The greatest fraction out of 2/5, 5/6, 11/12 and 7/8

Concept

To compare fractions with different denominators, convert each one to a decimal (divide the numerator by the denominator) or bring all of them to a common denominator; whichever fraction has the greatest decimal value (equivalently, the greatest numerator once written over the same denominator) is the greatest fraction.

Application

Convert each of the four fractions to its decimal equivalent:

• 2/5 = 0.4

• 5/6 is approximately 0.833

• 11/12 is approximately 0.917

• 7/8 = 0.875

Comparing the four decimal values, 0.917 is the largest, so 11/12 is the greatest fraction.

Cross-check

Verify with the common-denominator method. The LCM of 5, 6, 12 and 8 is 120. Rewriting each fraction over 120:

1. 2/5 = 48/120

2. 5/6 = 100/120

3. 11/12 = 110/120

4. 7/8 = 105/120

With a common denominator, the fraction with the greatest numerator is the greatest fraction. Among 48, 100, 110 and 105, the greatest numerator is 110, confirming 11/12 as the greatest fraction -- matching the decimal comparison above.