🔄 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 \(\frac{1}{3}\) and \(\frac{1}{6}\) 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 3 and 6, and the least common denominator (LCD) is 6.
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 0.333333 is greater than 0.166667, we confirm that \(\frac{1}{3} > \frac{1}{6}\). In percentage terms, \(\frac{1}{3}\) is 33.3333% and \(\frac{1}{6}\) is 16.6667%, a difference of 16.6667 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 3ths are larger pieces than 6ths, \(\frac{1}{3}\) is the bigger fraction even though both have 1 in the numerator.
\(\frac{1}{3}\) is bigger. As a decimal, \(\frac{1}{3}\) = 0.333333 while \(\frac{1}{6}\) = 0.166667.
The difference is \(\frac{1}{6}\), which equals 0.166667 in decimal form (16.6667 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 \(\frac{1}{3}\) \(>\) \(\frac{1}{6}\).