Question

\( \frac{1}{4} - \frac{1}{5} \)
\(\frac{1}{20} \)

• A. The quantity in Column A is greater.
• B. The quantity in Column B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

When comparing simple arithmetic expressions, always compute the value of the expression in Column A before making a comparison. For fraction arithmetic, finding a common denominator is the standard first step.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This question requires us to compare the result of a fraction subtraction with another fraction.
Step 2: Key Formula or Approach:
To subtract fractions, we need to find a common denominator. The formula is \( \frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd} \).
Step 3: Detailed Explanation:
Column A: We need to calculate the value of \( \frac{1}{4} - \frac{1}{5} \).
The least common multiple of the denominators 4 and 5 is 20.
\[ \frac{1}{4} - \frac{1}{5} = \frac{1 \times 5}{4 \times 5} - \frac{1 \times 4}{5 \times 4} = \frac{5}{20} - \frac{4}{20} = \frac{5-4}{20} = \frac{1}{20} \] Column B: The value is given as \( \frac{1}{20} \).
Comparison: The quantity in Column A is \( \frac{1}{20} \) and the quantity in Column B is \( \frac{1}{20} \).
The two quantities are equal.
Step 4: Final Answer:
Since both columns evaluate to \( \frac{1}{20} \), the correct answer is that the two quantities are equal.