Question

What is the value of 2 - (1/2 + 1/3)?

• A. 5/6
• B. 1
• C. 7/6
• D. 4/3
• E. 3/2

Hint:

When dealing with mixed operations involving whole numbers and fractions, it's often easiest to convert the whole number into a fraction with the required denominator right away.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem involves the subtraction of fractions and follows the order of operations (PEMDAS/BODMAS), which dictates that we must solve the expression inside the parentheses first.
Step 2: Key Formula or Approach:
To add or subtract fractions, they must have a common denominator. The Least Common Multiple (LCM) of the denominators is used for this.
1. Solve the expression in the parenthesis: \( \frac{1}{2} + \frac{1}{3} \).
2. Subtract the result from 2.
Step 3: Detailed Explanation:
First, calculate the sum inside the parentheses. The LCM of the denominators 2 and 3 is 6.
\[ \frac{1}{2} + \frac{1}{3} = \frac{1 \times 3}{2 \times 3} + \frac{1 \times 2}{3 \times 2} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \]
Now, substitute this result back into the original expression:
\[ 2 - \frac{5}{6} \]
To subtract the fraction, express 2 as a fraction with a denominator of 6:
\[ 2 = \frac{2 \times 6}{6} = \frac{12}{6} \]
Perform the subtraction:
\[ \frac{12}{6} - \frac{5}{6} = \frac{12 - 5}{6} = \frac{7}{6} \]
Step 4: Final Answer:
The result is \(\frac{7}{6}\), which corresponds to option (C).