1. Simplify the following: \( \begin{array}{ll}\text { a ) } 6\left(\frac{1}{2}+\frac{1}{3}\right) & \text { b) } \frac{1}{2}(18+36) \\ \text { c) } 12(13-8)-11(22-17) & \text { d) } 1,5 \times 3+1,5 \times 4 \\ \text { e ) } \frac{1}{8} \times 2 \times 8 & \text { f) } \frac{3}{4} \times \frac{4}{3} \times 12\end{array} \)

Sure! Let's simplify each of the given expressions step by step. ### a) \( 6\left(\frac{1}{2} + \frac{1}{3}\right) \) 1. **Add the fractions inside the parentheses:** \[ \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \] 2. **Multiply by 6:** \[ 6 \times \frac{5}{6} = 5 \] **Simplified Result:** \( 5 \) --- ### b) \( \frac{1}{2}(18 + 36) \) 1. **Add the numbers inside the parentheses:** \[ 18 + 36 = 54 \] 2. **Multiply by \(\frac{1}{2}\):** \[ \frac{1}{2} \times 54 = 27 \] **Simplified Result:** \( 27 \) --- ### c) \( 12(13 - 8) - 11(22 - 17) \) 1. **Calculate inside each set of parentheses:** \[ 13 - 8 = 5 \quad \text{and} \quad 22 - 17 = 5 \] 2. **Multiply and subtract:** \[ 12 \times 5 - 11 \times 5 = 60 - 55 = 5 \] **Simplified Result:** \( 5 \) --- ### d) \( 1.5 \times 3 + 1.5 \times 4 \) 1. **Factor out 1.5:** \[ 1.5 \times (3 + 4) = 1.5 \times 7 = 10.5 \] **Simplified Result:** \( 10.5 \) --- ### e) \( \frac{1}{8} \times 2 \times 8 \) 1. **Multiply the fractions and integers step by step:** \[ \frac{1}{8} \times 2 = \frac{2}{8} = \frac{1}{4} \] \[ \frac{1}{4} \times 8 = 2 \] **Simplified Result:** \( 2 \) --- ### f) \( \frac{3}{4} \times \frac{4}{3} \times 12 \) 1. **Multiply the fractions first:** \[ \frac{3}{4} \times \frac{4}{3} = 1 \] 2. **Multiply by 12:** \[ 1 \times 12 = 12 \] **Simplified Result:** \( 12 \) --- ### Summary of Results - **a)** \( 5 \) - **b)** \( 27 \) - **c)** \( 5 \) - **d)** \( 10.5 \) - **e)** \( 2 \) - **f)** \( 12 \)