Yes, \(\frac{2}{7}\) > \(\frac{2}{9}\)
To compare these fractions, we need a common denominator. The denominators are 7 and 9, and the least common denominator (LCD) is 63.
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 0.285714 is greater than 0.222222, we confirm that \(\frac{2}{7} > \frac{2}{9}\). In percentage terms, \(\frac{2}{7}\) is 28.5714% and \(\frac{2}{9}\) is 22.2222%, a difference of 6.3492 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 7ths, \(\frac{2}{7}\) is the bigger fraction even though both have 2 in the numerator.
\(\frac{2}{7}\) is bigger. As a decimal, \(\frac{2}{7}\) = 0.285714 while \(\frac{2}{9}\) = 0.222222.
The difference is \(\frac{4}{63}\), which equals 0.063492 in decimal form (6.3492 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 \(\frac{2}{7}\) \(>\) \(\frac{2}{9}\).