`11.6+9.28-: 0.464 - 0.2828 -: 0.07` =?

Options

A. `9.2`
B. `9.56`
C. `27.2 `
D. `27.56`

Answer

To solve the expression \( 11.6 + 9.28 \div 0.464 - 0.2828 \div 0.07 \), we will follow the order of operations (BODMAS/BIDMAS).

### Step 1: Divide \( 9.28 \) by \( 0.464 \)
\[ 9.28 \div 0.464 \]
To simplify this division, we can multiply both the numerator and the denominator by \( 1000 \) to eliminate the decimals:
\[ \frac{9.28 \times 1000}{0.464 \times 1000} = \frac{9280}{464} \]
Now, performing the division:
\[ 9280 \div 464 = 20 \]

### Step 2: Divide \( 0.2828 \) by \( 0.07 \)
\[ 0.2828 \div 0.07 \]
Again, we can multiply both the numerator and the denominator by \( 1000 \):
\[ \frac{0.2828 \times 1000}{0.07 \times 1000} = \frac{282.8}{70} \]
Now, performing the division:
\[ 282.8 \div 70 = 4.04 \]

### Step 3: Substitute the results back into the expression
Now we substitute the results of the divisions back into the original expression:
\[ 11.6 + 20 - 4.04 \]

### Step 4: Perform the addition and subtraction
First, we add \( 11.6 \) and \( 20 \):
\[ 11.6 + 20 = 31.6 \]
Now we subtract \( 4.04 \):
\[ 31.6 - 4.04 = 27.56 \]

### Final Answer
Thus, the final result is:
\[ \boxed{27.56} \]

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