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Wondering how to figure out which fraction is bigger without a calculator? Comparing \(\frac{5}{6}\) and \(\frac{5}{11}\) 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 6 and 11, and the least common denominator (LCD) is 66.
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 0.833333 is greater than 0.454545, we confirm that \(\frac{5}{6} > \frac{5}{11}\). In percentage terms, \(\frac{5}{6}\) is 83.3333% and \(\frac{5}{11}\) is 45.4545%, a difference of 37.8788 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 6ths are larger pieces than 11ths, \(\frac{5}{6}\) is the bigger fraction even though both have 5 in the numerator.
\(\frac{5}{6}\) is bigger. As a decimal, \(\frac{5}{6}\) = 0.833333 while \(\frac{5}{11}\) = 0.454545.
The difference is \(\frac{25}{66}\), which equals 0.378788 in decimal form (37.8788 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 \(\frac{5}{6}\) \(>\) \(\frac{5}{11}\).