1.3 1.4 \( 1,3 \times 8,9 \) \( 1.5\left(\frac{1}{2}+\frac{3}{4}\right)+\frac{5}{6} \) 1.7 \( 234+432+324 \quad 1.6\left(\frac{5}{9} \times \frac{2}{3}\right) \times \) 2 Complete the following using the associative prope \( 2.1276,4+(89,5+887,62)=(\ldots+\ldots)+\ldots=\ldots \) \( 2.2\left(\frac{2}{3}+\frac{7}{9}\right)+\frac{1}{6}=\ldots+(\ldots+\ldots)=\ldots \) \( 2.3 \quad(24,2 \times 4,4) \times 3,23=\ldots \times(\ldots \times \ldots)=\ldots \) \( 2.4 \frac{7}{8} \times\left(\frac{2}{3} \times \frac{1}{2}\right)=(\ldots \times \ldots) \times \ldots=\ldots \)

Calculate the value by following steps: - step0: Calculate: \(234+432+324\) - step1: Add the numbers: \(990\) Calculate or simplify the expression \( 1.3 + 1.4 + (1.3 * 8.9) \). Calculate the value by following steps: - step0: Calculate: \(1.3+1.4+\left(1.3\times 8.9\right)\) - step1: Multiply the numbers: \(1.3+1.4+11.57\) - step2: Add the numbers: \(14.27\) Calculate or simplify the expression \( 1.6 * (5/9 * 2/3) \). Calculate the value by following steps: - step0: Calculate: \(1.6\left(\frac{\frac{5}{9}\times 2}{3}\right)\) - step1: Multiply the numbers: \(1.6\left(\frac{\frac{10}{9}}{3}\right)\) - step2: Divide the terms: \(1.6\times \frac{10}{27}\) - step3: Convert the expressions: \(\frac{8}{5}\times \frac{10}{27}\) - step4: Multiply the numbers: \(\frac{16}{27}\) Calculate or simplify the expression \( 1.5 * (1/2 + 3/4) + 5/6 \). Calculate the value by following steps: - step0: Calculate: \(1.5\left(\frac{1}{2}+\frac{3}{4}\right)+\frac{5}{6}\) - step1: Add the numbers: \(1.5\times \frac{5}{4}+\frac{5}{6}\) - step2: Multiply the numbers: \(\frac{15}{8}+\frac{5}{6}\) - step3: Reduce fractions to a common denominator: \(\frac{15\times 3}{8\times 3}+\frac{5\times 4}{6\times 4}\) - step4: Multiply the numbers: \(\frac{15\times 3}{24}+\frac{5\times 4}{6\times 4}\) - step5: Multiply the numbers: \(\frac{15\times 3}{24}+\frac{5\times 4}{24}\) - step6: Transform the expression: \(\frac{15\times 3+5\times 4}{24}\) - step7: Multiply the numbers: \(\frac{45+5\times 4}{24}\) - step8: Multiply the numbers: \(\frac{45+20}{24}\) - step9: Add the numbers: \(\frac{65}{24}\) Let's solve the problems step by step. ### 1. Calculations 1. **Calculate \( 1.3 + 1.4 + (1.3 \times 8.9) \)**: - First, calculate \( 1.3 \times 8.9 \): \[ 1.3 \times 8.9 = 11.57 \] - Now, add \( 1.3 \) and \( 1.4 \): \[ 1.3 + 1.4 = 2.7 \] - Finally, add \( 2.7 + 11.57 \): \[ 2.7 + 11.57 = 14.27 \] **Result**: \( 14.27 \) 2. **Calculate \( 1.5\left(\frac{1}{2}+\frac{3}{4}\right)+\frac{5}{6} \)**: - First, calculate \( \frac{1}{2} + \frac{3}{4} \): \[ \frac{1}{2} = \frac{2}{4} \quad \Rightarrow \quad \frac{2}{4} + \frac{3}{4} = \frac{5}{4} \] - Now, calculate \( 1.5 \times \frac{5}{4} \): \[ 1.5 \times \frac{5}{4} = \frac{15}{8} = 1.875 \] - Finally, add \( 1.875 + \frac{5}{6} \): - Convert \( \frac{5}{6} \) to a decimal: \[ \frac{5}{6} \approx 0.8333 \] - Now add: \[ 1.875 + 0.8333 \approx 2.7083 \] **Result**: \( 2.7083 \) or \( 2\frac{17}{24} \) 3. **Calculate \( 234 + 432 + 324 \)**: - Add the numbers: \[ 234 + 432 + 324 = 990 \] **Result**: \( 990 \) 4. **Calculate \( 1.6\left(\frac{5}{9} \times \frac{2}{3}\right) \)**: - First, calculate \( \frac{5}{9} \times \frac{2}{3} \): \[ \frac{5 \times 2}{9 \times 3} = \frac{10}{27} \] - Now, calculate \( 1.6 \times \frac{10}{27} \): \[ 1.6 \times \frac{10}{27} = \frac{16}{27} \approx 0.5926 \] **Result**: \( \frac{16}{27} \) ### 2. Associative Property Now, let's complete the expressions using the associative property. 1. **For \( 2.1: 1276.4 + (89.5 + 887.62) \)**: \[ 1276.4 + (89.5 + 887.62) = (1276.4 + 89.5) + 887.62 = \ldots \] - Calculate \( 89.5 + 887.62 = 977.12 \) - Now, \( 1276.4 + 977.12 = 2253.52 \) **Result**: \( (1276.4 + 89.5) + 887.62 = 2253.52 \) 2. **For \( 2.2: \left(\frac{2}{3} + \frac{7}{9}\right) + \frac{1}{6} \)**: \[ \left(\frac{2}{3} + \frac{7}{9}\right) + \frac{1}{6} = \ldots + \left(\ldots + \ldots\right) = \ldots \] - Calculate \( \frac{2}{3} + \frac{7}{9} \): \[ \frac{2}{3} = \frac{6}{9} \quad \Rightarrow \quad \frac{6}{9} + \frac{7}{9} = \frac{13}{9} \] - Now, add \( \frac{13}{9} + \frac{1}{6} \): - Convert \( \frac{1}{6} \) to a common denominator: \[ \frac{1}{6} = \frac{3}{18} \quad \text{and} \quad \frac{13}{9} = \frac{26}{18} \] - Now add: \[ \frac{26}{18} + \frac{3}{18} = \frac{29}{18} \] **Result**: \( \left(\frac{2}{3} + \frac{7}{9}\right) + \frac{1}{6} = \frac{29}{18} \) 3. **For \( 2.3: (24.2 \times 4.4) \times 3.23 \)**: \[ (24.2 \times 4.4) \times 3.23 = \ldots \times (\ldots \times \ldots) = \ldots \] - Calculate \( 24.2 \times 4.4 \): \[ 24.2 \times 4.4 = 106.48 \] - Now, multiply by \( 3.23 \): \[ 106.48 \times 3.23 = 343.09 \] **Result**: \( (24.2 \times 4.4) \times 3.23 = 343.09 \) 4. **For \( 2.4: \frac{7}{8} \times \left(\frac{2}{3} \times \frac{1}{2}\right) \)**: \[ \frac{7}{8} \times \left(\frac{2}{3} \times \frac{1}{2}\right) = \ldots \times \ldots = \ldots \] - Calculate \( \frac{2}{3} \times \frac{1}{2} = \frac{2}{6} = \frac{1}{3} \) - Now, multiply: \[ \frac{7}{8} \times \frac