Solve: (-12¼) - (-8²/₇) Mixed Number Subtraction with Negatives

Let's solve the problem step-by-step:

• Step 1: Convert mixed numbers to improper fractions.

For $-12\frac{1}{4}$, convert to an improper fraction:

$-12\frac{1}{4} = -\left(12 + \frac{1}{4}\right) = -\left(\frac{48}{4} + \frac{1}{4}\right) = -\frac{49}{4}$

For $-8\frac{2}{7}$, convert to an improper fraction:

$-8\frac{2}{7} = -\left(8 + \frac{2}{7}\right) = -\left(\frac{56}{7} + \frac{2}{7}\right) = -\frac{58}{7}$

• Step 2: Subtract the second improper fraction from the first.

The operation becomes $-\frac{49}{4} - (-\frac{58}{7})$, which simplifies to $-\frac{49}{4} + \frac{58}{7}$.

Find a common denominator for $\frac{49}{4}$ and $\frac{58}{7}$. The least common denominator is 28.

Convert $-\frac{49}{4}$ and $\frac{58}{7}$ to equivalents with a denominator of 28:

$-\frac{49}{4} = -\frac{49 \times 7}{4 \times 7} = -\frac{343}{28}$

$\frac{58}{7} = \frac{58 \times 4}{7 \times 4} = \frac{232}{28}$

So, $-\frac{49}{4} + \frac{58}{7}$ becomes:

$-\frac{343}{28} + \frac{232}{28} = \frac{-343 + 232}{28} = \frac{-111}{28}$

• Step 3: Simplify the improper fraction $\frac{-111}{28}$ to a mixed number form.

Divide $-111$ by 28, which gives $-3$ and a remainder of 27. Thus:

$-3\frac{27}{28}$

Therefore, the solution to the problem is $-3\frac{27}{28}$.