Calculato the following without using a calculator and show your working: \( \begin{array}{l}4.1 .1-6-(-4) \\ 4.1 .2-8+3 \times(-6) \\ 4.1 .3-6 \times 4+(-8)+9^{2}\end{array} \)

Sure! Let's solve each of these expressions step by step. **For \(4.1 .1-6-(-4)\):** 1. Start with the expression: \(4.1 - 6 - (-4)\) 2. Remember that subtracting a negative is the same as adding a positive: \[ 4.1 - 6 + 4 = 4.1 - 2 \] 3. Calculate \(4.1 - 2 = 2.1\) **For \(4.1 .2-8+3 \times(-6)\):** 1. Start with the expression: \(4.1 - 8 + 3 \times (-6)\) 2. Calculate the multiplication first: \[ 3 \times (-6) = -18 \] 3. Now substitute back into the expression: \[ 4.1 - 8 - 18 \] 4. Combine the constants: \[ 4.1 - 8 = -3.9 \] 5. Finally add \(-18\): \[ -3.9 - 18 = -21.9 \] **For \(4.1 .3-6 \times 4+(-8)+9^{2}\):** 1. Start with the expression: \(4.1 - 6 \times 4 + (-8) + 9^2\) 2. Calculate \(6 \times 4\): \[ 6 \times 4 = 24 \] 3. Calculate \(9^2\): \[ 9^2 = 81 \] 4. Substitute back into the expression: \[ 4.1 - 24 - 8 + 81 \] 5. Combine \(4.1 - 24\): \[ 4.1 - 24 = -19.9 \] 6. Now subtract 8: \[ -19.9 - 8 = -27.9 \] 7. Finally add 81: \[ -27.9 + 81 = 53.1 \] So the final answers are: 1. \(2.1\) 2. \(-21.9\) 3. \(53.1\)