Question

$\frac{3}{4} + \frac{1}{6} =$

• A. $$\frac{11}{12}$$
• B. $$\frac{10}{12}$$
• C. $$\frac{7}{12}$$
• D. $$\frac{5}{12}$$

Answer 1

Answer:

$$\frac{11}{12}$$

Step-by-Step Calculation for Fraction Addition

• Identify the Denominators: The denominators are 4 and 6. To add fractions, they must share a common denominator.
• Find the Least Common Multiple (LCM): The LCM of 4 and 6 is 12. This serves as the Least Common Denominator (LCD).
• Convert the Fractions: Adjust each fraction to have the denominator of 12:
  • 3/4 = (3 × 3) / (4 × 3) = 9/12
  • 1/6 = (1 × 2) / (6 × 2) = 2/12
• Perform the Addition: Add the numerators while keeping the denominator the same: 9/12 + 2/12 = 11/12.

Important Mathematical Properties for Exams

• Fractional Simplification: Always check if the final result (11/12) can be simplified. Since 11 is a prime number and not a factor of 12, the fraction is in its simplest form.
• Time-Saving Tip: For competitive exams, using the cross-multiplication method can be faster for two fractions: (a/b) + (c/d) = (ad + bc) / bd. Applied here: (3×6 + 4×1) / (4×6) = (18 + 4) / 24 = 22/24, which simplifies to 11/12.