Question

Column A: \(\frac{3}{5} + \frac{2}{3}\)
Column B: 1

• 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:

A quick way to check is to use estimation. \(\frac{3}{5}\) is 0.6. \(\frac{2}{3}\) is approximately 0.67. Their sum, \(0.6 + 0.67 = 1.27\), is clearly greater than 1. This can give you the right answer much faster than finding a common denominator.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This question requires us to add two fractions and compare their sum to the number 1.
Step 2: Key Formula or Approach:
To add fractions, we need a common denominator. The least common multiple of the denominators 5 and 3 is 15.
Step 3: Detailed Explanation:
First, we convert each fraction to an equivalent fraction with the denominator 15.
\[ \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} \]
\[ \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \]
Now, add the two new fractions:
\[ \frac{9}{15} + \frac{10}{15} = \frac{9 + 10}{15} = \frac{19}{15} \]
So, the quantity in Column A is \(\frac{19}{15}\).
We now compare Column A with Column B.
\[ \frac{19}{15} \quad \text{vs.} \quad 1 \]
Since the numerator (19) is greater than the denominator (15), the fraction is an improper fraction, and its value is greater than 1.
Step 4: Final Answer:
The quantity in Column A (\(\frac{19}{15}\)) is greater than the quantity in Column B (1).