🔄 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 \(\frac{3}{7}\) 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 7, and the least common denominator (LCD) is 21.
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 less than 0.428571, we confirm that \(\frac{1}{3} < \frac{3}{7}\). In percentage terms, \(\frac{1}{3}\) is 33.3333% and \(\frac{3}{7}\) is 42.8571%, a difference of 9.5238 percentage points.
These fractions have different numerators and different denominators, so we can't compare them directly. By converting to a common denominator of 21, we're cutting both quantities into equal-sized pieces. Then 7 pieces vs 9 pieces is a straightforward comparison.
\(\frac{3}{7}\) is bigger. As a decimal, \(\frac{3}{7}\) = 0.428571 while \(\frac{1}{3}\) = 0.333333.
The difference is \(\frac{2}{21}\), which equals 0.095238 in decimal form (9.5238 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 \(\frac{3}{7}\) \(>\) \(\frac{1}{3}\).