Question

Perform the indicated operation. \(-5 \frac{2}{5}+\left(-6 \frac{4}{9}\right)\)

Short answer

Answer: The sum of the two negative mixed numbers -5 2/5 and -6 4/9 is -457/45.

Step-by-step solution

Convert mixed numbers to improper fractions

To convert the mixed numbers into improper fractions, use the following formula: (whole number × denominator) + numerator. For the first mixed number (-5 2/5), it will be: \((-5) × 5 + 2 = -25 + 2 = -23\) So, the first improper fraction is: \(\frac{-23}{5}\). For the second mixed number (-6 4/9), it will be: \((-6) × 9 + 4 = -54 + 4 = -50\) So, the second improper fraction is: \(\frac{-50}{9}\).

Add the two improper fractions

To add the two fractions, you will need a common denominator, which is the least common multiple (LCM) of the denominators. The LCM of 5 and 9 is 45. Next, find the equivalent fractions for both fractions with the denominator of 45: \(\frac{-23}{5}*\frac{9}{9}=\frac{-207}{45}\) \(\frac{-50}{9}*\frac{5}{5}=\frac{-250}{45}\) Now, add the numerators and keep the common denominator: \(\frac{-207}{45}+\frac{-250}{45}=\frac{-207 + (-250)}{45}=\frac{-457}{45}\) Therefore, \(-5 \frac{2}{5}+(-6 \frac{4}{9}) = \frac{-457}{45}\).