5 punto 2. Which answer is the best estimate for the sum of \( 12 \frac{2}{5}+\left(-3 \frac{1}{4}\right) \) ? 10 15 16 6 1 punto

To solve this problem, we need to add the two mixed numbers and then round the result to the nearest whole number. Let's break it down step by step: Step 1: Convert the mixed numbers to improper fractions. - \( 12 \frac{2}{5} \) can be written as \( \frac{62}{5} \) because \( 12 \times 5 + 2 = 62 \). - \( -3 \frac{1}{4} \) can be written as \( -\frac{13}{4} \) because \( 3 \times 4 + 1 = 13 \). Step 2: Add the two fractions. - To add \( \frac{62}{5} \) and \( -\frac{13}{4} \), we need a common denominator. The least common multiple of 5 and 4 is 20. - Convert both fractions to have a denominator of 20: - \( \frac{62}{5} \) becomes \( \frac{62 \times 4}{5 \times 4} = \frac{248}{20} \). - \( -\frac{13}{4} \) becomes \( -\frac{13 \times 5}{4 \times 5} = -\frac{65}{20} \). - Now we can add the fractions: \( \frac{248}{20} + \left(-\frac{65}{20}\right) = \frac{248 - 65}{20} = \frac{183}{20} \). Step 3: Convert the improper fraction back to a mixed number. - \( \frac{183}{20} \) can be written as \( 9 \frac{3}{20} \) because \( 183 \div 20 = 9 \) with a remainder of 3. Step 4: Round the result to the nearest whole number. - Since \( 9 \frac{3}{20} \) is closer to 9 than to 10, the best estimate for the sum is 9. Therefore, the best estimate for the sum of \( 12 \frac{2}{5} + \left(-3 \frac{1}{4}\right) \) is 9. None of the provided options (10, 15, 16, 6) are correct.