Solve: (-12 1/6) + (+10 1/3) Mixed Number Addition

$(-12\frac{1}{6})+(+10\frac{1}{3})=$

To solve this problem, we'll follow these steps:

• Step 1: Convert the mixed numbers to improper fractions.
• Step 2: Find a common denominator and add the fractions.
• Step 3: Convert the resulting improper fraction back into a mixed number.

Let's begin by converting the mixed numbers into improper fractions:

The mixed number $-12\frac{1}{6}$ can be converted as follows:

$-12\frac{1}{6} = -\left(\frac{12 \times 6 + 1}{6}\right) = -\frac{73}{6}$

The mixed number $+10\frac{1}{3}$ can be converted as follows:

$10\frac{1}{3} = \frac{10 \times 3 + 1}{3} = \frac{31}{3}$

Next, we need a common denominator to add these fractions together. The denominators are 6 and 3, and the least common denominator is 6.

Convert $\frac{31}{3}$ to have the denominator of 6:

$\frac{31}{3} = \frac{31 \times 2}{3 \times 2} = \frac{62}{6}$

Now, we add the fractions:

$-\frac{73}{6} + \frac{62}{6} = \frac{-73 + 62}{6} = \frac{-11}{6}$

Convert $\frac{-11}{6}$ back into a mixed number:

$\frac{-11}{6} = -1\frac{5}{6}$ (since $11 \div 6 = 1$ with a remainder of 5)

Therefore, the solution to the problem is $-1\frac{5}{6}$.