Which of the following is the largest\(\frac{5}{6},\ \frac{11}{12},\ \frac{7}{18},\ \frac{11}{21}?\)

Given:

Fractions to compare: (5/6), (11/12), (7/18), (11/21)

Formula Used:

To compare fractions, find their LCM (Least Common Multiple) of denominators and convert all fractions to have the same denominator. The fraction with the largest numerator is the largest fraction.

Calculation:

Denominators: 6, 12, 18, 21

LCM of denominators = 252

Convert each fraction to have the denominator 252:

(5/6) = (5 × 42)/(6 × 42) = 210/252

(11/12) = (11 × 21)/(12 × 21) = 231/252

(7/18) = (7 × 14)/(18 × 14) = 98/252

(11/21) = (11 × 12)/(21 × 12) = 132/252

Compare numerators: 210, 231, 98, 132

Largest numerator = 231

⇒ Largest fraction = (11/12)

The largest fraction is (11/12).