F ind the value of the following expression:
372 ÷ 56 × 7 - 5 + 2

To find the value of the given expression, we follow the order of operations (BODMAS/PEMDAS rule), which dictates that we perform division and multiplication (from left to right) before addition and subtraction.

The given expression is:
$372÷56\times 7-5+2$

Step 1: Perform the division first.
We can write the division $372÷56$ as a fraction:
$\frac{372}{56}$
Both the numerator and denominator can be simplified by dividing them by their common factor, 4:
$\frac{372÷4}{56÷4}=\frac{93}{14}$

Now, substitute this back into the expression:
$\frac{93}{14}\times 7-5+2$

Step 2: Perform the multiplication.
Next, we multiply $\frac{93}{14}$ by 7:
$\frac{93}{14}\times 7=\frac{93\times 7}{14}$
Since 14 is divisible by 7 (14 = 2 × 7), we can simplify this calculation:
$\frac{93}{2}$

Substitute this value back into the expression:
$\frac{93}{2}-5+2$

Step 3: Perform addition and subtraction.
We calculate the remaining operations from left to right:
$\frac{93}{2}-5+2=\frac{93}{2}-3$

To subtract 3 from the fraction, we convert 3 to have a common denominator of 2:
$3=\frac{6}{2}$
Now subtract:
$\frac{93}{2}-\frac{6}{2}=\frac{93-6}{2}=\frac{87}{2}$

Step 4: Convert the improper fraction to a mixed number.
Divide 87 by 2:
87 divided by 2 is 43 with a remainder of 1.
Therefore, we can write:
$\frac{87}{2}=43\frac{1}{2}$

Thus, the correct option is $43\frac{1}{2}$.