🔄 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 \(\frac{2}{9}\) and \(\frac{9}{10}\) 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 10, and the least common denominator (LCD) is 90.
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 0.9, we confirm that \(\frac{2}{9} < \frac{9}{10}\). In percentage terms, \(\frac{2}{9}\) is 22.2222% and \(\frac{9}{10}\) is 90%, a difference of 67.7778 percentage points.
These fractions have different numerators and different denominators, so we can't compare them directly. By converting to a common denominator of 90, we're cutting both quantities into equal-sized pieces. Then 20 pieces vs 81 pieces is a straightforward comparison.
\(\frac{9}{10}\) is bigger. As a decimal, \(\frac{9}{10}\) = 0.9 while \(\frac{2}{9}\) = 0.222222.
The difference is \(\frac{61}{90}\), which equals 0.677778 in decimal form (67.7778 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 \(\frac{9}{10}\) \(>\) \(\frac{2}{9}\).