Yes, \(\frac{1}{4}\) > \(\frac{1}{9}\)
To compare these fractions, we need a common denominator. The denominators are 4 and 9, and the least common denominator (LCD) is 36.
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 0.25 is greater than 0.111111, we confirm that \(\frac{1}{4} > \frac{1}{9}\). In percentage terms, \(\frac{1}{4}\) is 25% and \(\frac{1}{9}\) is 11.1111%, a difference of 13.8889 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 4ths, \(\frac{1}{4}\) is the bigger fraction even though both have 1 in the numerator.
\(\frac{1}{4}\) is bigger. As a decimal, \(\frac{1}{4}\) = 0.25 while \(\frac{1}{9}\) = 0.111111.
The difference is \(\frac{5}{36}\), which equals 0.138889 in decimal form (13.8889 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 \(\frac{1}{4}\) \(>\) \(\frac{1}{9}\).