No, \(\frac{2}{9}\) < \(\frac{7}{9}\)
These fractions already share the same denominator: 9. We just need to compare the numerators.
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 0.222222 is less than 0.777778, we confirm that \(\frac{2}{9} < \frac{7}{9}\). In percentage terms, \(\frac{2}{9}\) is 22.2222% and \(\frac{7}{9}\) is 77.7778%, a difference of 55.5556 percentage points.
When two fractions share the same denominator, the pieces are the same size. A fraction with more pieces (a larger numerator) is simply a larger amount. Since 7 pieces is more than 2 pieces of the same size, \(\frac{7}{9}\) is the larger fraction.
\(\frac{7}{9}\) is bigger. As a decimal, \(\frac{7}{9}\) = 0.777778 while \(\frac{2}{9}\) = 0.222222.
The difference is \(\frac{5}{9}\), which equals 0.555556 in decimal form (55.5556 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 \(\frac{7}{9}\) \(>\) \(\frac{2}{9}\).