac{18}{25}$. First, we convert $\frac{1}{5}$ to the same denominator as $\frac{18}{25}$:

$\frac{1}{5} = \frac{5}{25}$

Step 3: Add $\frac{18}{25}$ and $\frac{5}{25}$:

$\frac{18}{25} + \frac{5}{25} = \frac{18 + 5}{25} = \frac{23}{25}$

Thus, the solution to the problem is $\frac{23}{25}$.