Question

Column A: \(\frac{24}{23} + \frac{101}{100}\)
Column B: 2

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

Hint:

When comparing a sum of fractions to an integer, check if each fraction is greater or less than 1. If both fractions are "improper" (greater than 1), their sum will be greater than 2. This estimation method is much faster than finding a common denominator.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This question asks to compare a sum of two fractions to an integer. A quick way to solve this is by estimation, without calculating the full sum.
Step 2: Detailed Explanation:
Let's analyze the fractions in Column A.
The first fraction is \(\frac{24}{23}\). Since the numerator is greater than the denominator, this fraction is greater than 1. We can rewrite it as:
\[ \frac{24}{23} = \frac{23+1}{23} = 1 + \frac{1}{23} \] The second fraction is \(\frac{101}{100}\). This fraction is also greater than 1. We can rewrite it as:
\[ \frac{101}{100} = \frac{100+1}{100} = 1 + \frac{1}{100} \] Now, let's find the sum in Column A:
\[ \text{Column A} = \left(1 + \frac{1}{23}\right) + \left(1 + \frac{1}{100}\right) = 2 + \frac{1}{23} + \frac{1}{100} \] Step 3: Comparing the Quantities:
Column A: \(2 + \frac{1}{23} + \frac{1}{100}\)
Column B: 2
Since \(\frac{1}{23}\) and \(\frac{1}{100}\) are both positive numbers, their sum is positive. Therefore, the value in Column A is 2 plus a small positive amount, which is definitively greater than 2.