Let's solve the given expression step by step:
The expression is:
[tex]\[ \left( \frac{20}{5} \right) \div 2 + \left( \frac{16}{8} \right) \times 2 + \left( \frac{10}{5} \right) \times (3 + 2) \][/tex]
### Breaking it down into segments:
1. First Segment:
[tex]\[ \left( \frac{20}{5} \right) \div 2 \][/tex]
First, calculate the fraction inside the parentheses:
[tex]\[ \frac{20}{5} = 4 \][/tex]
Next, divide by 2:
[tex]\[ 4 \div 2 = 2.0 \][/tex]
So the value of the first segment is:
[tex]\[ 2.0 \][/tex]
2. Second Segment:
[tex]\[ \left( \frac{16}{8} \right) \times 2 \][/tex]
Calculate the fraction:
[tex]\[ \frac{16}{8} = 2 \][/tex]
Then multiply by 2:
[tex]\[ 2 \times 2 = 4.0 \][/tex]
So the value of the second segment is:
[tex]\[ 4.0 \][/tex]
3. Third Segment:
[tex]\[ \left( \frac{10}{5} \right) \times (3 + 2) \][/tex]
First, calculate the fraction:
[tex]\[ \frac{10}{5} = 2 \][/tex]
Then, calculate the value inside the parentheses:
[tex]\[ 3 + 2 = 5 \][/tex]
Finally, multiply these results:
[tex]\[ 2 \times 5 = 10.0 \][/tex]
So the value of the third segment is:
[tex]\[ 10.0 \][/tex]
### Adding all segments together:
Now, sum the values of all three segments:
[tex]\[ 2.0 + 4.0 + 10.0 \][/tex]
Adding these:
[tex]\[ 2.0 + 4.0 = 6.0 \][/tex]
[tex]\[ 6.0 + 10.0 = 16.0 \][/tex]
So, the total value of the expression is:
[tex]\[ 16.0 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{16} \][/tex]
