Add Mixed Numbers: Solving (-13¼) + (-9⅖) Step by Step

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

• Step 1: Convert mixed numbers to improper fractions.
• Step 2: Find the least common denominator.
• Step 3: Perform the addition and convert back to a mixed number.

Let's work through each step:

Step 1: Convert mixed numbers to improper fractions.

$-13\frac{1}{4}$ = $-\left( 13 + \frac{1}{4} \right) = -\left( \frac{52}{4} + \frac{1}{4} \right) = -\frac{53}{4}$

$-9\frac{2}{7}$ = $-\left( 9 + \frac{2}{7} \right) = -\left( \frac{63}{7} + \frac{2}{7} \right) = -\frac{65}{7}$

Step 2: Determine a common denominator. The least common multiple of 4 and 7 is 28.

Convert the fractions:

$-\frac{53}{4} = -\frac{53 \times 7}{4 \times 7} = -\frac{371}{28}$

$-\frac{65}{7} = -\frac{65 \times 4}{7 \times 4} = -\frac{260}{28}$

Step 3: Add the fractions:

$-\frac{371}{28} + \left(-\frac{260}{28}\right) = -\frac{371 + 260}{28} = -\frac{631}{28}$

Converting $-\frac{631}{28}$ back to a mixed number:

Perform the division: $631 \div 28 \approx 22$ remainder 15.

This gives us a mixed number: $-22\frac{15}{28}$

Therefore, the solution to the problem is $-22\frac{15}{28}$.