Question

The value of \( 35.7 - \left[ 3 + \frac{1}{3 + \frac{1}{3}} \right] - \left[ 2 + \frac{1}{2 + \frac{1}{2}} \right] \) is:

• A. \( 30 \)
• B. \( 34.8 \)
• C. \( 36.6 \)
• D. \( 41.4 \)

Hint:

Simplify complex fractions from the inside out.

Answer 1

The Correct Option is A

Step 1: Simplify the first complex fraction. \[ 3 + \frac{1}{3} = \frac{10}{3} \] \[ 3 + \frac{1}{\frac{10}{3}} = 3 + \frac{3}{10} = \frac{33}{10} = 3.3 \] Step 2: Simplify the second complex fraction. \[ 2 + \frac{1}{2} = \frac{5}{2} \] \[ 2 + \frac{1}{\frac{5}{2}} = 2 + \frac{2}{5} = \frac{12}{5} = 2.4 \] Step 3: Substitute the simplified values back into the original expression. \[ 35.7 - 3.3 - 2.4 \] Step 4: Perform the subtraction. \[ 35.7 - 3.3 = 32.4 \] \[ 32.4 - 2.4 = 30.0 \]