Yes, \(\frac{1}{6}\) > \(\frac{1}{9}\)
To compare these fractions, we need a common denominator. The denominators are 6 and 9, and the least common denominator (LCD) is 18.
A quicker way to compare fractions is to cross-multiply. Multiply each numerator by the other fraction's denominator:
Convert each fraction to a decimal by dividing the numerator by the denominator:
Since 0.166667 is greater than 0.111111, we confirm that \(\frac{1}{6} > \frac{1}{9}\). In percentage terms, \(\frac{1}{6}\) is 16.6667% and \(\frac{1}{9}\) is 11.1111%, a difference of 5.5556 percentage points.
When two fractions have the same numerator, you have the same number of pieces — but the pieces are different sizes. A smaller denominator means each piece is larger. Since 9ths are larger pieces than 6ths, \(\frac{1}{6}\) is the bigger fraction even though both have 1 in the numerator.
\(\frac{1}{6}\) is bigger. As a decimal, \(\frac{1}{6}\) = 0.166667 while \(\frac{1}{9}\) = 0.111111.
The difference is \(\frac{1}{18}\), which equals 0.055556 in decimal form (5.5556 percentage points).
You can use three methods: find a common denominator and compare numerators, cross-multiply and compare the products, or convert both fractions to decimals. All three methods confirm that \(\frac{1}{6}\) \(>\) \(\frac{1}{9}\).