No, \(\frac{8}{11}\) < \(\frac{9}{11}\)
These fractions already share the same denominator: 11. 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 0.727273 is less than 0.818182, we confirm that \(\frac{8}{11} < \frac{9}{11}\). In percentage terms, \(\frac{8}{11}\) is 72.7273% and \(\frac{9}{11}\) is 81.8182%, a difference of 9.0909 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 9 pieces is more than 8 pieces of the same size, \(\frac{9}{11}\) is the larger fraction.
\(\frac{9}{11}\) is bigger. As a decimal, \(\frac{9}{11}\) = 0.818182 while \(\frac{8}{11}\) = 0.727273.
The difference is \(\frac{1}{11}\), which equals 0.090909 in decimal form (9.0909 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 \(\frac{9}{11}\) \(>\) \(\frac{8}{11}\).