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Wondering how to figure out which fraction is bigger without a calculator? Comparing \(\frac{8}{9}\) and \(\frac{8}{11}\) 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 0.727273, we confirm that \(\frac{8}{9} > \frac{8}{11}\). In percentage terms, \(\frac{8}{9}\) is 88.8889% and \(\frac{8}{11}\) is 72.7273%, a difference of 16.1616 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 11ths, \(\frac{8}{9}\) is the bigger fraction even though both have 8 in the numerator.
\(\frac{8}{9}\) is bigger. As a decimal, \(\frac{8}{9}\) = 0.888889 while \(\frac{8}{11}\) = 0.727273.
The difference is \(\frac{16}{99}\), which equals 0.161616 in decimal form (16.1616 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 \(\frac{8}{9}\) \(>\) \(\frac{8}{11}\).