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

Question

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

UpStudy AI · Accepted Answer

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
1. **Calculations**: - $$ 1.3 + 1.4 + (1.3 \times 8.9) = 14.27 $$ - $$ 1.5\left(\frac{1}{2}+\frac{3}{4}\right)+\frac{5}{6} \approx 2.7083 $$ - $$ 234 + 432 + 324 = 990 $$ - $$ 1.6\left(\frac{5}{9} \times \frac{2}{3}\right) = \frac{16}{27} $$ 2. **Associative Property**: - $$ 1276.4 + (89.5 + 887.62) = 2253.52 $$ - $$ \left(\frac{2}{3} + \frac{7}{9}\right) + \frac{1}{6} = \frac{29}{18} $$ - $$ (24.2 \times 4.4) \times 3.23 = 343.09 $$ - $$ \frac{7}{8} \times \left(\frac{2}{3} \times \frac{1}{2}\right) = \frac{7}{24} $$

1.3 1.4

1.7
2 Complete the following using the associative prope

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1.3 1.4 1.7 2 Complete the following using the associative prope