b) \( -\frac{1}{31}+\frac{15}{125}+\left(-\frac{43}{45}\right)+3= \)

To solve the expression, let's combine the fractions and the whole number step by step. First, convert the fractions to a common denominator. The least common multiple of the denominators (31, 125, and 45) is 2325. Now, convert each fraction: 1. \( -\frac{1}{31} = -\frac{75}{2325} \) (because \( 1 \times 75 = 75 \) and \( 31 \times 75 = 2325 \)) 2. \( \frac{15}{125} = \frac{279}{2325} \) (because \( 15 \times 18.6 \approx 279 \) and \( 125 \times 18.6 \approx 2325 \)) 3. \( -\frac{43}{45} = -\frac{1115}{2325} \) (because \( 43 \times 51.8 \approx 1115 \) and \( 45 \times 51.8 \approx 2325 \)) 4. The number 3 can be converted as well: \( 3 = \frac{6975}{2325} \) (because \( 3 \times 2325 = 6975 \)) Now, add them together: \[ -\frac{75}{2325} + \frac{279}{2325} - \frac{1115}{2325} + \frac{6975}{2325} = \frac{6975 + 279 - 75 - 1115}{2325} = \frac{6064}{2325} \] Simplifying \( \frac{6064}{2325} \) gives: \[ \frac{6064 \div 31}{2325 \div 31} = \frac{196}{75} \] The result of the expression \( -\frac{1}{31}+\frac{15}{125}+\left(-\frac{43}{45}\right)+3 \) is therefore: \[ \frac{196}{75} \]