1. Estimate the sum. \( \frac{12}{13}+\frac{19}{20} \)

To estimate the sum \( \frac{12}{13} + \frac{19}{20} \), we can round each fraction to a simpler one. \( \frac{12}{13} \) is approximately \( 1 \) since it's very close to a whole, and \( \frac{19}{20} \) is also about \( 1 \) for the same reason. So, the estimated sum is \( 1 + 1 = 2 \). Now, if you want to be a bit more precise, you can compute the exact sum. First, find a common denominator: \( 13 \times 20 = 260 \). Then rewrite the fractions: \[ \frac{12}{13} = \frac{12 \times 20}{260} = \frac{240}{260}, \quad \frac{19}{20} = \frac{19 \times 13}{260} = \frac{247}{260} \] Adding these gives: \[ \frac{240 + 247}{260} = \frac{487}{260} \approx 1.87 \] So the exact sum is approximately \( 1.87 \).