Step 1. Make the denominators of the fractions equivalent:
- Given set of fractions: 5/81, 75/81, 10/9, 11/9
To make the denominators of the given fractions equivalent, we need to determine the LCM of the denominators. Clearly, the denominators of the set of fractions are 81, 81, 9, and 9 respectively.
- 81 ⇔ 81, 162, 243...
- 9 ⇔ 9, 18, 27, 36, 45, 54, 63, 72, 81, 90....
LCM = 81 (81 × 1 = 81 and 9 × 9 = 81)
Multiply the denominators such that the denominator is equivalent to 81. Keep in mind that if we are multiplying a number (x), the numerator must be multiplied by the same number (x) .
⇒ 5/81, 75/81, 10/9, 11/9
⇒ (5 × 1)/(81 × 1), (75 × 1)/(81 × 1), (10 × 9)/(9 × 9), (11 × 9)/(9 × 9)
⇒ (5)/(81), (75)/(81), (90)/(81), (99)/(81)
⇒ 5/81, 75/81, 90/81, 99/81
Step 2. Compare the fractions in the given set:
Since 99 > 90 > 75 > 5, we can tell that 99/81 is the largest as:
- 5/81 (5/81) < 75/81 (75/81) < 90/81 (10/9) < 99/81 (11/9)
Therefore, 11/9 is the largest fraction in the set.