Which of the following fractions is the largest?
​$$\frac{11}{12}, \frac{12}{13}, \frac{15}{16}, \frac{13}{14}$$​​

Correct option is A

Solution:

1. Convert $$\frac{11}{12}$$​ to a percentage:

​$$\frac{11}{12} \times 100 = \frac{1100}{12} \approx 91.67\%$$​​

2. Convert$$\frac{12}{13}$$​to a percentage:

​$$\frac{12}{13} \times 100 = \frac{1200}{13} \approx 92.31\%$$​​

3. Convert$$\frac{15}{16}$$ to a percentage:

​$$\frac{15}{16} \times 100 = 93.75\%$$​​

4. Convert  $$\frac{13}{14}$$​ to a percentage:

​$$\frac{13}{14} \times 100 = \frac{1300}{14} \approx 92.86\%$$​​

The largest fraction is $$\frac{15}{16}$$.

​

Alternate Solution:

Step 1: Find the Least Common Denominator (LCD) for 12, 13, 16, and 14 

The LCM of 12, 13, 16, and 14 is 4368.

Step 2: Convert each fraction to have a denominator of 4368:

​$$\frac{11}{12} = \frac{11 \times 364}{12 \times 364} = \frac{4004}{4368}\\\ \\\frac{12}{13} = \frac{12 \times 336}{13 \times 336} = \frac{4032}{4368}\\\ \\\frac{15}{16} = \frac{15 \times 273}{16 \times 273} = \frac{4095}{4368}\\\ \\\frac{13}{14} = \frac{13 \times 312}{14 \times 312} = \frac{4056}{4368}\\\ \\$$​​

Step 3: Compare the numerators:

4004, 4032, 4095, and 4056

The largest numerator is 4095, so the largest fraction is: $$\frac{15}{16}$$​​