Sure, let's break down and solve each part of the given expression step-by-step:
Expression:
[tex]\[ 10.5 \times (7.5 - 2.5) + 3.6 \div (0.98 + 1.02) + 14.4 \div 9.77 \][/tex]
### Step 1: Solving the expression inside the first parentheses
[tex]\[ 10.5 \times (7.5 - 2.5) \][/tex]
- Subtract [tex]\(2.5\)[/tex] from [tex]\(7.5\)[/tex] inside the parentheses:
[tex]\[ 7.5 - 2.5 = 5 \][/tex]
- Next, multiply [tex]\(10.5\)[/tex] by the result:
[tex]\[ 10.5 \times 5 = 52.5 \][/tex]
### Step 2: Solving the expression inside the second parentheses
[tex]\[ 3.6 \div (0.98 + 1.02) \][/tex]
- Add [tex]\(0.98\)[/tex] and [tex]\(1.02\)[/tex] inside the parentheses:
[tex]\[ 0.98 + 1.02 = 2 \][/tex]
- Then, divide [tex]\(3.6\)[/tex] by the result:
[tex]\[ 3.6 \div 2 = 1.8 \][/tex]
### Step 3: Solving the division
[tex]\[ 14.4 \div 9.77 \][/tex]
- Perform the division:
[tex]\[ 14.4 \div 9.77 \approx 1.473899692937564 \][/tex]
### Step 4: Adding up all the parts
Now, we sum up the three results obtained from the steps above:
[tex]\[ 52.5 + 1.8 + 1.473899692937564 \][/tex]
- Adding these up:
[tex]\[ 52.5 + 1.8 = 54.3 \][/tex]
[tex]\[ 54.3 + 1.473899692937564 = 55.77389969293756 \][/tex]
### Final Result
Therefore, the final result of the given expression is:
[tex]\[ \boxed{55.77389969293756} \][/tex]
