1. Add or Subtract by: \( \begin{array}{ll}\text { a) } & \begin{array}{l}\text { i) stating the LCD } \\ \text { ii) writing the equivalent fractions } \\ \text { iii) performing the operation, and } \\ \text { iv) simplifying, if necessary }\end{array} \\ \text { is }-\frac{9}{15} & \text { b) }-\frac{3}{8}-\frac{7}{12}\end{array} \) \( \begin{array}{ll}4-\frac{4}{3} & \text { d) } \frac{9}{5}+\frac{3}{y}\end{array} \)

**a) Simplify \(-\frac{9}{15}\)** 1. Identify the greatest common divisor (GCD) of 9 and 15, which is 3. 2. Divide the numerator and the denominator by 3: \[ -\frac{9}{15} = -\frac{9\div3}{15\div3} = -\frac{3}{5}. \] **b) Compute \(-\frac{3}{8} - \frac{7}{12}\)** 1. **LCD:** The denominators are 8 and 12. The least common denominator (LCD) is 24. 2. **Equivalent Fractions:** Multiply the numerator and denominator of each fraction to convert them to have the denominator 24. \[ -\frac{3}{8} = -\frac{3\times3}{8\times3} = -\frac{9}{24}, \] \[ -\frac{7}{12} = -\frac{7\times2}{12\times2} = -\frac{14}{24}. \] 3. **Perform the Operation:** \[ -\frac{9}{24} - \frac{14}{24} = -\frac{9+14}{24} = -\frac{23}{24}. \] 4. **Simplify:** The fraction \(-\frac{23}{24}\) is already in its simplest form. **c) Compute \(4 - \frac{4}{3}\)** 1. **Express the Whole Number as a Fraction:** Write 4 with denominator 3: \[ 4 = \frac{4\times3}{3} = \frac{12}{3}. \] 2. **Perform the Operation:** \[ \frac{12}{3} - \frac{4}{3} = \frac{12-4}{3} = \frac{8}{3}. \] **d) Compute \(\frac{9}{5}+\frac{3}{y}\)** 1. **LCD:** The denominators are 5 and \(y\). The least common denominator is \(5y\). 2. **Equivalent Fractions:** Convert each fraction to have the denominator \(5y\): \[ \frac{9}{5} = \frac{9 \times y}{5 \times y} = \frac{9y}{5y}, \] \[ \frac{3}{y} = \frac{3 \times 5}{y \times 5} = \frac{15}{5y}. \] 3. **Perform the Operation:** \[ \frac{9y}{5y} + \frac{15}{5y} = \frac{9y+15}{5y}. \] 4. **Simplify:** Factor the numerator: \[ 9y+15 = 3(3y+5). \] Thus, the expression becomes: \[ \frac{9y+15}{5y} = \frac{3(3y+5)}{5y}. \]