Solve: (-17¼) - (+11⅛) Mixed Number Subtraction

To solve the problem $(-17\frac{1}{4}) - (+11\frac{1}{8})$, we need to perform the following steps:

• Step 1: Convert each mixed number to an improper fraction.
  $-17\frac{1}{4}$ converts to an improper fraction as follows:
  $-17\frac{1}{4} = -\left(\frac{17 \times 4 + 1}{4}\right) = -\left(\frac{68 + 1}{4}\right) = -\left(\frac{69}{4}\right).$
  $+11\frac{1}{8}$ converts to an improper fraction as follows:
  $+11\frac{1}{8} = \left(\frac{11 \times 8 + 1}{8}\right) = \left(\frac{88 + 1}{8}\right) = \left(\frac{89}{8}\right).$
• Step 2: Ensure both fractions have a common denominator. Here, the least common denominator (LCD) between 4 and 8 is 8.
  $-\left(\frac{69}{4}\right)$ must be converted to have a denominator of 8:
  $-\left(\frac{69 \times 2}{4 \times 2}\right) = -\left(\frac{138}{8}\right).$
• Step 3: Perform the subtraction:
  Subtraction: $-\left(\frac{138}{8}\right) - \left(\frac{89}{8}\right) = -\left(\frac{138 + 89}{8}\right) = -\left(\frac{227}{8}\right).$
• Step 4: Convert the result back to a mixed number, if necessary.
  Divide 227 by 8: $227 \div 8 = 28$ with a remainder of 3. Hence, the result is:
  $-\left(28 + \frac{3}{8}\right) = -28\frac{3}{8}.$

Therefore, the solution to the problem is $-28\frac{3}{8}$.