Question

What is the value of 11/12 + 13/14?

• A. 1 19/25
• B. 1 43/84
• C. 1 71/84
• D. 2 19/25
• E. 2 43/84

Hint:

When adding fractions, always double-check your multiplication when finding equivalent fractions, as this is a common source of error. If your calculated answer is not in the options, re-read the question carefully for any misinterpretations, and then check for potential typos in the options themselves.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The problem requires the addition of two fractions with different denominators. To do this, we must first find a common denominator.
Step 2: Key Formula or Approach:
1. Find the Least Common Multiple (LCM) of the denominators.
2. Convert each fraction to an equivalent fraction with the LCM as the new denominator.
3. Add the numerators of the new fractions.
4. Simplify the resulting fraction and convert it to a mixed number if necessary.
Step 3: Detailed Explanation:
The denominators are 12 and 14. We find their LCM.
The prime factorization of 12 is \(2^2 \times 3\).
The prime factorization of 14 is \(2 \times 7\).
The LCM is the highest power of each prime factor multiplied together: \(2^2 \times 3 \times 7 = 4 \times 21 = 84\).
Now, convert the fractions:
\[ \frac{11}{12} = \frac{11 \times 7}{12 \times 7} = \frac{77}{84} \]
\[ \frac{13}{14} = \frac{13 \times 6}{14 \times 6} = \frac{78}{84} \]
Add the equivalent fractions:
\[ \frac{77}{84} + \frac{78}{84} = \frac{77 + 78}{84} = \frac{155}{84} \]
Convert the improper fraction to a mixed number:
\[ \frac{155}{84} = 1 \frac{71}{84} \]
Step 4: Final Answer:
Based on the provided answer key, the answer is \(1 \frac{71}{84}\), which corresponds to option (C).