Question

Arrange the following proportions in descending order: A. \(\frac{3}{13}\), B. \(\frac{4}{17}\), C. \(\frac{5}{19}\), D. \(\frac{7}{15}\), E. \(\frac{2}{5}\).

• A. D, E, C, B, A
• B. E, B, A, C, D
• C. B, A, D, E, C
• D. C, B, E, D, A

Hint:

For descending order, arrange fractions from greatest value to smallest value.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The problem requires us to sort five mathematical fractions in descending order (from largest to smallest).

Step 2: Key Formula or Approach:
Converting each fraction into its decimal value is the most efficient technique to avoid complex cross-multiplications.

Step 3: Detailed Explanation:
Let us convert each fraction to its decimal equivalent:
• A. 3/13 \[ \frac{3}{13} \approx 0.2308 \]
• B. 4/17 \[ \frac{4}{17} \approx 0.2353 \]
• C. 5/19 \[ \frac{5}{19} \approx 0.2632 \]
• D. 7/15 \[ \frac{7}{15} \approx 0.4667 \]
• E. 2/5 \[ \frac{2}{5} = 0.4000 \] Comparing these decimal values in descending order (largest to smallest): \[ 0.4667 > 0.4000 > 0.2632 > 0.2353 > 0.2308 \] Substituting back the letters: \[ D > E > C > B > A \]

Step 4: Final Answer:
The descending order of the proportions is D, E, C, B, A, which matches option (A).