9 1/2 - -8 1/2

Answer 1

To subtract \(-8 \frac{1}{2}\) from \(9 \frac{1}{2}\), first convert both mixed numbers to improper fractions.

1. Convert \(9 \frac{1}{2}\): \[ 9 \frac{1}{2} = \frac{9 \times 2 + 1}{2} = \frac{18 + 1}{2} = \frac{19}{2} \]

2. Convert \(-8 \frac{1}{2}\): \[ -8 \frac{1}{2} = -\left(\frac{8 \times 2 + 1}{2}\right) = -\left(\frac{16 + 1}{2}\right) = -\frac{17}{2} \]

Now, perform the subtraction: \[ 9 \frac{1}{2} - (-8 \frac{1}{2}) = \frac{19}{2} - \left(-\frac{17}{2}\right) \] This simplifies to: \[ \frac{19}{2} + \frac{17}{2} = \frac{19 + 17}{2} = \frac{36}{2} = 18 \]

So, \(9 \frac{1}{2} - (-8 \frac{1}{2}) = 18\).