Question

Arrange the numbers in the descending order : 3/11, 7/13, 9/19, 6/17

• A. 3/11, 9/19, 7/13, 6/17
• B. 7/13, 9/19, 6/17, 3/11
• C. 3/11, 7/13, 9/19, 6/17
• D. 3/11, 6/17, 7/13, 9/19

Hint:

If fractions are close together, the "Cross Multiplication" method is useful. To compare $7/13$ and $9/19$: \[ 7 \times 19 = 133 \quad \text{vs} \quad 9 \times 13 = 117 \] Since $133 > 117$, then $7/13 > 9/19$.

Answer 1

The Correct Option is B

Concept: Descending order means arranging values from the highest to the lowest. To compare fractions effectively, we can either find a common denominator or convert each fraction into its decimal equivalent for direct comparison.

Step 1: Convert each fraction into decimal form.
Let's perform the division for each fraction provided in the question: $3 \div 11 \approx 0.2727$
$7 \div 13 \approx 0.5384$
$9 \div 19 \approx 0.4736$
$6 \div 17 \approx 0.3529$

Step 2: Compare the decimal values.
Now, we list the calculated decimals in order from largest to smallest: $0.5384 > 0.4736 > 0.3529 > 0.2727$

Step 3: Map the decimals back to the original fractions.
Substituting the fractions back into the established order: $7/13 > 9/19 > 6/17 > 3/11$ This sequence matches the arrangement provided in Option (B). Final Answer: Option B