🔄 Want to compare different fractions? Change the numbers above and click Compare again.
Wondering how to figure out which fraction is bigger without a calculator? Comparing \(\frac{8}{9}\) and \(\frac{9}{11}\) is straightforward once you know the right approach. Below we walk through three proven methods for comparing fractions: finding a common denominator, cross multiplication, and converting to decimals. Each method will give you the same answer, so choose the one that feels easiest.
To compare these fractions, we need a common denominator. The denominators are 9 and 11, and the least common denominator (LCD) is 99.
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 0.888889 is greater than 0.818182, we confirm that \(\frac{8}{9} > \frac{9}{11}\). In percentage terms, \(\frac{8}{9}\) is 88.8889% and \(\frac{9}{11}\) is 81.8182%, a difference of 7.0707 percentage points.
These fractions have different numerators and different denominators, so we can't compare them directly. By converting to a common denominator of 99, we're cutting both quantities into equal-sized pieces. Then 88 pieces vs 81 pieces is a straightforward comparison.
\(\frac{8}{9}\) is bigger. As a decimal, \(\frac{8}{9}\) = 0.888889 while \(\frac{9}{11}\) = 0.818182.
The difference is \(\frac{7}{99}\), which equals 0.070707 in decimal form (7.0707 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 \(\frac{8}{9}\) \(>\) \(\frac{9}{11}\).