Question on: WAEC Mathematics - 2009

Here's how to simplify the expression:

1. Convert mixed fractions to improper fractions:

   • 3\(\frac{1}{2}\) = \(\frac{7}{2}\)
   • 4\(\frac{1}{3}\) = \(\frac{13}{3}\)

2. Solve the addition within the first parentheses:

   • \(\frac{7}{2} + \frac{13}{3}\) = \(\frac{21}{6} + \frac{26}{6}\) = \(\frac{47}{6}\)

3. Solve the subtraction within the second parentheses:

   • \(\frac{5}{6} - \frac{2}{3}\) = \(\frac{5}{6} - \frac{4}{6}\) = \(\frac{1}{6}\)

4. Perform the division:

   • \(\frac{47}{6} \div \frac{1}{6}\) = \(\frac{47}{6} \times \frac{6}{1}\) = 47

Therefore, the answer is 47, but none of the options is exactly 47. It seems like there might be an error in the options given. However, if we had to pick one that is closest, we may consider changing one of the signs or one of the numbers. Let's solve the problem to see where the closest answer will be.

• 3\(\frac{1}{2}\) + 4\(\frac{1}{3}\) = 3.5 + 4.33 = 7.83
• \(\frac{5}{6}\) - \(\frac{2}{3}\) = .83 - .66 = .17
• 7.83 / .17 = 46, closest to 47, let us evaluate the options to confirm which answer is correct.
• A = 1\(\frac{1}{4}\) = 1.25
• B = 8\(\frac{1}{2}\) = 8.5
• C = 35
• D = 47 So, the closest answer is 47.