Compare : `11.45- 3.25 +12.5 `_______`15.75-4.65+9.85` .

Options

A. `{:("(i)","(ii)","(iii)"),(5,lt,15.548):}`
B. `{:("(i)","(ii)","(iii)"),(9,lt,15.558):}`
C. `{:("(i)","(ii)","(iii)"),(9,gt,15.547):}`
D. `{:("(i)","(ii)","(iii)"),(2,lt,15.548):}`

Explanation

To compare the two expressions \( 11.45 - 3.25 + 12.5 \) and \( 15.75 - 4.65 + 9.85 \), we will calculate each side step by step.

### Step 1: Calculate the Left-Hand Side (LHS)
The LHS is given by:
\[ 11.45 - 3.25 + 12.5 \]

#### Step 1.1: Add \( 11.45 \) and \( 12.5 \)
First, we add \( 11.45 \) and \( 12.5 \):
\[ 11.45 + 12.5 = 23.95 \]
(Here, \( 11 + 12 = 23 \) and \( 0.45 + 0.50 = 0.95 \))

#### Step 1.2: Subtract \( 3.25 \)
Now, we subtract \( 3.25 \) from \( 23.95 \):
\[ 23.95 - 3.25 = 20.70 \]
(Performing the subtraction: \( 5 - 5 = 0 \), \( 9 - 2 = 7 \), \( 23 - 3 = 20 \))

### Step 2: Calculate the Right-Hand Side (RHS)
The RHS is given by:
\[ 15.75 - 4.65 + 9.85 \]

#### Step 2.1: Subtract \( 4.65 \) from \( 15.75 \)
First, we subtract \( 4.65 \) from \( 15.75 \):
\[ 15.75 - 4.65 = 11.10 \]
(Performing the subtraction: \( 5 - 5 = 0 \), \( 7 - 6 = 1 \), \( 15 - 4 = 11 \))

#### Step 2.2: Add \( 9.85 \)
Now, we add \( 9.85 \) to \( 11.10 \):
\[ 11.10 + 9.85 = 20.95 \]
(Here, \( 11 + 9 = 20 \) and \( 0.10 + 0.85 = 0.95 \))

### Step 3: Compare the Results
Now we have:
- LHS = \( 20.70 \)
- RHS = \( 20.95 \)

To compare:
\[ 20.70 < 20.95 \]

### Final Comparison Statement
Thus, we can conclude:
\[ 11.45 - 3.25 + 12.5 < 15.75 - 4.65 + 9.85 \]