Convert each fraction to its decimal equivalent, add them, and then convert the sum back to a fraction.

Convert each fraction to its decimal equivalent, add them, and then convert the sum back to a fraction.

Add the decimals:

To convert 0.8333... back to a fraction:
Let $x = 0.8333...$
Multiply by 10: $10x = 8.3333...$ (Equation 1)
Multiply by 100: $100x = 83.3333...$ (Equation 2)
Subtract Equation 1 from Equation 2:

Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 15:

The simplified answer is $\boxed{\frac{5}{6}}$.

First, find the least common multiple (LCM) of the denominators, which is 6. This means the common unit fraction is $\frac{1}{6}$.
Express each fraction as a multiple of this common unit fraction:

Now, add these expressions by factoring out the common unit fraction $\frac{1}{6}$:

The simplified answer is $\boxed{\frac{5}{6}}$.

This method involves multiplying the numerator of each fraction by the denominator of the other fraction, adding these products, and placing the sum over the product of the denominators.
For $\frac{1}{2} + \frac{1}{3}$:
Multiply the numerator of the first fraction (1) by the denominator of the second fraction (3): $1 \times 3 = 3$.
Multiply the numerator of the second fraction (1) by the denominator of the first fraction (2): $1 \times 2 = 2$.
Multiply the denominators together: $2 \times 3 = 6$.
Add the cross-products and place over the product of denominators:

The simplified answer is $\boxed{\frac{5}{6}}$.

Imagine a rectangle divided into a grid where one dimension represents the first denominator and the other represents the second. For denominators 2 and 3, create a $2 \times 3$ grid, resulting in 6 small squares.
To represent $\frac{1}{2}$, shade one row (or column) out of the two. If we shade one row of three squares, we shade 3 out of 6 squares.
To represent $\frac{1}{3}$, shade one column (or row) out of the three. If we shade one column of two squares, we shade 2 out of 6 squares.
When combining these shaded areas, we have 3 squares from $\frac{1}{2}$ and 2 squares from $\frac{1}{3}$. In total, we have $3+2=5$ shaded squares out of the 6 total squares in the grid.
Thus, the sum is $\frac{5}{6}$.
The simplified answer is $\boxed{\frac{5}{6}}$.

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